In this article, a qualitative notion of subjective plausibility and its revision based on a preorder relation are implemented in higher-order logic. This notion of plausibility is used for modeling pragmatic aspects of communication on top of traditional two-dimensional semantic representations.

Higher-Order Logic (HOL) is a proof development system intended for applications to both hardware and software. It is principally used in two ways: for directly proving theorems, and as theorem-proving support for application-specific verification systems. HOL is currently being applied to a wide variety of problems, including the specification and verification of critical systems. Introduction to HOL provides a coherent and self-contained description of HOL containing both a tutorial introduction and most of the material (...) that is needed for day-to-day work with the system. After a quick overview that gives a "hands-on feel" for the way HOL is used, there follows a detailed description of the ML language. The logic that HOL supports and how this logic is embedded in ML, are then described in detail. This is followed by an explanation of the theorem-proving infrastructure provided by HOL. Finally two appendices contain a subset of the reference manual, and an overview of the HOL library, including an example of an actual library documentation. (shrink)

This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, (...) it is then shown how we can use pure higher-order logic to ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)

In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the simple observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-theoretic pluralist’ claims that the (...) search for the true axioms of set theory is. We show that the obvious responses to this argument fail. However, a new response has emerged that purports to prove, from higher-order logical principles, that metaphysical possibility is the broadest kind of possibility applying to propositions, and is to that extent special. We distill two lines of reasoning from the literature, and argue that their import depends on premises that any ‘modal pluralist’ should deny. Both presuppose that there is a unique typed hierarchy, which is what the modal pluralist, in the context of higher-order logic, should disavow. In other words, both presupposes that there is a unique candidate for what higher-order claims could mean. We consider the worry that, in a higher-order setting, modal pluralism faces an insuperable problem of articulation, collapses into modal monism, is vulnerable to the Russell-Myhill paradox, or even contravenes the truism that there is a unique actual world, and argue that these worries are misplaced. We also sketch the bearing of the resulting ‘Higher-Order Pluralism’ on the theory of content. One theme of the discussion is that, if Higher-Order Pluralism is correct, then there is no fixed metatheory from which to characterize higher-order reality. (shrink)

This is the first comprehensive textbook on higher order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages -- their model theory and proof theory, the theory of λ-abstraction and its generalizations -- and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making (...) it more appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics. A Philosophical Introduction to Higher Order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study. Author Andrew Bacon organizes the book's 18 chapters around four main parts: I. Typed Language II. Higher Order Languages III. General Higher-Order Languages IV. Higher-Order Model Theory In addition, two appendices cover the Curry-Howard isomorphism and its applications for modeling propositional structure. Each chapter includes exercises that move from easier to more difficult, strategically placed throughout the chapter, and concludes with an annotated suggested reading list providing graduate students with most valuable additional resources. Key Features Is the first comprehensive introduction to higher-order logic as a grounding for addressing problems in metaphysics Introduces the basic formal tools that are needed to theorize in, and model, higher order languages Offers an abundance of: - Simple exercises throughout the book, serving as comprehension checks on basic concepts and definitions - More difficult exercises designed to facilitate long-term learning Contains annotated sections on further reading, pointing the reader to related literature, learning resources, and historical context. (shrink)

ABSTRACT Four philosophical concerns about higher-order logic in general and the specific demands placed on it by the neo-logicist project are distinguished. The paper critically reviews recent responses to these concerns by, respectively, the late Bob Hale, Richard Kimberly Heck, and myself. It is argued that these score some successes. The main aim of the paper, however, is to argue that the most serious objection to the applications of higher-order logic required by the (...) neo-logicist project has not been properly understood. The paper concludes by outlining a strategy, prefigured in recent work of Øystein Linnebo, for meeting this objection. (shrink)

This edited book focuses on non-classical logics and their applications, highlighting the rapid advances and the new perspectives that are emerging in this area. Non-classical logics are logical formalisms that violate or go beyond classical logic laws, and their specific features make them particularly suited to describing and reason about aspects of social interaction. The richness and diversity of non-classical logics mean that this area is a natural catalyst for ideas and insights from many different fields, from information (...) theory to game theory and business science. This volume is the post-proceedings of the 8th International Conference on Logic and Cognition, held at Sun Yat-Sen University Institute of Logic and Cognition in Guangzhou, China in December 2016. The conference series started in 2001, and is organized by the ILC, often in collaboration with various international research groups. This eighth installment was jointly organized by ILC and Alessandra Palmigiano's Applied Logic research group. The conference series aims to foster the development of effective logical tools to study social behavior from a philosophical, cognitive and formal perspective in order to challenge the field of logic in ways that open up new and exciting research directions. Chapter "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms" of this book is available open access under a CC BY 4.0 license at link.springer.com. (shrink)

In this paper a proposal by Henkin of a nominalistic interpretation for second and higher-order logic is developed in detail and analysed. It was proposed as a response to Quine’s claim that second and higher-order logic not only are committed to the existence of sets, but also are committed to the existence of more sets than can ever be referred to in the language. Henkin’s interpretation is rarely cited in the debate on semantics and (...) ontological commitments for these logics, though it has many interesting ideas that are worth exploring. The detailed development will show that it employs an early strategy of using substitutional quantification in order to reduce ontological commitments. It will be argued that the perspective adopted for the predicate variables renders it a natural extension of Quine’s nominalistic interpretation for first-order logic. However, we will argue that, with respect to Quine’s nominalistic program and his notion of ontological commitment, still holds and thus Henkin’s interpretation is not nominalistic. Nevertheless, it will be seen that is addressed successfully and this provides further insights on the so-called “Skolem Paradox”. Moreover, the interpretation is ontologically parsimonious and, in this respect, it arguably fares better than a recent proposal by Bob Hale. (shrink)

This comprehensive volume features the proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, held in Hangzhou, China on September 8-9 and 11-12, 2023. The collection offers a diverse range of papers that explore the intersection of logic, artificial intelligence, and law. With contributions from some of the leading experts in the field, this volume provides insights into the latest research and developments (...) in the applications of logic in these areas. It is an essential resource for researchers, practitioners, and students interested in the latest advancements in logic and its applications to artificial intelligence and law. (shrink)

