Rice Combinational and Sequential Logic This text provides a guide to combinational and sequential logic, introducing students to the basic concepts then progressing to HND/first year undergraduate level. It has a highly practical emphasis, enabling the reader to simulate, build and test the circuits discussed in the text. Electronics Workbench files are provided for simulation, while easy-to-use XPLA software and specially designed hardware encourage the reader to build and test the circuits using programmable logic. The text (...) itself contains many self-assessment questions, complete with detailed answers, allowing students to test themselves as they learn. No previous experience of the topic is required and an abundance of practical examples helps students to apply the basic principles. The accompanying CD-ROM provides the XPLA development system software and Electronics Workbench files, as well as the Xilinx Webpack development system and 'walkthrough'. Hardware for Programmable Logic experiments can either be purchased or built following instructions from the text. Altogether, the text, software and hardware provide an interactive and stimulating teaching and learning resource. F. (shrink)

Field-Programmable Gate Arrays (FPGAs) have emerged as an attractive means of implementing logic circuits, providing instant manufacturing turnaround and negligible prototype costs. They hold the promise of replacing much of the VLSI market now held by mask-programmed gate arrays. FPGAs offer an affordable solution for customized VLSI, over a wide variety of applications, and have also opened up new possibilities in designing reconfigurable digital systems. Field-Programmable Gate Arrays discusses the most important aspects of FPGAs in a textbook (...) manner. It provides the reader with a focused view of the key issues, using a consistent notation and style of presentation. It provides detailed descriptions of commercially available FPGAs and an in-depth treatment of the FPGA architecture and CAD issues that are the subjects of current research. The material presented is of interest to a variety of readers, including those who are not familiar with FPGA technology, but wish to be introduced to it, as well as those who already have an understanding of FPGAs, but who are interested in learning about the research directions that are of current interest. (shrink)

Contents. Introduction. 1. Preliminaries. 2. Normal Form Games. 3. Extensive Games. 4. Applications of Game Theory. 5. The Methodology of Game Theory. Conclusion. Appendix. Bibliography. Index. Does game theory—the mathematical theory of strategic interaction—provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory—the first monograph on the philosophy of game theory—is an attempt to combine insights from epistemic logic and the philosophy of science (...) to investigate the applicability of game theory in such fields as economics, philosophy and strategic consultancy. I prove new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and explore in detail the logical form of game theory as it is used in explanatory and normative contexts. I argue that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, I argue, has been rather successful in achieving this aim. "The 'epistemic' approach to game theory has emerged over the past twenty-five years. What is this approach? How does it differ from the conventional equilibrium-based approach to game theory? What have been its strengths and weaknesses to date? To find out, read this comprehensive and excellently written account". Adam Brandenburger, J. P. Valles Professor of Business Economics and Strategy, Stern School of Business, New York University "Reading Boudewijn de Bruin's book should be rewarding both for game theorists interested in the conceptual foundations of their discipline and for philosophers who want to learn more about formal analysis of strategic interaction. It provides an in-depth logical study of the currently dominant epistemic approaches to non-cooperative games, with an eye both to the attractions and to the serious challenges facing the Epistemic Programme". Wlodek Rabinowicz, Professor of Practical Philosophy, Department of Philosophy, Lund University . (shrink)

The general aim of this project is to fundamentally re-think the design of teaching materials in view of what is now known about cognitive deficits and about what Howard Gardner has termed ‘multiple intelligences’. The applicant has implemented this strategy in two distinct areas, the first involving the writing of an English language programme for Chinese speakers, the second involving the construction of specialized equipment for teaching elementary logic to blind students. The next phase is to test the effectiveness (...) of the logic device, because in theory – the one to be tested – materials the design of which is informed by the above rationale will provide a richer learning experience for non-impaired users. (shrink)

