Among Dunn’s many important contributions to relevance logic was his work on the system RM (R-mingle). Although RM is an interesting system in its own right, it is widely considered to be too strong. In this chapter, I revisit a closely related system, RM0 (sometimes known as ‘constructive mingle’), which includes the mingle axiom while not degenerating in the way that RM itself does. My main interest will be in examining this logic from two related semantical perspectives. First, I give (...) a purely operational bisemilattice semantics for it by adapting previous work of Humberstone. Second, I examine a more conventional algebraic semantics for it and discuss how this relates to the operational semantics. A novel operational semantics for J (intuitionistic logic) as well as its conventional Heyting algebraic semantics emerge as special cases of the corresponding semantics for RM0. The results of this chapter suggest that RM0 is a more interesting logic than has been appreciated and that Humberstone’s operational semantic framework similarly deserves more attention than it has received. (shrink)

This work adopts H. Kelsen’s concept of legal system, proposes a formal definition for such notion, and introduces an operational semantical framework for legal systems that are situated in agent societies. Agent societies are defined. Relevant formal properties of situated legal systems are discussed; the way they are exposed in the operational semantical framework is explained, and their truth formally proved. Also, for the sake of a better understanding of the legal-theoretic assumptions of the paper, recurring issues regarding (...) Kelsen’s theory of law are briefly reviewed. They are put in confrontation with the points of view of R. Dworkin, H. Hart, and J. Raz, and an attempt is made to clarify them from the perspective of the provided formalization. A brief case study in agent-based modeling and simulation of public policy processes is presented, as an illustration of the way of using situated legal systems, and the proposed operational semantical framework, in a practical application. (shrink)

The Operator Argument against eternalism holds that having non-vacuous tense operators in the language is incompatible with the claim that every proposition has its truth-value eternally. Assuming that (1) there are non-vacuous tense operators, (2) tense operators operate on propositions and (3) tense operators which operate on eternal entities are vacuous, it may be argued that eternalism is false. In this paper, I examine the Operator Argument. The goal is threefold. First, I want to present some aspects of the debate (...) in a more elaborate way, especially those concerning formal matters. Secondly, I will argue that eternalism can escape the Operator Argument. There are two main strategies for handling the Operator Argument. The first one is based on replacing temporal operators with object-language quantifiers. The second rejects the identification of compositional semantic value with assertoric content. My third goal is to show that none of them is as good as the strategy that adopts Timestamp Semantics (Fritz in Philosl Stud 176:2933–2959, 2019). I am going to argue that the quantificational treatment of tenses is compatible with temporalism and that the arguments for rejecting the identification of compositional semantic value with assertoric content provide, in fact, a motivation for the temporalist position. At the end, I will develop Timestamp Semantics by providing a novel formalization of it, and defend it against three potential counter-arguments. (shrink)

Disaster response is a highly collaborative and critical process that requires the involvement of multiple emergency responders (ERs), ideally working together under a unified command, to enable a rapid and effective operational response. Following the 9/11 and 11/13 terrorist attacks and the devastation of hurricanes Katrina and Rita, it is apparent that inadequate communication and a lack of interoperability among the ERs engaged on-site can adversely affect disaster response efforts. Within this context, we present a scenario-based terrorism case study (...) to highlight the challenges of operational disaster command and response. In this article, which is based on the French emergency response doctrine, we outline a semantics-based common operational command system that is designed to guarantee an efficient information flow among ERs. Our focus is on offering to all ERs, a real-time operational picture of the situation in order to enable multilevel coordination among firefighters, police, healthcare units, public authorities, and other stakeholders. Our approach consolidates information to promote timely sharing of data among ERs. The proposed system is based on an ontology that has been developed to represent the different types of knowledge on the part of ERs, providing a shared vocabulary that covers a variety of interoperability concerns. (shrink)

The minimal weakening \ of Belnap-Dunn logic under the polarity semantics for negation as a modal operator is formulated as a sequent system which is characterized by the class of all birelational frames. Some extensions of \ with additional sequents as axioms are introduced. In particular, all three modal negation logics characterized by a frame with a single state are formalized as extensions of \. These logics have the finite model property and they are decidable.

This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premises. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred (...) ones. A proposition α is a nonmonotonic consequence of a set of propositions Γ iff α holds in all the most preferred Γ-states. In the literature on revealed preference theory, there are a number of well-known theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilized here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection, infinitary belief revision operations that allow for the revision of a theory with a possibly infinite set of propositions are introduced and characterized axiomatically. (shrink)

Theoria, Volume 88, Issue 3, Page 494-528, June 2022.