Kleene's realizability interpretation for first-order arithmetic was shown by Hyland to fit into the internal logic of an elementary topos, the “Effective topos” . In this paper it is shown, that there is an internal realizability definition in , i.e. a syntactical translation of the internal language of into itself of form “n realizes ” , which extends Kleene's definition, and such that for sentences , the equivalence [harr]n is true in . The internal realizability definition depends on (...) finding separated covers for non-separated objects of . However, for the objects arising in higher-order arithmetic, canonical covers are available, which are definable in higher-order arithmetic. These canonical covers yield “covering axioms”. It is shown that these covering axioms, together with uniformity principles and Extended Church's Thesis, axiomatize a formalized extension of Kleene realizability to a constructive system of higher-order arithmetic. The details are worked out for second and third-order arithmetic, but the method can be extended to any order. As an application, it is shown in the final section that a certain completeness property of the category of “modest sets” can be derived in third-order arithmetic from the realizability axioms. (shrink)

The history of building automated theorem provers for higher-order logic is almost as old as the field of deduction systems itself. The first successful attempts to mechanize and implement higher-order logic were those of Huet [13] and Jensen and Pietrzykowski [17]. They combine the resolution principle for higher-order logic (first studied in [1]) with higher-order unification. The unification problem in typed λ-calculi is much more complex than that for first- (...) class='Hi'>order terms, since it has to take the theory of αβη-equality into account. As a consequence, the higher-order unification problem is undecidable and sets of solutions need not even always have most general elements that represent them. Thus the mentioned calculi for higher-order logic have take special measures to circumvent the problems posed by the theoretical complexity of higher-order unification. In this paper, we will exemplify the methods and proof- and model-theoretic tools needed for extending first-order automated theorem proving to higherorder logic. For the sake of simplicity take the tableau method as a basis (for a general introduction to first-order tableaux see part I.1) and discuss the higherorder tableau calculi HT and HTE first presented in [19]. The methods in this paper also apply to higher-order resolution calculi [1, 13, 6] or the higher-order matings method of Peter [3], which extend their first-order counterparts in much the same way. Since higher-order calculi cannot be complete for the standard semantics by Gödel’s incompleteness theorem [11], only the weaker notion of Henkin models [12] leads to a meaningful notion of completeness in higher-order logic. It turns out that the calculi in [1, 13, 3, 19] are not Henkin-complete, since they fail to capture the extensionality principles of higher-order logic. We will characterize the deductive power of our calculus HT (which is roughly equivalent to these calculi) by the semantics of functional Σ-models. To arrive at a calculus that is complete with respect to Henkin models, we build on ideas from [6] and augment HT with tableau construction rules that use the extensionality principles in a goal-oriented way.. (shrink)

We shall introduce in this paper a language whose formulas will be interpreted by games of imperfect information. Such games will be defined in the same way as the games for first-order formulas except that the players do not have complete information of the earlier course of the game. Some simple logical properties of these games will be stated together with the relation of such games of imperfect information to higher-order logic. Finally, a set of (...) class='Hi'>applications will be outlined. (shrink)

This is the latest volume in the Workshops in Computing series and contains papers to be presented at the Third International Workshop on Deontic Logic in Computer Science (DEON '96) to be held in Sesimbra, Portugal 11 - 13 January 1996. It contains a variety of contributions covering the relationship between deontic logics, logics of action and normative systems (i.e. systems of or about interacting agents whose behaviour is subject to ideal constraints that may not always be (...) fulfilled in practice). The papers range from the theoretical studies of the logical and conceptual tools needed, to studies of various applications. The resulting volume will be of interest to researchers working in a variety of fields from philosophy, logic and legal theory, through to artificial intelligence and computer/management sciences. (shrink)

This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its (...) class='Hi'>applications and thus presents the state of the art in the area. (shrink)

This volume contains finalized versions of papers presented at an international workshop on extensions of logic programming, held at the Seminar for Natural Language Systems at the University of Tübingen in December 1989. Several recent extensions of definite Horn clause programming, especially those with a proof-theoretic background, have much in common. One common thread is a new emphasis on hypothetical reasoning, which is typically inspired by Gentzen-style sequent or natural deduction systems. This is not only of theoretical (...) significance, but also bears upon computational issues. It was one purpose of the workshop to bring some of these recent developments together. The volume covers topics such as the languages Lambda-Prolog, N-Prolog, and GCLA, the relationship between logic programming and functional programming, and the relationship between extensions of logic programming and automated theorem proving. It contains the results of the first conference concentrating on proof-theoretic approaches to logic programming. (shrink)

This is a collection of essays about logic and its applications to various philosophical problems. In general, it is argued that logic constitutes an important device of philosophical analysis. Concerning the nature of logic the author defends the thesis that first-order logic is the logic. Among the philosophical problems to which logic is applied in the essays are: truth, consistency, realism, foundations of semantics, psychologism, undetermination of theories by empirical data, modalities, value (...) concepts, identity, vagueness, God's existence, transcendentals, legal reasoning, category mistakes, bivalence, the cognitive relation, and meaningfulness. (shrink)

This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conservatively extends the internal logic of the topos. This forcing interpretation applies to an arbitrary elementary topos, since any (...) such is equivalent to one carrying a dssi. We prove that the set theory BIST+Coll is sound and complete relative to forcing interpretations in toposes with natural numbers object . Furthermore, in the case that the structural system of inclusions is superdirected, the full Separation schema is modelled. We show that all cocomplete and realizability toposes can be endowed with such superdirected systems of inclusions.A large part of the paper is devoted to an alternative notion of category-theoretic model for BIST, which, following the general approach of Joyal and Moerdijkʼs Algebraic Set Theory, axiomatizes the structure possessed by categories of classes compatible with BIST. We prove soundness and completeness results for BIST relative to the class-category semantics. Furthermore, BIST+Coll is complete relative to the restricted collection of categories of classes given by categories of ideals over elementary toposes with nno and dssi. It is via this result that the completeness of the original forcing interpretation is obtained, since the internal logic of categories of ideals coincides with the forcing interpretation. (shrink)