An essential element of human resource management is employee growth and development. Two aspects of this development involve growth in job related behaviours and the less tangible but vital aspect of personal growth. The paper focuses on the latter topic. The aim is an exploration of the relationship between experience and education as they relate to personal growth. Since many schools of management and in-house HRM programmes involve the use of experiential approaches to learning, it seems a relevant issue for (...) discussion. In fact, a strong case is made for the use of experience as a critical part of the personal education and growth process. Logical, rational analysis, poetic device, and teaching stories are used to highlight the role of experience. Extensive use is made of developmental notions from Buddhism, Confucianism, Sufism and Taoism. Reference is made to the Kolb et al. learning cycle model to help examine the personal growth experience. The paper discusses both the role of the educator and the role of the employee or seeker of personal growth. The educational process is discussed in terms of negating as well as affirming, abandoning old ideas as well as gaining new ones. Proposed educational aims for the learner are identified. (shrink)

The article inquires into some of the most relevant current transformations of the idea of the social in contemporary European welfare capitalism. Some crucial institutional ideas — employability and activation — of EU welfare capitalism and their connections with the new spirit of capitalism — network capitalism — are discussed. In particular, the way these ideas contribute to enacting institutional regimes of justification, framing in this a new idea of the social, is explored. The features of the latter will be (...) deepened with particular concern for two constitutive elements of European societal self-representation — individualization (as a social ideal and project) and publicness (as a fundamental characteristic of the institutional programme) — and regarding emerging paradoxes characterizing their current development. Arguments will be advanced in order to show that the currently dominant institutional regime of justification does not have a univocal, one-way fate of development, and both ties and opportunities are reconfigured. The idea of the social, even if reframed according to the social and institutional logics the article explores, is a terrain of (cultural, political, social and institutional) conflict. In this, possible counter-factual interpretations of the emerging institutional devices and practices, already at work on the social stage, can be further developed and strengthened. (shrink)

My working hypothesis is based on the project of a theory of science (Wissenschaftslehre) at the very beginning of the Prolegomena and it consists in conceiving this theory of science as the program which insures their cohesion to the whole of the Investigations in this work. In order to test this hypothesis, I will first examine the different steps which led to the project of a theory of science in the pre-phenomenological period. I will secondly expound the guidelines of the (...) theory of science, insisting in particular on its relation to pure logic. In the third section, I will attempt to define the function of the theory of knowledge and of phenomenology in such a programme. I will conclude with some remarks on the fate of this theory of science after the Logical Investigations. Most of Husserl’s allusions to the theory of science, be it in his lecture notes, the manuscripts that were written after 1901 or other works published during Husserl’s lifetime, seem to suggest that the theory of science kept on assuming the very role it was playing in Husserl’s seminal work: the theory of science provides its basis to Husserl’s philosophical agenda. (shrink)

The introspective devices framework proposed by Kammerer and Frankish (this issue) offers an attractive conceptual tool for evaluating and developing accounts of introspection. However, the framework assumes that different views about the nature of introspection can be easily evaluated against a set of common criteria. In this paper, I set out to test this assumption by analysing two formal models of introspection using the introspective device framework. The question I aim to answer is not only whether models developed outside (...) of philosophy can be successfully evaluated against the set of conceptual criteria proposed by Kammerer and Frankish, but also whether this kind of evaluation can reveal some limitations inherent to the framework. (shrink)

What Robots Can and Can't Be (hereinafter Robots) is, as Selmer Bringsjord says "intended to be a collection of formal-arguments-that-border-on-proofs for the proposition that in all worlds, at all times, machines can't be minds" (Bringsjord, forthcoming). In his (1994) "Précis of What Robots Can and Can't Be" Bringsjord styles certain of these arguments as proceeding "repeatedly . . . through instantiations of" the "simple schema".

This paper compares the roles classical and intuitionistic logic play in restricting the free use of truth principles in arithmetic. We consider fifteen of the most commonly used axiomatic principles of truth and classify every subset of them as either consistent or inconsistent over a weak purely intuitionistic theory of truth.