We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to ‘recover’ the properties of classical logic in a controlled manner. These structures are known as topological Boolean algebras, which are Boolean algebras extended with additional operations subject to specific conditions of a topological nature. In this study, we focus on the paradigmatic case of negation. We demonstrate how these algebras are well-suited to provide (...) a semantics for some families of paraconsistent Logics of Formal Inconsistency and paracomplete Logics of Formal Undeterminedness. These logics feature recovery operators used to earmark propositions that behave ‘classically’ when interacting with non-classical negations. Unlike traditional semantical investigations, which are carried out in natural language (extended with mathematical shorthand), our formal meta-language is a system of higher-order logic (HOL) for which automated reasoning tools exist. In our approach, topological Boolean algebras are encoded as algebras of sets via their Stone-type representation. We use our higher-order meta-logic to define and interrelate several transformations on unary set operations, which naturally give rise to a topological cube of opposition. Additionally, our approach enables a uniform characterization of propositional, first-order and higher-order quantification, including restrictions to constant and varying domains. With this work, we aim to make a case for the utilization of automated theorem proving technology for conducting computer-supported research in non-classical logics. All the results presented in this paper have been formally verified, and in many cases obtained, using the Isabelle/HOL proof assistant. (shrink)

Storage operators are λ-terms which simulate call-by-value in call-by-name for a given set of terms. Krivine's storage operator theorem shows that any term of type ¬D → ¬D*, where D* is the Gödel translation of D, is a storage operator for the terms of type D when D is a data-type or a formula with only positive second order quantifiers. We prove that a new semantical version of Krivine's theorem is valid for every types. This also gives a simpler proof (...) of Krivine's theorem using the properties of data-types. (shrink)

-/- A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. -/- Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give a (...) correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture was later proved independently by the authors and by Newton da Costa. -/- The expression (vy:F) is called a variable bound term (vbt). In case F has only y free, (vy:F) has the syntactic propreties of an individual constant; and under a suitable interpretation of the language vy:F) denotes an individual. By a semantic analysis of vbtos we mean a proposal for amending the standard notions of (1) "an interpretation o f a first -order language" and (2) " the denotation of a term under an interpretation and an assignment", such that (1') an interpretation o f a first -order language associates a set-theoretic structure with each vbto and (2') under any interpretation and assignment each vb t denotes an individual. (shrink)

Towards NonBeing (Priest, 2005) gives a noneist account of the semantics of intentional operators and predicates. The semantics for intentional operators are modelled on those for the , is given and assessed.

The operational semantics of Urquhart is a deep and important part of the development of relevant logics. In this paper, I present an overview of work on Urquhart’s operational semantics. I then present the basics of collection frames. Finally, I show how one kind of collection frame, namely, functional set frames, is equivalent to Urquhart’s semilattice semantics.

In [2] a semantics for implication is offered that makes use of stories — sets of sentences assembled under various constraints. Sentences are evaluated at an actual world and in each member of a set of stories. A sentence B is true in a story s just when B s. A implies B iff for all stories and the actual world, whenever A is true, B is true. In this article the first-order language of [2] is extended by the (...) addition of the operator the story... says that..., as in The story Flashman among the Redskins says that Flashman met Sitting Bull. The resulting language is shown to be sound and complete. (shrink)

The paper proposes a semantic value for the logical constants (connectives and quantifiers) within the framework of proof-theoretic semantics, basic meaning on the introduction rules of a meaning conferring natural deduction proof system. The semantic value is defined based on Fregecontributions” to sentential meanings as determined by the function-argument structure as induced by a type-logical grammar. In doing so, the paper proposes a novel proof-theoretic interpretation of the semantic types, traditionally interpreted in Henkin models. The compositionality of the resulting (...) attribution of semantic values is discussed. Elsewhere, the same method was used for defining proof-theoretic meaning of subsentential phrases in a fragment of natural language. Doing the same for (the simpler and clearer case of) logic sheds more light on the proposal. (shrink)