This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conservatively extends the internal logic of the topos. This forcing interpretation applies to an arbitrary elementary topos, since any (...) such is equivalent to one carrying a dssi. We prove that the set theory BIST+Coll is sound and complete relative to forcing interpretations in toposes with natural numbers object. Furthermore, in the case that the structural system of inclusions is superdirected, the full Separation schema is modelled. We show that all cocomplete and realizability toposes can be endowed with such superdirected systems of inclusions.A large part of the paper is devoted to an alternative notion of category-theoretic model for BIST, which, following the general approach of Joyal and Moerdijkʼs Algebraic Set Theory, axiomatizes the structure possessed by categories of classes compatible with BIST. We prove soundness and completeness results for BIST relative to the class-category semantics. Furthermore, BIST+Coll is complete relative to the restricted collection of categories of classes given by categories of ideals over elementary toposes with nno and dssi. It is via this result that the completeness of the original forcing interpretation is obtained, since the internal logic of categories of ideals coincides with the forcing interpretation. (shrink)

On at least one of its uses, ‘higher-order evidence’ refers to evidence about what opinions are rationalized by your evidence. This chapter surveys the foundational epistemological questions raised by such evidence, the methods that have proven useful for answering them, and the potential consequences and applications of such answers.

This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with (...) naturally defined maps h and s that define a Galois connection on the power set PW of W. These maps can be used to define two distinct boundary operators bd and BD on W. The main theorem of the paper states that higher-order vagueness with respect to bd collapses to second-order vagueness. This does not hold for BD, the iterations of which behave in quite an erratic way. In contrast, the operator bd defines a variety of tolerance principles that do not fall prey to the sorites paradox and, moreover, do not always satisfy the principles of positive and negative introspection. (shrink)

It has been argued that nonreductive physicalism’s problems with mental causation disappear if we abandon the intuitive but naïve production-based conception of causation in favor of one based on counterfactual dependence and difference-making. In recent years, this response has been thoroughly developed and defended by James Woodward, who contends that Kim’s causal exclusion argument, widely thought to be the most serious threat to nonreductive mental causation, cannot even be given a coherent formulation within Woodward’s preferred interventionist framework. But Woodward has, (...) even more recently, defended a pair of necessary conditions on mental causation and higher-order causation more generally, and it is here that the interventionist framework proves less friendly to nonreductive mental causation. Functionalism is arguably the most important species of nonreductive physicalism concerning specifically mental properties, but, as I argue, functional properties fail both of Woodward’s tests of causal relevance, one of them in two different ways. The problem, moreover, seems unique to functionalism, for other types of higher-order properties appear to pass Woodward’s tests. If functionalism faces defeat even in such friendly territory, its problems with mental causation are not an artifact of naïve metaphysics. They run deep. (shrink)

This volume contains papers presented at the second international workshop on extensions of logic programming, which was held at the Swedish Institute of Computer Science, Stockhom, January 27-29, 1991. The 12 papers describe and discuss several approaches to extensions of logic programming languages such as PROLOG, as well as connections between logic programming and functional programming, theoretical foundations of extensions, applications, and programming methodologies. The first workshop in this series was held in T}bingen (...) in 1989 and its proceedings areavailable as LNCS 475. The third workshop will be held in Bologna in 1992. (shrink)

This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 (...) introduces Local Set Theory, an important form of type theory based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called 'doctrine of propositions as types'. We conclude with an Appendix in which the semantics for Local Set Theory - based on category theory - is outlined. (shrink)

We present a class of first-order modal logics, called transformational logics, which are designed for working with sentences that hold up to a certain type of transformation. An inference system is given, and com- pleteness for the basic transformational logic HOS is proved. In order to capture ‘up to isomorphism’, we express a very weak version of higher category theory in terms of first-order models, which makes tranforma- tional logics applicable to category theory. A category-theoretical (...) concept of isomorphism is used to arrive at a modal operator nisoφ expressing ‘up to isomorphism, φ’, which is such that category equivalence comes out as literally isomorphism up to isomorphism. In the final part of the paper, we explore the possibility of using trans- formational logics to define weak higher categories. We end with two informal comparisons: one between HOS and counterpart semantics, and one between isomorphism logic, as a transformational logic, and Homo- topy Type Theory. (shrink)

Although the cognition is significant in strategic reasoning, its role has been weakly analyzed, because only the average intelligence is usually considered. For example, prisoner's dilemma in game theory, would have different outcomes for persons with different intelligence. I show how various levels of intelligence influence the quality of reasoning, decision, or the probability of psychosis. I explain my original methodology developed for my MA thesis in clinical psychology in 1998, and grant research in 1999, demonstrating the bias of the (...) classic IQ method, and how the intelligence limits thinking. Based on that I defined Personality Model, providing insight into understanding of psychosis (schizophrenia, bi-polar), which has not been explained yet by psychology or psychiatry. In addition, it enables to analyze and assess non-linear problems, utilizable in computer programming, visualization (animation) or other fields including Baduk game. I've already applied some principles in complex information system www.each.co.uk, and video-animations exhibited in London, Germany, Tokyo. I need to mention my experience in chess composition between 1994 and 2000, winning a few international prizes and inventing a special class of fairy rules redefining the mate. The chess composition principles or patterns show the way to organize logical series to higher advanced mechanisms (like calculus), applicable to other fields. One of such principles is a logical aesthetic innovation: new strategy, defined by Italian composers. Finally I show how the simple redefinition of the classic utility concept links economics and psychology to explain irrational / destructive behavior. All presented results (from the research) can be repeated. (shrink)

We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the Bernays postulates for quantifiers and the comprehension schemata of ZF and other set theories. We prove that it is consistent in any finite Boolean subset lattice. We investigate the antinomies of Russell, Cantor, Burali-Forti, and others, and discuss the relationship of the system to other set-theoretic (...) systems ZF, NBG, and NF. We discuss two methods of axiomatizing higher order quantification and abstraction, and then very briefly discuss the application of one of these methods to areas of mathematics outside of logic. (shrink)