The young Wittgenstein called his conception of logic “New Logic” and opposed it to the “Old Logic”, i.e. Frege’s and Russell’s systems of logic. In this paper the basic objects of Wittgenstein’s conception of a New Logic are outlined in contrast to classical logic. The detailed elaboration of Wittgenstein’s conception depends on the realization of his ab-notation for first order logic.

This work aims to make tense logic a more robust tool for ontologists, philosophers, knowledge engineers and programmers by outlining a fusion of tense logic and ontology of time. In order to make tense logic better understandable, the central formal primitives of standard tense logic are derived as theorems from an informal and intuitive ontology of time. In order to make formulation of temporal propositions easier, temporal operators that were introduced by Georg Henrik von Wright are (...) developed, and mapped to the ontology of time. (shrink)

Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system-a collection of rules and axioms, which define a universe of logical proofs-is what gives us programming languages and (...) modern-day programming. This book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses-natural deduction-is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations. The book is divided into four parts: Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words. Part II "Formal Syntactic Proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle. Part III "Formal Semantic Disproof" shows you how to construct mathematical counterexamples to shoe that proof is impossible. Jape can check the counterexamples you build. Part IV " Program Specification and Proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows. Aimed at undergraduates and graduates in computer science, logic, mathematics and philosophy, the text includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web. (shrink)

Turing's programme, the idea that intelligence can be modelled computationally, is set in the context of a parallel between certain elements from metamathematics and Popper's schema for the evolution of knowledge. The parallel is developed at both the formal level, where it hinges on the recursive structuring of Popper's schema, and at the contentual level, where a few key issues common to both epistemology and metamathematics are briefly discussed. In light of this connection Popper's principle of transference, akin to Turing's (...) belief in the relevance of the theory of computation for modelling psychological functions, is widened into the extended principle of transference. Thus Turing's programme gains a solid epistemological footing. *I am grateful to Claude Lamontagne and Jean-Pierre Delage for their comments on this paper. (shrink)

Combinatory logic started as a programme in the foundation of mathematics and in an historical context at a time when such endeavours attracted the most gifted among the mathematicians. This small volume arose under quite differ ent circumstances, namely within the context of reworking the mathematical foundations of computer science. I have been very lucky in finding gifted students who agreed to work with me and chose, for their Ph. D. theses, subjects that arose from my own attempts 1 (...) to create a coherent mathematical view of these foundations. The result of this collaborative work is presented here in the hope that it does justice to the individual contributor and that the reader has a chance of judging the work as a whole. E. Engeler ETH Zurich, April 1994 lCollected in Chapter III, An Algebraization of Algorithmics, in Algorithmic Properties of Structures, Selected Papers of Erwin Engeler, World Scientific PubJ. Co. , Singapore, 1993, pp. 183-257. I Historical and Philosophical Background Erwin Engeler In the fall of 1928 a young American turned up at the Mathematical Institute of Gottingen, a mecca of mathematicians at the time; he was a young man with a dream and his name was H. B. Curry. He felt that he had the tools in hand with which to solve the problem of foundations of mathematics mice and for all. His was an approach that came to be called "formalist" and embodied that later became known as Combinatory Logic. (shrink)

Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, "The logic and meaning of plurals, II", aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic and meaning (...) of plural constructions that result from the view that plural constructions are, by and large, devices for talking about many things (as such). The account of logic presented in the papers surpasses contemporary Fregean accounts in its scope. This extension of the scope of logic results from extending the range of languages that logic can directly relate to. Underlying the view of language that makes room for this is a perspective on reality that locates in the world what plural constructions can relate to. The papers suggest that reflections on plural constructions point to a broader framework for understanding logic, language, and reality that can replace the contemporary Fregean framework as this has replaced its Aristotelian ancestor. (shrink)

In this sequel to "The logic and meaning of plurals. Part I", I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of (...) truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages. (shrink)