In order to handle inconsistent knowledge bases in a reasonable way, one needs a logic which allows nontrivial inconsistent theories. Logics of this sort are called paraconsistent. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa’s approach, which seeks to allow the use of classical logic whenever it is safe to do so, but behaves completely differently when contradictions are involved. Da Costa’s approach has led to the family of logics (...) of formal (in)consistency (LFIs). In this paper we provide in a modular way simple non-deterministic semantics for 64 of the most important logics from this family. Our semantics is 3-valued for some of the systems, and infinite-valued for the others. We prove that these results cannot be improved: neither of the systems with a three-valued non-deterministic semantics has either a finite characteristic ordinary matrix or a two-valued characteristic non-deterministic matrix, and neither of the other systems we investigate has a finite characteristic non-deterministic matrix. Still, our semantics provides decision procedures for all the systems investigated, as well as easy proofs of important proof-theoretical properties of them. (shrink)

Minimal Semantics asks what a theory of literal linguistic meaning is for - if you were to be given a working theory of meaning for a language right now, what would you be able to do with it? Emma Borg sets out to defend a formal approach to semantic theorising from a relatively new type of opponent - advocates of what she call 'dual pragmatics'. According to dual pragmatists, rich pragmatic processes play two distinct roles in linguistic comprehension: as (...) well as operating in a post-semantic capacity to determine the implicatures of an utterance, they also operate prior to the determination of truth-conditional content for a sentence. That is to say, they have an integral role to play within what is usually thought of as the semantic realm. Borg believes dual pragmatic accounts constitute the strongest contemporary challenge to standard formal approaches to semantics since they challenge the formal theorist to show not merely that there is some role for formal processes on route to determination of semantic content, but that such processes are sufficient for determining content. Minimal Semantics provides a detailed examination of this school of thought, introducing readers who are unfamiliar with the topic to key ideas like relevance theory and contextualism, and looking in detail at where these accounts diverge from the formal approach. Borg's defence of formal semantics has two main parts: first, she argues that the formal approach is most naturally compatible with an important and well-grounded psychological theory, namely the Fodorian modular picture of the mind. Then she argues that the main arguments adduced by dual pragmatists against formal semantics - concerning apparent contextual intrusions into semantic content - can in fact be countered by a formal theory. The defence holds, however, only if we are sensitive to the proper conditions of success for a semantic theory. Specifically, we should reject a range of onerous constraints on semantic theorizing (e.g., that it answer epistemic or metaphysical questions, or that it explain our communicative skills) and instead adopt a quite minimal picture of semantics. (shrink)

Intelligent agents are often faced with the problem of trying to combine possibly conflicting pieces of information obtained from different sources into a coherent view of the world. We propose a framework for the modelling of such combination operations with roots in the work of Spohn [Spo88, Spo91]. We construct a number of combination operations and we measure them against various properties that such operations ought to satisfy. We conclude by discussing the connection between combination operations and the use of (...) infobases [Mey99, MLH00]. (shrink)

This is a purely conceptual paper. It aims at presenting and putting into perspective the idea of a proof-theoretic semantics of the logical operations. The first section briefly surveys various semantic paradigms, and Section 2 focuses on one particular paradigm, namely the proof-theoretic semantics of the logical operations.

An essential part of natural language understanding, and hence of formal semantics, is the interpretation of temporal expressions. But the very variety of temporal phenomena---such as tense, aspect, aktionsart, temporal adverbials, and the temporal structure of extended text---has tended to result in formal semantic analyses using a wide variety of formal tools, often of a complex nature. It seems important to try and find unifying perspectives on this work, and above all, to try and gain some insight into the (...) logical resources needed to deal with natural language temporal phenomena. (shrink)

The semantics for a deontic action logic based on Boolean algebra is extended with an interpretation of action expressions in terms of sets of alternative actions, intended as a way to model choice. This results in a non-classical interpretation of action expressions, while sentences not in the scope of deontic operators are kept classical. A deontic structure based on Simons’ supercover semantics is used to interpret permission and obligation. It is argued that these constructions provide ways to handle (...) various problems related to free choice permission. The main result is a sound and complete axiomatization of the semantics. (shrink)

Certain passages in Kaplan’s ‘Demonstratives’ are often taken to show that non-vacuous sentential operators associated with a certain parameter of sentential truth require a corresponding relativism concerning assertoric contents: namely, their truth values also must vary with that parameter. Thus, for example, the non-vacuity of a temporal sentential operator ‘always’ would require some of its operands to have contents that have different truth values at different times. While making no claims about Kaplan’s intentions, we provide several reconstructions of how such (...) an argument might go, focusing on the case of time and temporal operators as an illustration. What we regard as the most plausible reconstruction of the argument establishes a conclusion similar enough to that attributed to Kaplan. However, the argument overgenerates, leading to absurd consequences. We conclude that we must distinguish assertoric contents from compositional semantic values, and argue that once they are distinguished, the argument fails to establish any substantial conclusions. We also briefly discuss a related argument commonly attributed to Lewis, and a recent variant due to Weber. (shrink)