Since last year, major initiatives have been undertaken by the chair of theoretical philosophy at the University of Tübingen in order to enhance the reception of analytic metaphysics in the European landscape. Here we review the 2013 summer workshop, intended to be the first of an annual series, on “Existence, Truth and Fundamentality”, the invited speakers being Graham Priest (Melbourne), Stephan Leuenberger (Glasgow), Dan López de Sa (Barcelona), Francesco Berto (Aberdeen), Friederike Moltmann (Paris – Pantheon Sorbonne) and Jason (...) Turner (Leeds). The workshop’s scope is fairly large, focusing on three different aspects of contemporary research in metaphysics. However, the underlying idea of organizers Thomas Sattig and Alessandro Torza consisted in exploring their interconnections and even new areas which possibly share the same problem spectrum. Also, they thought of bringing together both young and senior protagonists of the contemporary debate. In this sense, the main thread followed by the speakers consisted in enquiring the ideas of fundamentality, dependence and grounding with respect to ontology (Berto, López de Sa, Turner) and the truthmaking debate (Priest, Moltmann, Leuenberger), thus pretty much in line with some latest tendencies in metaphysics, such as, prima inter paria, the works of Kit Fine. When we say that something is more fundamental than something else, we move into a non-conventional (for the standards of 20 th century philosophy) metodological framework, hardly focusing on the question about what there is, and rather tackling the issue of how fundamentally there is what there is, or how the existence of something is required as a ground for the existence of other things. Here is how Jonathan Schaffer explains the methodological transition in his influential “On What Grounds What” (2009): -/- Among the many assumptions Quine and Carnap share is that metaphysical questions are existence questions, such as whether numbers exist. They only disagree on the further issue of whether such questions are meaningful (at least as the metaphysician might pose them). But why think that metaphysical questions are existence question of this sort? Return to Aristotle’s Metaphysics. There are virtually no existence question posed. The whole discussion is about substances (fundamental units of being). At one point Aristotle pauses to ask if numbers exist, and his answer is a brief and dismissive yes. [. . . ] For Aristotle, the question about numbers is whether they are transcendent substances or grounded in concreta. The question is not whether numbers exist, but how. (Schaffer, 2009, p. 347) -/- The conference opened with Graham Priest’s intriguing and peculiar review of Buddhist cornerstone “The Fundamental Verses of the Middle Way” (Mūlamadhyakamakārikā) by Nāgārjuna (ca. 150-ca. 250 AD), seen as a unrecognized forerunner of multi-valued semantics and dialetheism. Priest shows that Nagarjuna’s thought indeed has valuable analytic grip (contrary to the traditional mystical dismiss of his works altogether) and is even in accord to some formal schemas rejecting both the laws of excluded middle and non-contradiction. Dan López de Sa was interested in the topic of grounding, raising concerns about how to explain the kind of “reality” exemplified by what is not fundamental, but rather derivative on something else. He proposes a conceptual and non-primitive analysis of grounding as linked to fundamentality and derivation, and argues that the view can be advocated along with the acceptance that at least something is not fundamental. Subsequently, he illustrates an impressive range of applications linked to contemporary debates in meta-ontology, truthmaking and philosophy of time. Stephan Leuenberger discussed a semantics for “total logic”, a variant of first order logic which is claimed to have several applications with respect to the issue of excluding negative existentials from the scope of theories accounting for a given ’totality’ of facts. For example, materialism is the claim that everything there is can be traced back to physical facts or to truth implied by those facts. What about the claim that “There are no angels”? According to Leuenberger, ordinary logic falls prey of modal arguments (if it is possible that there are angels, by modus tollens, that it is not metaphysically necessary that everything there is is physical). So, there is space for the introduction of a new operator, the totality operator, claiming of what enters its scope that “that’s the whole truth”. Consequently, total logic’s semantics tackles David Chalmers’ well-known conceivability-based argument in favour of zombie’s (subjects producing behaviour but experiencing no qualia) possible existence. Friederike Moltmann presented a massive array of natural language-based examples on the role played by case-constructions, such as “it is the case that Caesar crossed the Rubicon”, “the case of the stolen statue”, “the case in which it might rain”, and so forth. She suggests that we should take surface phenomena of our language very seriously with regard to the determination of ontological categories and truth-makers. Cases are provided by many natural languages with their own existence predicates (“to occur” and “to present itself ”), and these do not apply to other kind of entities, such as objects and events. Trying to derive a substantive thesis on their nature, she claims that they are filtered entities, a structure taking into account some features of the corresponding objects and events and preserving their relational pattern. Jason Turner discussed meta-ontological concerns against the claim that ontological debates are defective. Analysed the structure of a metaphysical theory and identified two different forms of defectiveness that can occur in ontological questions, the defection from without and the defection from within, the author provided an original solution in order to avoid such difficulties. He argued thus in favor of a logical constancy, a translation principle thanks to it would be possible reconceive an ontological defection. Lastly, Francesco Berto’s talk closed the workshop with a sagacious discussion of meinongian quantification. He substains that Meinongians and Quineans experience no conceptual equivocation. Even if the former claims that “There are things that do not exist”, something that the latter contrasts with the interpretation of existential quantifiers as all-including, they still rely upon the same concept of “existence” and they understand each other when they are outside the ontology room, so that it cannot be that they lack competence. Subsequently, Berto deals with the objection that Meinongians commit analytic falsehood in separating the meaning of “to be” from that of “exists”. The Quinean has no independent evidence for analytic equivalence aside from her emphatic stress on the “is” in “there is”. Meinongians, however, can retort to linguistic considerations and claim that existence predicates display fairly different functions. -/- As for what regards our internal division of the “philosophical labor”, Fabio Ceravolo reviewed Moltmann and Berto’s talks; whereas Mattia Cozzi took care of Priest’s and Leuenberger’s, and Mattia Sorgon of those given by López de Sa and Turner. Conclusively, we would like to thank Thomas Sattig and Alessandro Torza for all of their organizational efforts and the kind welcome they reserved to us. We hope we will have further opportunities to collaborate with Tübingen in supporting similarly innovative and valiant european initiatives. (shrink)