This book is designed to explain the technical ideas that are taken for granted in much contemporary philosophical writing. Notions like "denumerability," "modal scope distinction," "Bayesian conditionalization," and "logical completeness" are usually only elucidated deep within difficult specialist texts. By offering simple explanations that by-pass much irrelevant and boring detail, Philosophical Devices is able to cover a wealth of material that is normally only available to specialists. The book contains four sections, each of three chapters. The first section is (...) about sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis. The second is about analyticity, a prioricity, and necessity. The third is about probability, outlining the difference between objective and subjective probability and exploring aspects of conditionalization and correlation. The fourth deals with metalogic, focusing on the contrast between syntax and semantics, and finishing with a sketch of Godel's theorem. Philosophical Devices will be useful for university students who have got past the foothills of philosophy and are starting to read more widely, but it does not assume any prior expertise. All the issues discussed are intrinsically interesting, and often downright fascinating. It can be read with pleasure and profit by anybody who is curious about the technical infrastructure of contemporary philosophy."--p. 4 of cover. (shrink)

Logical Empiricism is commonly regarded as uninterested in, if not hostile to sociological investigations of science. This paper reconstructs the views of Otto Neurath and Philipp Frank on the legitimacy and relevance of sociological investigations of theory choice. It is argued that while there obtains a surprising degree of convergence between their programmatic pronouncements and the Strong Programme, the two types of project nevertheless remain distinct. The key to this differences lies in the different assessment of a supposed dilemma facing (...) post-Mertonian sociologists of science. (shrink)

Deflationists about truth seek to undermine debates about the nature of truth by arguing that the truth predicate is merely a device that allows us to express a certain kind of generality. I argue that a parallel approach is available in the case of logical consequence. Just as deflationism about truth offers an alternative to accounts of truth's nature in terms of correspondence or justification, deflationism about consequence promises an alternative to model-theoretic or proof-theoretic accounts of consequence's nature. I then (...) argue, against considerations put forward by Field and Beall, that Curry's paradox no more rules out deflationism about consequence than the liar paradox rules out deflationism about truth. (shrink)

In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.

Many criticisms of epistemic logic have centered around its use of devices such as idealized knowers with logical omniscience and perfect self-knowledge. One possible response to such criticisms is to say that these idealizations are normative devices, and that epistemic logic tells us how agents ought to behave. This paper will take a different approach, treating epistemic logic as descriptive, and drawing the analogy between its formal models and idealized scientific models on that basis. Treating (...) it as descriptive matches the way in which some philosophers, including one of its founders, Jaako Hintikka, have thought about epistemic logic early in its history. Further, the analogy between the two fields will give us a way to defuse criticisms that see epistemic logic as unrealistic. For example, criticizing models of epistemic logic in which agents know all propositional tautologies as being unrealistic would be like criticizing frictionless planes in physics for being unrealistic. Each one would certainly be an unsuitable model for studying some kinds of phenomena, but is entirely appropriate for others. After outlining the analogy between epistemic and scientific models, we will discuss some ways in which idealizations are used by different research programs in epistemic logic. (shrink)

This paper compares two ways of holding that logic is special among the sciences in that it has no restricted class of entities as its subject matter, but instead concerns all entities alike. One way is Williamson’s explanation of how inquiry into logical consequence and logical truth only superficially concerns the linguistic or conceptual entities that bear these properties. Williamson draws on ideas familiar from deflationism about truth, and his account has been called “deflationary.” I argue that the analogy (...) is misleading. While there’s a broad sense in which Williamson offers a deflationary account of logical inquiry, his view differs from deflationism about truth in being best understood as a form of instrumentalism. By contrast, I elaborate a deflationism about logical properties modeled on deflationism about truth. I defend this expressive device deflationism as an explanation of our use of logical predicates. (shrink)