Semantic Leaps explores how people combine knowledge from different domains in order to understand and express new ideas. Concentrating on dynamic aspects of on-line meaning construction, Coulson identifies two related sets of processes: frame-shifting and conceptual blending. Frame-shifting is semantic reanalysis in which existing elements in the contextual representation are reorganized into a new frame. Conceptual blending is a set of cognitive operations for combining partial cognitive models. By addressing linguistic phenomena often ignored in traditional meaning research, Coulson explains how (...) processes of cross-domain mapping, frame-shifting, and conceptual blending enhance the explanatory adequacy of traditional frame-based systems for natural language processing. The focus is on how the constructive processes speakers use to assemble, link, and adapt simple cognitive models underlie a broad range of productive language behavior. (shrink)

In the paper we examine the problem of logical systems that are extensions of Classical Propositional Logic with new, intensional connectives of agency: monadic and dyadic _bringing it about that_. These systems are usually studied within the neighbourhood semantics. Here we propose a different strategy. We study all of the accepted laws and rules of logic of agency and define a translation of the agency operators into connectives interpreted in relating semantics. After this translation we can make a (...) reduction to more basic semantic properties that are required by the particular groups of laws and axioms. Finally, we define proper semantic structures and prove that they are complete with respect to all possible logical systems determined by the combinations of the axioms and rules. (shrink)

This paper deals with substructural nuclear (image-based) logics and their algebraic and Kripke-style semantics. More precisely, we first introduce a class of substructural logics with connective N satisfying nucleus property, called here substructural nuclear logics, and its subclass, called here substructural nuclear image-based logics, where N further satisfies homomorphic image property. We then consider their algebraic semantics together with algebraic characterizations of those logics. Finally, we introduce operational Kripke-style semantics for those logics and provide two sorts (...) of completeness results for them, one of which is based on algebraic completeness for all the logics and the other of which is based on set-theoretic one for the nuclear image-based logics. (shrink)

Among the most important of Sten Lindström’s achievements in philosophy and logic is that he was the first researcher to realise that the theory of rational choice can be brought to bear in the domain of logic and reasoning. The new conception was that a sentence α is a consequence of a set of sentences Γ just in case α is true in all selected ("best", "most plausible") possible worlds in which all sentences in Γ are true (rather than in (...) all possible worlds in which all sentences in Γ are true). And the selection of possible worlds should conform to the constraints on rational choices. Sten worked out this idea in stunning depth, detail and precision in his seminal paper "A semantic approach to nonmonotonic reasoning: Inference operations and choice." The paper was ready in draft form in April 1991 and presented in two talks later that year. It was included, in almost the same form, in the report series Uppsala Prints and Preprints in Philosophy in 1994, but it was never regularly published. The 2022 publication in Theoria seeks to compensate for this omission. (shrink)

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) is (...) high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (shrink)

Many expressions intuitively have different epistemic and modal profiles. For example, co-referring proper names are substitutable salva veritate in modal contexts but not in belief-contexts. Two-dimensional semantics, according to which terms have both a so-called primary and a secondary intension, is a framework that promises to accommodate and explain these diverging intuitions. The framework can be applied to indexicals, proper names or predicates. Graeme Forbes argues that the two-dimensional semantics of David Chalmers fails to account for so-called nested (...) contexts. These are linguistic contexts where a sentence is embedded under both epistemic and modal operators. Chalmers and Rabern suggest a two-dimensional solution to the problem. Their semantics solves the nesting-problem, but at the cost of invalidating certain plausible principles. We suggest a solution that is both simpler and avoids this cost. (shrink)

The literature on indicative conditionals contains two appealing views. The first is the selectional view: on this view, conditionals operate by selecting a single possibility, which is used to evaluate the consequent. The second is the informational view: on this view, conditionals don’t express propositions, but rather impose constraints on information states of speakers. Both views are supported by strong arguments, but they are incompatible on their standard formulations. Hence it appears that we have to choose between mutually exclusive options. (...) But the options are not exclusive. This paper develops a theory of the semantics and assertability of conditionals that is both selectional and informational. The theory vindicates the signature inferences of both selectional and informational theories, including so-called Conditionals Excluded Middle and principles about the interplay between conditionals and ‘might’. It also predicts some interesting and puzzling facts about the assertion of conditionals. (shrink)