The generation of the pitch control signal in a wind turbine (WT) is not straightforward due to the nonlinear dynamics of the system and the coupling of its internal variables; in addition, they are subjected to the uncertainty that comes from the random nature of the wind. Fuzzy logic has proved useful in applications with changing system parameters or where uncertainty is relevant as in this one, but the tuning of the fuzzy logic controller (FLC) parameters is (...) neither straightforward nor an easy task. On the other hand, reinforcement learning (RL) allows systems to automatically learn, and this capability can be exploited to tune the FLC. In this work, a WT pitch control architecture that uses RL to tune the membership functions and scale the output of a fuzzy controller is proposed. The RL strategy calculates the fuzzy controller gains in order to reduce the output power error of the WT according to the wind speed. Different reward mechanisms based on the output power error have been considered. Simulation results with different wind profiles show that this architecture performs better (123.7 W) in terms of power errors than an FLC without RL (133.2 W) or a simpler PID (208.8 W). Even more, it provides a smooth response and outperforms other hybrid controllers such as RL-PID and radial basis function neural network control. (shrink)

"This volume comprises the proceedings of the First All-Berlin Workshop on Nonclassical Logics and Information Processing, held at the Free University of Berlin, November 9-10, 1990. The scope of the ten papers in the volume is broad, covering various different subfields of logic - particularly nonclassical logic - and its applications in artificial intelligence. The papers are grouped according to the four major topics that emerged at the meeting: modal systems, logic programming, nonmonotonic logics, and (...) proof theory. The classification is only a rough guide since the four areas overlap considerably."--PUBLISHER'S WEBSITE. (shrink)

Situation theory is the result of an interdisciplinary effort to create a full-fledged theory of information. Created by scholars and scientists from cognitive science, computer science, AI, linguistics, logic, philosophy, and mathematics, the theory is forging a common set of tools for the analysis of phenomena from all these fields. This volume presents work that evolved out of the Second Conference on Situation Theory and its Applications. Twenty-six essays exhibit the wide range of the theory, covering such topics (...) as natural language semantics, philosophical issues about information, mathematical applications, and the visual representation of information in computer systems.Jon Barwise is a professor of philosophy, mathematics, and logic at Indiana University in Bloomington. Jean Mark Gawron is a researcher at SRI International and a consultant at Hewlett-Packard Laboratories. Gordon Plotkin is a professor of theoretical computer science at the University of Edinburgh. Syun Tutiya is in the philosophy department at Chiba University in Japan. (shrink)

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of (...) this paper is to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete. (shrink)

This volume contains several invited papers as well as a selection of the other contributions. The conference was the first meeting of the Soviet logicians interested in com- puter science with their Western counterparts. The papers report new results and techniques in applications of deductive systems, deductive program synthesis and analysis, computer experiments in logic related fields, theorem proving and logic programming. It provides access to intensive work on computer logic both in the USSR and (...) in Western countries. (shrink)

Cantor’s proof that the reals are uncountable forms a central pillar in the edifices of higher order recursion theory and set theory. It also has important applications in model theory, and in the foundations of topology and analysis. Due partly to these factors, and to the simplicity and elegance of the proof, it has come to be accepted as part of the ABC’s of mathematics. But even if as an Archimedean point it supports tomes of mathematical theory, (...) there is a question that demands clarification: What, exactly, does Cantor’s proof show? One of few places where this question is addressed is Appendix II of Wittgenstein’s Remarks on the Foundations of Mathematics. This essay is devoted to clarifying Wittgenstein’s remarks in that section. (shrink)

This book constitutes the proceedings of the Third International Conference on Conceptual Structures, ICCS '95, held in Santa Cruz, California in August 1995. Conceptual structures are a modern treatment of Peirce's existential graphs, a graphic notation for classical logic with higher order extensions. Besides three invited papers, there are included 21 revised full papers selected from 58 submission. The volume reflects the state-of-the-art in this research area of growing interest. The papers are organized in sections on (...) natural language, applications, programming in conceptual graphs, machine learning and knowledge acquisition, hardware and implementation, graph operations, and ontologies and theory. (shrink)