The paper discusses some logical problems concerning analogy. The traditional understanding of analogy as _proportion_ (proportion) is inadequate, at least if proportionality is taken in mathematical sense. This situation is clear if we considered various special cases of analogy for instance _analogia legis_ and _analogia juris._ Since analogy assumes a similarity of analogata (items being or investigated) as analogical, a general analysis of analogical relation must begin with the concept of similarity. It can be defined as possessing a common property. (...) This idea is formalized by devices borrowed from logic and set theory. (shrink)

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth-conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the `logicality of language', accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter-examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...) with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is `blind' to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non-classical---indeed quite exotic---kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis-a-vis its open class terms and employs a deductive system that is basically classical. (shrink)

In business and government, databases contain large quantities of digital transactional data (purchases made, services used, finances transferred, benefits received, licences acquired, borders crossed, tickets purchased). The data can be understood as ongoing and dynamic measurements of the activities and doings of people. In government, numerous database devices have been developed to connect such data across services to discover patterns and identify and evaluate the performance of individuals and populations. Under the UK’s New Labour government, the development of such (...) devices was part of a broader policy known as ‘joined-up thinking and government’. Analyses of this policy have typically understood joining up as an operation of adding together distributed data about subjects, which can then be used in the service of government surveillance, the database state or informational capitalism. But rather than such technical or managerialist analytics, I argue that topological analytics capture what these database devices enact and do: they materialize the ‘individuality’ of subjects in intensified, distributed and fluctuating ways and materialize and intensify a logic of what Deleuze describes as modulating controls. Through examples of UK New Labour social policy initiatives over the past decade, I argue that topological analytics can account for these as immanent rather than exceptional properties of database devices and, as such, part and parcel of a governmental logic and ontology of subjects. (shrink)

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth‐conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the ‘logicality of language’, accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter‐examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...) with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is ‘blind’ to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non‐classical—indeed quite exotic—kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis‐á‐vis its open class terms and employs a deductive system that is basically classical. (shrink)

The Handbook of the Logic of Argument and Inference is an authoritative reference work in a single volume, designed for the attention of senior undergraduates, graduate students and researchers in all the leading research areas concerned with the logic of practical argument and inference. After an introductory chapter, the role of standard logics is surveyed in two chapters. These chapters can serve as a mini-course for interested readers, in deductive and inductive logic, or as a refresher. Then (...) follow two chapters of criticism; one the internal critique and the other the empirical critique. The first deals with objections to standard logics (as theories of argument and inference) arising from the research programme in philosophical logic. The second canvasses criticisms arising from work in cognitive and experimental psychology. The next five chapters deal with developments in dialogue logic, interrogative logic, informal logic, probability logic and artificial intelligence. The last chapter surveys formal approaches to practical reasoning and anticipates possible future developments. Taken as a whole the Handbook is a single-volume indication of the present state of the logic of argument and inference at its conceptual and theoretical best. Future editions will periodically incorporate significant new developments. (shrink)

John Woods' The Logic of Fiction, now thirty-five years old, is a ground-breaking event in the establishment of the semantics of fiction as a stand-alone research programme in the philosophies of language and logic. There is now a large literature about these matters, but Woods' book retains a striking freshness, and still serves as a convincing template of the treatment options for the field's key problems. The book now appears in a second edition with a new Foreword by (...) Nicholas Griffin and an extended bibliography covering the period 1969-2009. As Griffin notes in his Foreword, it is "surprising on looking back to discover how little was written on the semantics of fiction before John Woods' The Logic of Fiction was published in 1974. The surprise is the greater because Woods' book appeared after almost a quarter century of fierce philosophical debate about reference Fictional discourse, one would have thought, would be an important testing ground for philosophical theories of referential expressions and one, moreover, in which the standard theories would likely be tested to destruction. " " One of the great merits of Woods' book is that it takes seriously the wide-ranging demands that fiction imposes on logic and semantics, and does not try to force fiction into some pre-conceived logical mould. but thanks to Woods' pioneering efforts, we are much closer to one now than we were when he set out to write his book. His book was not the last word on the logic of fiction; it was much more important: it was nearly the first." NICHOLAS GRIFFIN is Canada Research Chair in Philosophy at McMaster University. Recent publications include Russell vs Meinong: The Legacy of "On Denoting," edited with Dale Jacquette. JOHN WOODS is Director of the Abductive Systems Group at the University of British Columbia and Charles S. Peirce Visiting Professor of Logic in the Group on Logic and Computational Science, King's College London. He has two forthcoming books on fiction - an edited volume, Fictions and Models: New Essays, and a research monograph, Sherlock's Member: New Perspectives on the Semantics of Fiction, both to appear in 2010. (shrink)