Graeme Forbes (2011) raises some problems for two-dimensional semantic theories. The problems concern nested environments: linguistic environments where sentences are nested under both modal and epistemic operators. Closely related problems involving nested environments have been raised by Scott Soames (2005) and Josh Dever (2007). Soames goes so far as to say that nested environments pose the “chief technical problem” for strong two-dimensionalism. We call the problem of handling nested environments within two-dimensional semantics “the nesting problem”. We show that the (...) two-dimensional semantics for attitude ascriptions developed in Chalmers (2011a) has no trouble accommodating certain forms of the nesting problem that involve factive verbs such as “know” or “establish”. A certain form of the nesting problem involving apriority and necessity operators does raise an interesting puzzle, but we show how a generalized version of the nesting problem arises independently of two-dimensional semantics—it arises, in fact, for anyone who accepts the contingent a priori. We, then, provide a two-dimensional treatment of the apriority operator that fits the two-dimensional treatment of attitude verbs and apply it to the generalized nesting problem. We conclude that two-dimensionalism is not seriously threatened by cases involving the nesting of epistemic and modal operators. (shrink)

Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations examines how to introduce intuitionistic-type negations into RM-semantics. RM-semantics is highly malleable and capable of modeling families of logics which are very different from each other. This semantics was introduced in the early 1970s, and was devised for interpreting relevance logics. In RM-semantics, negation is interpreted by means of the Routley operator, which has been almost exclusively used for modeling De Morgan negations. This book provides research on particular (...) features of intuitionistic-type of negations in RM-semantics, while also defining the basic systems and many of their extensions by using models with or without a set of designated points. (shrink)

We explore some possibilities for developing epistemic logic using truthmaker semantics. We identify three possible targets of analysis for the epistemic logician. We then list some candidate epistemic principles and review the arguments that render some controversial. We then present the classic Hintikkan approach to epistemic logic and note—as per the ‘problem of logical omniscience’—that it validates all of the aforementioned principles, controversial or otherwise. We then lay out a truthmaker framework in the style of Kit Fine and present (...) six different ways of extending this semantics with a conditional knowledge operator, drawing on notions of implication and content that are prominent in Fine’s work. We demonstrate that different logics are thereby generated, bearing on the aforementioned epistemic principles. Finally, we offer preliminary observations about the prospects for each logic. (shrink)

In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as predicates of entities as in Montague’s semantics. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on predicates. The theory of coercive subtyping adequately extends the modern type theories and, as shown in this paper, plays a very useful role in making (...) type theories more expressive for formal semantics. It not only gives a satisfactory solution to the basic problem of ‘multiple categorisation’ caused by interpreting common nouns as types, but provides a powerful formal framework to model interesting linguistic phenomena such as copredication, whose formal treatment has been found difficult in a Montagovian setting. In particular, we show how to formally introduce dot-types in a type theory with coercive subtyping and study some type-theoretic constructs that provide useful representational tools for reference transfers and multiple word meanings in formal lexical semantics. (shrink)

This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.

A provocative ontological-cum-semantic position asserting that the right ontology is austere in its exclusion of numerous common-sense and scientific posits and that many statements employing such posits are nonetheless true. The authors of Austere Realism describe and defend a provocative ontological-cum-semantic position, asserting that the right ontology is minimal or austere, in that it excludes numerous common-sense posits, and that statements employing such posits are nonetheless true, when truth is understood to be semantic correctness under contextually operative semantic standards. Terence (...) Horgan and Matjaz Potrc argue that austere realism emerges naturally from consideration of the deep problems within the naive common-sense approach to truth and ontology. They offer an account of truth that confronts these deep internal problems and is independently plausible: contextual semantics, which asserts that truth is semantically correct affirmability. Under contextual semantics, much ordinary and scientific thought and discourse is true because its truth is indirect correspondence to the world. After offering further arguments for austere realism and addressing objections to it, Horgan and Potrc consider various alternative austere ontologies. They advance a specific version they call "blobjectivism"--the view that the right ontology includes only one concrete particular, the entire cosmos, which, although it has enormous local spatiotemporal variability, does not have any proper parts. The arguments in Austere Realism are powerfully made and concisely and lucidly set out. The authors' contentions and their methodological approach--products of a decade-long collaboration--will generate lively debate among scholars in metaphysics, ontology, and philosophy. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the (...) validity of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core– in the case studied here, this common core is classical positive propositional logic (CPL + ). The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of logics of formal inconsistency and undeterminedness (LFIUs), namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion at once. The last sections offer an algebraic account for such logics by adapting the swap-structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite non-deterministic matrices. (shrink)

This thesis argues for two main points concerning the philosophy of natural language semantics. Firstly, that the objects of assertion are distinct from the entities appealed to in the compositional rules of natural language semantics. Secondly, natural languages contain context-shifting operators known as "monsters". In fact, it will be shown that these theses are simply two sides of the same coin.