Photo by Hannah Busing on Unsplash INTRODUCTION Religion has long provided guidance that has led to standards reflected in some aspects of medical practices and traditions. The recent bioethical literature addresses numerous new problems posed by advancing medical technology and demonstrates an erosion of standards rooted in religion and long widely accepted as almost axiomatic. In the deep soul-searching that pervades the publications on bioethics, several disturbing and dangerous trends neglect some basic lessons of philosophy, logic, and history. The (...) bioethics discourse on medical aid in dying emphasizes similarity over previously recognized important distinguishing features. For example, it overplays a likeness between assistance in dying and the withdrawal of life-saving technology. In many bioethics’ topics, arguments based on a logical continuum are used to question the lines demarcating important moral differences. l. The Line Between Ethical and Not: Logic Based on Continuum Careful case selection, often either end of a continuum, allows the tearing down or ridiculing of many rules and codes across most professions and fields of interest. This situation holds true for traffic laws as well as medical ethics guidelines. It is relatively simple for those who desire to attack a particular viewpoint by selecting a case that makes that position seem untenable. In the ethics realm, good and bad medicine exist at opposite ends of an ethical continuum, with many practices lying in between. For example, much of medical ethics exists between the Nazi criminal physicians and the most sainted nurse or physician. A gradual progression occurred over less than two decades from a utilitarian position that supported limited euthanasia for those with certain mental illnesses to genocide. German society embraced a utilitarian ethic in which the value of human life no longer was intrinsic but instrumental.[1] Many morally significant points on a continuum were then ignored as the misguided utilitarian policy rampantly continued. A point in the continuum to distinguish between ethically justifiable and that which is not can be difficult to identify compared to the two extremes. This continuum is not unique to ethics but can be applied to almost any other aspect of human life and endeavor. Between a severely ill schizophrenic person and a superbly well-adjusted individual, there is a continuum of mental and psychological function. The existence of a continuum should not paralyze thinking and prevent us from drawing lines and identifying moral differences based on objective criteria as well as moral philosophy. Yet, by focusing on a continuum, many bioethicists use logic to disregard dividing lines between an "ethical" and an "unethical" act. Unfortunately, sometimes bioethicists draw revolutionary conclusions that would change the scope of medical practices which is accepted as ethical. There are many examples of similar shifts on the continuum. Many authors argue for the ethical permissibility of abortion by pointing out that the human fetus is no different in various characteristics, one arguing it is as like an ape or chick as it is like a person,[2] and does not achieve unique human and individual characteristics until well into the first year of life.[3] While human fetuses arguably do not have certain distinctive qualities of personhood, most people shy away from the logical next conclusion: permitting infanticide. For example, Joshua Lederberg condemns infanticide, in the face of biological illogic, because of our emotional commitment to infants, to me, a relatively weak explanation. Sir Francis Crick suggests we might consider birth at two days of life in order to decide whether an infant is a "suitable" member of society.[4] Giublini and Minerva suggest that infanticide should be permissible since late pregnancy abortions are permissible, arguing there is no significant difference between a fetus just before birth and an infant just after birth.[5] Clearly the continuum approach would allow for subjective arguments in favor of later infanticide at other points many days post-birth. Years ago, with a cynical tone, I mentioned infanticide as a further step on the continuum beyond abortion, and I was rightly shouted down as being deliberately provocative to assert the logic would ever stretch so far. While it is not an accepted mainstream position, the movement in academic settings from widespread condemnation to limited possible acceptance of infanticide has taken place in an incredibly short time. Public opinion and medical opinion in these areas have shifted dramatically in a short time. In another area, from a biological and chemical point of view, there is a continuum from man down to a single carbon atom. Yet, it would not seem logical to ignore the emotional differences, the meaning of personhood, or the moral distinction between killing an insect and killing a person. ll. A False Continuum: Medical Aid in Dying I assert that there has been an erosion of ethical guidelines in recent years attributable to using continuums to camouflage important distinctions. James Rachels’ work on active and passive euthanasia, which contends that the two are ethically identical, exemplifies that logic.[6] He illustrates this thesis, using a continuum to compare different scenarios with like consequences as morally equivalent, by comparing the deliberate drowning of a child with a deliberate failure to rescue a drowning child when easily able to do so. The author's comparison proposes that since much of the medical profession has already made peace with withholding treatment in order to hasten death, consistency inexorably demands that we permit active euthanasia as well.[7] When permission for active euthanasia was first introduced, it was limited exclusively to patients suffering severely from an intractable, incurable, and irreversible disease. These guidelines have been continuously eroded. There is now a substantial serious consideration for permitting active euthanasia of healthy elderly individuals who feel that they have completed their lives and are "tired of living."[8] There are many moral and factual differences along the ethical continuum. In human life, there is a difference between a live baby and a fetus, between a viable fetus and one that is not, between a fetus and a zygote, and between a zygote and a sperm cell. Similarly, there is a difference between pulling a trigger to kill someone and not interfering in preventing his death, which is reprehensible though both may be. There is a difference between not resuscitating an 80-year-old man with cancer when his heart stops and injecting him with a fatal dose of potassium chloride. I argue that an overt act of taking life repels civilized human beings is to be commended and encouraged as the reverence for human life or even for just a moment of human life is one of the great contributions of our civilization. CONCLUSION As an orthodox Jew, I feel that divinely inspired guidelines that have stood the test of centuries shape my beliefs, and such guidelines contradict medical aid in dying. I cannot speak to the viewpoint of those who do not access religion in defining their moral stance, nor do I implicate them in the current bioethics' trends, as I am not aware of the personal role of religion in the lives of most such authors. While many nonreligious people have a firm philosophical grounding and oppose medical aid in dying, I suggest that in the absence of any religious or other absolute standards, developing logically defensible ethical guidelines may be challenging. At the least, religion may play a role in defining the points on the continuums that are ethically meaningful and refuting the trending beliefs that if the endpoint is the same, allowing different methods of arriving at that end are somehow ethically equal. The continuum of ways death may result does not negate analysis of whether death is brought about in ways that recognize the importance of life. The German philosopher Hans Jonas said, "It is a question whether without restoring the category of the sacred, the category most thoroughly destroyed by the scientific enlightenment, we can have an ethics able to cope with the extreme powers that we possess today and constantly increase and are compelled to use."[9] While countries vary on the role of religion in policy, with many emphasizing freedoms of religion, a recent position paper released by a group of Jewish, Christian, and Moslem leaders suggested the need for agreement on the unique sanctity of human life.[10] I would recommend that such a document serve as an example of consensus on critical foundational bioethical guidelines for democratic secular societies. - [1] Alexander L Medical science under dictatorship. New England Journal of Medicine, 241, p39-47 DOI10.1056/NEJM194907142410201 [2] Lederberg J. A geneticist looks at contraception and abortion, Annals of Internal Medicine 67, sup 2, 25-27. https:/doi.org/10.7326/0003-4819-67-3-25 [3] Ibid. [4] Editorial, Sociology: Logic of biology. Nature 220, 429 https://www.nature.com/articles/220429b0 [5] Giublini A Minerva F After-birth abortion: why should the baby live. J Med Ethics 39, 261- [6] Rachels J Active and passive euthanasia. New England Journal of Medicine 292, 78-80 [7] Ibid. [8] Cohen-Almagor R Euthanizing people who are "tired of life". in Euthanasia and Assisted Suicide-Lessons from Belgium. Ch 11 of Euthanasia and Assisted Suicide, Cambridge University Press pp173-187. 2017 and DOI; https://doi.org/10.1017/9781108182799.012 [9] Hans Jonas, Technology and Responsibility: Reflections on the New Tasks of Ethics, 1972, found as Chapter IX, Philosophical Essays, 1980. https://inters.org/jonas-technology-responsability [10] A position paper of the Abrahamic Monotheistic religions on matters concerning the end-of-life. Vatican Press 28 October 2019 https://press.vatican.va/content/salastampa/en/bollettino/pubblico/2019/10/28/191028f.html. (shrink)

The systems Kα of transfinite cumulative types up to α are extended to systems K∞α that include a natural infinitary inference rule, the so-called limit rule. For countable α a semantic completeness theorem for K∞α is proved by the method of reduction trees, and it is shown that every model of K∞α is equivalent to a cumulative hierarchy of sets. This is used to show that several axiomatic first-order set theories can be interpreted in K∞α, for suitable α.

The usage of sorts in first-order automated deduction has brought greater conciseness of representation and a considerable gain in efficiency by reducing the search spaces involved. This suggests that sort information can be employed in higher-order theorem proving with similar results.