Belnap–Dunn’s relevance logic, \(\textsf{BD}\), was designed seeking a suitable logical device for dealing with multiple information sources which sometimes may provide inconsistent and/or incomplete pieces of information. \(\textsf{BD}\) is a four-valued logic which is both paraconsistent and paracomplete. On the other hand, De and Omori, while investigating what classical negation amounts to in a paracomplete and paraconsistent four-valued setting, proposed the expansion \(\textsf{BD2}\) of the four valued Belnap–Dunn logic by a classical negation. In this paper, we introduce (...) a four-valued expansion of BD called \({\textsf{BD}^\copyright }\), obtained by adding an unary connective \({\copyright }\,\ \) which is a consistency operator (in the sense of the Logics of Formal Inconsistency, _LFI_s). In addition, this operator is the unique one with the following features: it extends to \(\textsf{BD}\) the consistency operator of LFI1, a well-known three-valued _LFI_, still satisfying axiom _ciw_ (which states that any sentence is either consistent or contradictory), and allowing to define an undeterminedness operator (in the sense of Logic of Formal Undeterminedness, _LFU_s). Moreover, \({\textsf{BD}^\copyright }\) is maximal w.r.t. LFI1, and it is proved to be equivalent to BD2, up to signature. After presenting a natural Hilbert-style characterization of \({\textsf{BD}^\copyright }\) obtained by means of twist-structures semantics, we propose a first-order version of \({\textsf{BD}^\copyright }\) called \({\textsf{QBD}^\copyright }\), with semantics based on an appropriate notion of four-valued Tarskian-like structures called \(\textbf{4}\) -structures. We show that in \({\textsf{QBD}^\copyright }\), the existential and universal quantifiers are interdefinable in terms of the paracomplete and paraconsistent negation, and not by means of the classical negation. Finally, a Hilbert-style calculus for \({\textsf{QBD}^\copyright }\) is presented, proving the corresponding soundness and completeness theorems. (shrink)

We advance a theoretical framework which combines recent insights of research in logic, psychology, and formal semantics, on the nature of diagrammatic representation and reasoning. In particular, we wish to explain the varied efficacy of reasoning and representing with diagrams. In general we consider diagrammatic representations to be restricted in expressive power, and we wish to explain efficacy of reasoning with diagrams via the semantical and computational properties of such restricted `languages'. Connecting these foundational insights (from semantics and complexity (...) theory) to the psychology of reasoning with diagrams requires us to develop the notion of the {\it availability} (to an agent) of {\it constraints} operating within representation systems, as a consequence of their direct semantic interpretation. Thus we offer a number of fundamental definitions as well as a research programme which aligns current efforts in the logical and psychological analysis of diagrammatic representation systems. (shrink)

This book is a consideration of the differences between Aristotelian and symbolic logic (and the metaphysical assumptions they come packaged with) and the consequences these have for how we view the world. What Veatch propose is to try to exhibit with respect to several of the key logical tools and devices – propositions, inductive and deductive arguments, scientific and historical explanations, definitions, etc. – how these several instruments are differently conceived, both as to their natures and their functions, (...) in each of these respective logics. (shrink)

The logical character of I is obligatorily deictic. Some variant devices have obligatory anaphoric reference, some are free, and some again have obligatory deictic reference. It is by singling out individuals made salient in the extra-sentential context that uses of this third sort refer. Substitution instances reveal and matching constraints confirm that each use of I must fall into this third category.