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of the original (...) pure system with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). (shrink)

By considering the semantic footings of the so-called antinomies of pure reason, this article contributes to the debate about whether Kant was committed to semantic realism or anti-realism. That is, whether verification-transcendent judgements are truth-apt (realism) or not (anti-realism). Against the (empiricist) semantic principle that Strawson, and others, have ascribed to Kant as the “principle of significance,” the bedrock of my article is what I call Kant’s Real Principle of Significance: an extension-based and normative principle stating that a judgement can (...) have no “significance” or “objective validity” (truth-value) without a universally recognizable norm for verifying it. This principle entails semantic anti-realism. I argue that we can extract the principle from the antinomy chapter of KrV, since in there Kant concludes that judgements of the form “the world as such is x” are without “significance” (lack a truth-value) in virtue of being unverifiable as a matter of principle. I propose that Kant’s reference to some of the antinomical judgements as “false” is not incompatible with this anti-realist reading because he operates with two distinct world-concepts: an illegitimate transcendental realist one and a legitimate transcendental idealist one. In contrast to most anti-realist Kant-interpretations, it is furthermore argued that any satisfactory anti-realist construal of Kant’s view must be compatible with his assertion that the thesis in the third antinomy about freedom “can be true.” That requires a thicker conception of “significance” or “objective validity” than what is often ascribed to Kant, which is encapsulated by the Real Principle of Significance. (shrink)

The authors of Austere Realism describe and defend a provocative ontological-cum-semantic position, asserting that the right ontology is minimal or austere, in that it excludes numerous common-sense posits, and that statements employing such posits are nonetheless true, when truth is understood to be semantic correctness under contextually operative semantic standards. Terence Horgan and Matjaz [hacek over z] Potrc [hacek over c] argue that austere realism emerges naturally from consideration of the deep problems within the naive common-sense approach to truth and (...) ontology. They offer an account of truth that confronts these deep internal problems and is independently plausible: contextual semantics, which asserts that truth is semantically correct affirmability. Under contextual semantics, much ordinary and scientific thought and discourse is true because its truth is indirect correspondence to the world. After offering further arguments for austere realism and addressing objections to it, Horgan and Potrc [hacek over c] consider various alternative austere ontologies. They advance a specific version they call "blobjectivism"--the view that the right ontology includes only one concrete particular, the entire cosmos, which, although it has enormous local spatiotemporal variability, does not have any proper parts. The arguments in Austere Realism are powerfully made and concisely and lucidly set out. The authors' contentions and their methodological approach--products of a decade-long collaboration--will generate lively debate among scholars in metaphysics, ontology, and philosophy. Terence E. Horgan is Professor of Philosophy at the University of Arizona. Matjaz [hacek over z] Potrc [hacek over c] is Professor of Philosophy at the University of Ljubljana. (shrink)

We define dual and symmetric combinatory calculi (inequational and equational ones), and prove their consistency. Then, we introduce algebraic and set theoretical relational and operational - semantics, and prove soundness and completeness. We analyze the relationship between these logics, and argue that inequational dual logics are the best suited to model computation.

This article outlines a semantic approach to the logics of unknown truths, and the logic of false beliefs, using neighborhood structures, giving results on soundness, completeness, and expressivity. Relational semantics for the logics of unknown truths are also addressed, specically the conditions under which sound axiomatizations of these logics might be obtained from their normal counterparts, and the relationship between refexive insensitive logics and logics containing the provability operator as the primary modal operator.

This paper argues, first, that the information problem poses a foundational challenge to mainstream semantics. It proposes, second, to address this problem by drawing on notions from Kit Fine’s essentialist framework. More specifically, it claims that the information problem can be avoided by strengthening standard truth theories, employing an operator expressing the notion of a relative constitutive semantic requirement. As a result, the paper proposes to construe semantic theories as theories of semantic requirements, and semantic knowledge as knowledge of (...) such requirements. (shrink)