The aim of this thesis is to examine the debate between Quine and Boolos over the logical status of higher-order logic-with Quine taking the position that higher-logic is more properly understood as set theory and Boolos arguing in opposition that higher-order logic is of a genuinely logical character. My purpose here then will be to stay as neutral as possible over the question of whether or not higher-order logic counts (...) as logic and to instead focus on the exposition of the debate itself as exemplified in the work of Quine and Boolos. Chapter I will be a detailed consideration of Quine's conception of logic and its place within the wider context of his philosophy. Only once this backdrop is in place will I then examine his views on higher-order logic. In Chapter II, I turn to Boolos's response to Quine-his attempt to examine the extent to which we may want to count higher-order logic as logic and the extent to which we may want to count it as set theory. With each point Boolos raises, I attempt to give what I think would have been Quine's reply. Finally, in Chapter III, I consider Boolos's attempt to show that monadic second-order logic should be understood as pure logic as it does not commit us to the existence of classes, as we may take the standard interpretation of MSOL to do. I discuss here some of the major reactions to Boolos's plural interpretation, and conclude with more speculative remarks on what Quine's own response might have been. Throughout this thesis, my primary method has been one of close textual analysis. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

Many theories of rational belief give a special place to logic. They say that an ideally rational agent would never be uncertain about logical facts. In short: they say that ideal rationality requires "logical omniscience." Here I argue against the view that ideal rationality requires logical omniscience on the grounds that the requirement of logical omniscience can come into conflict with the requirement to proportion one’s beliefs to the evidence. I proceed in two steps. First, I rehearse an influential (...) line of argument from the "higher-order evidence" debate, which purports to show that it would be dogmatic, even for a cognitively infallible agent, to refuse to revise her beliefs about logical matters in response to evidence indicating that those beliefs are irrational. Second, I defend this "anti-dogmatism" argument against two responses put forth by Declan Smithies and David Christensen. Against Smithies’ response, I argue that it leads to irrational self-ascriptions of epistemic luck, and that it obscures the distinction between propositional and doxastic justification. Against Christensen’s response, I argue that it clashes with one of two attractive deontic principles, and that it is extensionally inadequate. Taken together, these criticisms will suggest that the connection between logic and rationality cannot be what it is standardly taken to be—ideal rationality does not require logical omniscience. (shrink)

Relying on the systematic, logical, and analytical methods, national legislation and some internationally accepted guidelines, as well as on the research conducted by the Lithuanian scientists and law practitioners, this article consistently and comprehensively deals with the problems arising in the areas of interpretation and application of tax law. The article examines the relevant tax concepts, studies the tax law system, deals with the relevant issues arising in the field of application of legal regulations on taxation, and provides a particularly (...) detailed analysis of court jurisprudence within the context of the relationship between tax and law. On the basis of the analysis conducted, it was established that the basis for the Lithuanian tax law system consists of the Constitution of the Republic of Lithuania; the Law on Tax Administration; tax laws that lay down specific taxes and of by-laws adopted on their basis; national legal regulations that contain a consideration attribute and set mandatory payments to the State budget; the Law on Customs; ratified international agreements; the European Union legal regulations to the extent they are related to the duties, import excise duty, and value added tax; and the European Union directives in respect of direct and indirect taxes and the extent to which they are related to tax administration. When relationships in public law are directly regulated by the relevant public law regulations, it is not private law regulations, but the corresponding public law regulations that must be applied. In order to determine the need for tax authorities to rely on the regulations of the Civil Code, it is necessary to state the necessity to assess legal relationships from the point of view of private law or to identify a gap in legal regulation of public law due to which the norms of the Civil Code are subsidiary. Prior to establishing the tax base, the tax authority does not have to rebut transactions in civil procedure. The taxpayer’s obligation to fulfil tax liabilities that are properly prescribed by tax laws is not called into question by unlawful acts of other persons which constitute grounds for their civil (non-contractual) liability for the damages caused. The factual circumstances of tax relations established in the court cases heard in criminal and/or administrative procedures, do not need to be proved again – they are relied on in the course of tax inspections or when hearing tax disputes. The principle of equality of taxpayers requires tax administrators to give equal treatment to the facts with respect to all participants regarding the same tax relationship and obliges taxpayers to pay taxes honestly, because non-payment of taxes is a breach of public interest and therefore of this principle. In accordance with the principle of general applicability and equality, each taxpayer has an obligation to pay taxes as prescribed in tax legislation observing the calculation and payment procedures stipulated in the tax legal regulations, whereas the amount payable as established by the tax administrator shall be regarded as well-founded to the extent that it does not exceed the criterion of equality and reasonableness. The principle of clarity of taxation requires the tax administrator to adopt clear and comprehensive decisions with respect to the taxpayer and therefore to ensure their rights and legitimate interests. In the calculation of tax by applying the principle of primacy of content over form, it is necessary to establish that a transaction, an economic deal or indeed any group thereof has been concluded for the purpose of obtaining tax benefits. (shrink)

Though deceptively simple and plausible on the face of it, Craig's interpolation theorem has proved to be a central logical property that has been used to reveal a deep harmony between the syntax and semantics of first order logic. Craig's theorem was generalized soon after by Lyndon, with application to the characterization of first order properties preserved under homomorphism. After retracing the early history, this article is mainly devoted to a survey of subsequent generalizations and applications, (...) especially of many-sorted interpolation theorems. Attention is also paid to methodological considerations, since the Craig theorem and its generalizations were initially obtained by proof-theoretic arguments while most of the applications are model-theoretic in nature. The article concludes with the role of the interpolation property in the quest for "reasonable" logics extending first-order logic within the framework of abstract model theory. (shrink)

This book honors J. Michael Dunn, who was a preeminent relevance logician. Dunn's career spanned over 50 years and his research results had an impact on philosophy, mathematics and informatics. Dunn often used algebraic techniques in his research into logics such as relevance, orthomodular and substructural logics. He invented the logic R-mingle and the sequent calculus LR+; he proved crucial theorems about 2-valued first-order logic and non-classical higher-order logics - among many other results. The papers (...) in this volume touch upon topics that Dunn was concerned with. Some authors were students or colleagues of Dunn; some other authors had not met Dunn in person, but share his research interests. None of the articles published here have appeared in print before; indeed, most of the papers were written specifically for this collection. The diversity of the themes of the articles reflects the scope of Dunn's own research in logic. It will also ensure that anybody with an interest in logic - whether a student, a logician or a scholar in another field - will find reading this book a worthwhile endeavor. The editor, Katalin Bimbó was the 14th Ph.D. student of J. Michael Dunn at Indiana University in Bloomington, IN, U.S.A.; currently, she is a professor of philosophy at the University of Alberta in Canada. (shrink)