Architectural Drawings as Investigating Devices explores how the changing modes of representation in architecture and urbanism relate to the transformation of how the addressees of architecture and urbanism are conceived. The book diagnoses the dominant epistemological debates in architecture and urbanism during the 20th and 21st centuries. It traces their transformations, paying special attention to Le Corbusier and Ludwig Mies van der Rohe’s preference for perspective representation, to the diagrams of Team 10 architects, to the critiques of functionalism, and (...) the upgrade of the artefactual value of architectural drawings in Aldo Rossi, John Hejduk, Peter Eisenman, and Oswald Mathias Ungers, and, finally, to the reinvention of architectural programme through the event in Bernard Tschumi and the Office for Metropolitan Architecture (OMA). Particular emphasis is placed on the spirit of truth and clarity in modernist architecture, the relationship between the individual and the community in post-war era architecture, the decodification of design process as syntactic analogy and the paradigm of autonomy in the 1970s and 1980s architecture, the concern about the dynamic character of urban conditions and the potentialities hidden in architectural programme in the post-autonomy era. This book is based on extensive archival research in Canada, the USA and Europe, and will be of interest to architects, artists, researchers and students in architecture, architectural history, theory, cultural theory, philosophy and aesthetics. (shrink)

ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles (...) of propositional logic; 4. Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)

Music is the carrier through which human beings express their emotions. It can clean up their hearts and seek emotional resonance. The combination of music and artificial intelligence, when music meets artificial intelligence, the mathematical logic part of data and algorithm replaces the image thinking, resulting in automatic music production. The basic principle of music creation is to use artificial intelligence technology to conduct in-depth training on a large number of songs, and then build a database. Then, within a (...) certain period of time, extract a segment from several songs, and then decompose it to form a new melody. The automatic music production is the collision of music and technology. With the flying of code and notes, it creates a different kind of beauty. Music culture is a new field of music application. With its refreshing audio-visual effect, it has made people have a new understanding of music and has become a hot topic in current mass cultural activities. The sound quality characteristics of music culture programs determine the characteristics of simple, fast and efficient design. However, the current audio and video design still stays in the traditional audio and video form design, with low design efficiency, long cycle, high cost and high requirements for designers. In view of the fact that the traditional audio and video design mode in China's music and cultural programs cannot meet the needs of performance programs at present, this paper proposes a design scheme of audio and visual effects of music and cultural programs with intelligent devices as the core, and develops a complete set of audio and visual effects aided design system on this basis. (shrink)

Abstract: One of the institutional highlights of the encounter between Austrian “wissen¬schaftliche Philosophie” and French “philosophie scientifique” in the first half of the 20th century was the “First International Congress for Unity of Science” that took place 1935 in Paris. In my contribution I deal with an episode of the philosophical mega-event whose protagonist was the American philosopher and semiotician Charles William Morris. At the Paris congress he presented his programme of a comprehensive, practice-oriented scientific philosophy and, in a more (...) elaborated version he published it two years later in Logical Positivism, Pragmatism and Scientific Empiricism (Morris 1937). Morris aimed at a synthesis of formalism, pragmatism, and traditional empiricism that combined the virtues of these accounts while avoided their shortocmings. The core of approach was a comprehensive theory of the concept of meaning. Through an analysis of the concept of meaning he sought to sort out the existing differences and the options for a possible future rapprochment between logical empiricism and pragmatism. Against the overly narrow logical empiricist understanding of philosophy as the syntax of the language of science Morris argued for a “scientific pragmatism” that comprised four levels: (1) Philosophy as Logic of Science, (2) Philosophy as Clarification of Meaning (Peirce), (3) Philosophy as Empirical Axiology (Dewey), and (4) Philosophy as Empirical Cosmology (Whitehead). (shrink)

Most of the Bolzano literature is exegetical, neglecting, unfortunately, the great potential of his logic as the beginning of a PROGRAMME. Specifically, his unorthodox construai of the consequence relation as triadic, and his account of logical form are promising beginnings which even as they stand shed light on question of relevance, the ancient problems of enthymemes and others. Instead of developing these suggestions, Bolzano scholars have been occupied with elucidating the ontology of sentences in themselves, and related topics. I (...) argue, and believe to be in agreement with Bolzano, that the nature of sentences is fully explained by the relations that hold between them, just as money has no nature or essence beyond the transactions it makes possible. It follows that the development of his logic would contribute at least as much to the understanding of sentences than any exegesis. (shrink)

Kaplan (1989a) insists that natural languages do not contain displacing devices that operate on character—such displacing devices are called monsters. This thesis has recently faced various empirical challenges (e.g., Schlenker 2003; Anand and Nevins 2004). In this note, the thesis is challenged on grounds of a more theoretical nature. It is argued that the standard compositional semantics of variable binding employs monstrous operations. As a dramatic first example, Kaplan’s formal language, the Logic of Demonstratives, is shown to (...) contain monsters. For similar reasons, the orthodox lambda-calculus-based semantics for variable binding is argued to be monstrous. This technical point promises to provide some far-reaching implications for our understanding of semantic theory and content. The theoretical upshot of the discussion is at least threefold: (i) the Kaplanian thesis that “directly referential” terms are not shiftable/bindable is unmotivated, (ii) since monsters operate on something distinct from the assertoric content of their operands, we must distinguish ingredient sense from assertoric content (cf. Dummett 1973; Evans 1979; Stanley 1997), and (iii) since the case of variable binding provides a paradigm of semantic shift that differs from the other types, it is plausible to think that indexicals—which are standardly treated by means of the assignment function—might undergo the same kind of shift. (shrink)

A logic of questions and answers exists within the logic of statements, if we make the following identifications (roughly): "Whether" questions are identified with true exclusive disjunctions, and "which" questions are identified with true existential quantifications. The question-and-answer process is interpreted as an information-matching game. The question mark is not needed except as a device of abbreviation. Complete and partial answers can be distinguished and various relations of relevance, independence, and resolution defined.

It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logical consequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logical consequence.

Hilbert's plan for understanding the concept of infinity required the elimination of non‐finitist machinery from proofs of finitist assertions. The failure of the original plan leads to a hierarchy of progressively less elementary, but still constructive methods instead of finitist ones . A mathematical proof of this failure requires a definition of « finitist ».—The paper sketches the three principal methods for the syntactic analysis of non‐constructive mathematics, the resulting consistency proofs and constructive interpretations, modelled on Herbrand's theorem, and their (...) mathematical and logical consequences. A characterization of finitist proofs is sketched. A remark on the completeness of the predicate calculus concludes the paper. Throughout open problems and alternative approaches are emphasized.ZusammenfassungHilbert sah das Verstehen des Begriffs des Unendlichen in der Eliminierung nichtfiniter Methoden aus Beweisen finiter Sätze. Das Versagen dieses Unternehmens führt zu einer Hierarchic progressiv weniger elementarer, aber noch konstruktiver Methoden, statt der finiten . Ein Unmöglichkeitsbeweis des ursprünglichen Planes setzt eine Definition von « finit » voraus.—Die drei wichtigsten Methoden der syntaktischen Analyse nichtkonstruktiver mathematischer Theorien, die daraus gewonnenen Widerspruchsfreiheitsbeweise and konstruktiven Interpretationen and deren mathematische and logische Anwendungen werden besprochen. Eine Prazisierung des Begriffs « finit » wird skizziert. Eine Bemerkung zur Vollstandigkeit des engeren Funktionenkalküls beschliesst die Abhandlung.—Oflene Fragen and komplementare Fragestellungen werden betont. (shrink)