Quine’s most important charge against second-, and more generally, higher-order logic is that it carries massive existential commitments. The force of this charge does not depend upon Quine’s questionable assimilation of second-order logic to set theory. Even if we take second-order variables to range over properties, rather than sets, the charge remains in force, as long as properties are individuated purely extensionally. I argue that if we interpret them as ranging over properties more reasonably (...) construed, in accordance with an abundant or deflationary conception, Quine’s charge can be resisted. This interpretation need not be seen as precluding the use of model-theoretic semantics for second-order languages; but it will preclude the use of the standard semantics, along with the more general Henkin semantics, of which it is a special case. To that extent, the approach I recommend has revisionary implications which some may find unpalatable; it is, however, compatible with the quite different special case in which the second-order variables are taken to range over definable subsets of the first-order domain, and with respect to such a semantics, some important metalogical results obtainable under the standard semantics may still be obtained. In my final section, I discuss the relations between second-order logic, interpreted as I recommend, and a strong version of schematic ancestral logic promoted in recent work by Richard Heck. I argue that while there is an interpretation on which Heck’s logic can be contrasted with second-order logic as standardly interpreted, when it is so interpreted, its differences from the more modest form of second-order logic I advocate are much less substantial, and may be largely presentational. (shrink)

The emphasis in this collection is clearly on logic, and this is one reason why it lacks the overall diversity and richness of the 1960 Stanford volume. However, the eight sections do contain much interesting material; in the mathematical logic section Kochen and Specker continue their study of logics appropriate for quantum theory, Vaught presents several new results about the Löwenheim-Skolem theorem, and Büchi studies second-order ordinal theory from the viewpoint of automata theory; the section on foundations (...) of mathematical theories contains papers on higher-order logic by Kaplan and Montague, model theory and ultra-products by Keisler, definability in set theory by Lévy. The topic of the justification of formal theories was the essential topic of the philosophy of logic section: an especially interesting paper is that of A. Robinson in which the present state of Hilbertean Formalism is analyzed, and in which the notion of potential truth is formalized. The section on the philosophy of science contains a single paper, by Hesse, on metaphor and explanation; Braithwaite, Hintikka, Jeffrey, and Kyburg contribute to a lively section on probability and induction; the section on methodology in physical science takes as topics the theory of relativity, causality, and irreversibility. The last two sections, on the philosophy of the life sciences, and on history of logic and philosophy of science, contain, respectively, papers by Davidson and Suppes on meaning and concept formation, and essays by Church and Geach on existential import historically considered and intentionality among the medievals. The collection would have been better if more of the contributed papers had been included.—P. J. M. (shrink)

Situation theory is the result of an interdisciplinary effort to create a full-fledged theory of information. Created by scholars and scientists from cognitive science, computer science, AI, linguistics, logic, philosophy, and mathematics, the theory is forging a common set of tools for the analysis of phenomena from all these fields. This volume presents work that evolved out of the Second Conference on Situation Theory and its Applications. Twenty-six essays exhibit the wide range of the theory, covering such topics (...) as natural language semantics, philosophical issues about information, mathematical applications, and the visual representation of information in computer systems.Jon Barwise is a professor of philosophy, mathematics, and logic at Indiana University in Bloomington. Jean Mark Gawron is a researcher at SRI International and a consultant at Hewlett-Packard Laboratories. Gordon Plotkin is a professor of theoretical computer science at the University of Edinburgh. Syun Tutiya is in the philosophy department at Chiba University in Japan. (shrink)

Includes tutorials, invited lectures, and refereed papers on all aspects of logic programming including: Constraints, Concurrency and Parallelism, Deductive Databases, Implementations, Meta and Higher-order Programming, Theory, and Semantic Analysis. September 2-6, 1996, Bonn, Germany Every four years, the two major international scientific conferences on logic programming merge in one joint event. JICSLP'96 is the thirteenth in the two series of annual conferences sponsored by The Association for Logic Programming. It includes tutorials, invited lectures, and (...) refereed papers on all aspects of logic programming including: Constraints, Concurrency and Parallelism, Deductive Databases, Implementations, Meta and Higher-order Programming, Theory, and Semantic Analysis. The contributors are international, with strong contingents from the United States, United Kingdom, France, and Japan. Logic Programming series, Research Reports and Notes. (shrink)

The gray prediction model, based on the GM method, is an important branch of gray theory with the most active research and the most fruitful results, and it is the most widely used because of its small sample size, simple modeling process, and easy to use. Such advantages have been successfully applied in many fields such as transportation, agriculture, energy, medicine, and environment and have been gradually developed into a mainstream predictive modeling method. This study combines the Three-parameter Whitenization Grey (...) Model ), which fits the inhomogeneous exponential law sequence, and the Particle Swarm Algorithm to optimize the order and background value coefficients under the condition of the minimum sum of squares of simulation errors, and hence, to solve the problem that the cumulative order is fixed to “1” and the background value coefficient value is fixed to “0.5.” As a result, a parameter-optimized gray system model with flexibility, adaptability, and dynamic adjustment is designed to simulate and predict China’s higher education gross enrollment rate. The application shows that the model has better overall simulation and prediction performance than others. On the one hand, the parametric optimization model significantly improves its own performance, and on the other hand, its intelligent and adjustable adaptivity improves the accuracy and further extends its application. (shrink)

Though deceptively simple and plausible on the face of it, Craig's interpolation theorem (published 50 years ago) has proved to be a central logical property that has been used to reveal a deep harmony between the syntax and semantics of first order logic. Craig's theorem was generalized soon after by Lyndon, with application to the characterization of first order properties preserved under homomorphism. After retracing the early history, this article is mainly devoted to a survey of subsequent (...) generalizations and applications, especially of many-sorted interpolation theorems. Attention is also paid to methodological considerations, since the Craig theorem and its generalizations were initially obtained by proof-theoretic arguments while most of the applications are model-theoretic in nature. The article concludes with the role of the interpolation property in the quest for "reasonable" logics extending first-order logic within the framework of abstract model theory. (shrink)