Logical puzzles like the doctrinal paradox raise the problem of how to aggregate individual judgements into a collective judgement, or alternatively, how to merge collectively inconsistent knowledge bases. In this paper, we view judgement aggregation as a function on propositional logic valuations, and we investigate how logic constrains judgement aggregation. In particular, we show that there is no non-dictatorial decision method for aggregating sets of judgements in a logically consistent way if the decision method is local, i.e., only depends (...) on the individual judgements on the proposition under consideration. (shrink)

Logical puzzles like the doctrinal paradox raise the problem of how to aggregate individual judgements into a collective judgement, or alternatively, how to merge collectively inconsistent knowledge bases. In this paper, we view judgement aggregation as a function on propositional logic valuations, and we investigate how logic constrains judgement aggregation. In particular, we show that there is no non-dictatorial decision method for aggregating sets of judgements in a logically consistent way if the decision method is local, i.e., only depends (...) on the individual judgements on the proposition under consideration. (shrink)

What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way - either one believes a proposition, or one doesn't. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that one's beliefs be logically consistent, and that one believe the logical consequences of one's beliefs. A less popular picture sees belief as a graded phenomenon.

James Sterba uses the Pauline Principle to argue that the occurrence of significant, horrendous evils is logically incompatible with the existence of a good God. The Pauline Principle states that (as a rule) one must never do evil so that good may come from it, and according to Sterba, this principle implies that God may not permit significant evils even if that permission would be necessary to secure other, greater goods. By contrast, I argue that the occurrence of significant evils (...) is logically compatible with the existence of a good God because victims of significant evils may themselves reasonably consent to their suffering. In particular, I argue that they may be able to accept their suffering if it turns out that there was no way for God to secure relevant greater goods (or prevent other, greater evils) except by way of allowing their suffering, and God also provides them with other compensating, heavenly comforts. After using this consent-based argument to address Sterba’s logical problem from evil, I briefly consider how this argument may also help address a related evidential problem from evil, which suggests that while it is possible that victims of significant evils would consent to their suffering, it is unlikely that they would do so. While I do not provide a definitive solution to this evidential problem of evil, I highlight one important example of a trade-off that God may need to make that would—along with the provision of compensating, heavenly comforts—potentially persuade victims of significant evils to consent to their suffering. Specifically, I argue that there may be a necessary trade-off that God needs to make between permitting significant evils (on the one hand) and protecting a certain, morally significant form of free will (on the other hand). (shrink)

In his new book, Logical Form, Andrea Iacona distinguishes between two different roles that have been ascribed to the notion of logical form: the logical role and the semantic role. These two roles entail a bifurcation of the notion of logical form. Both notions of logical form, according to Iacona, are descriptive, having to do with different features of natural language sentences. I agree that the notion of logical form bifurcates, but not that the (...) logical role is merely descriptive. In this paper, I focus on formalization, a process by which logical form, on its logical role, is attributed to natural language sentences. According to some, formalization is a form of explication, and it involves normative, pragmatic, as well as creative aspects. I present a view by which formalization involves explicit commitments on behalf of a reasoner or an interpreter, which serve the normative grounds for the evaluation of a given text. In previous work, I proposed the framework of semantic constraints for the explication of logical consequence. Here, I extend the framework to include formalization constraints. The various constraints then serve the role of commitments. I discuss specific issues raised by Iacona concerning univocality, co-reference and equivocation, and I show how our views on these matters diverge as a result of our different starting assumptions. (shrink)

In a previous paper we developed a general theory of input/output logics. These are operations resembling inference, but where inputs need not be included among outputs, and outputs need not be reusable as inputs. In the present paper we study what happens when they are constrained to render output consistent with input. This is of interest for deontic logic, where it provides a manner of handling contrary-to-duty obligations. Our procedure is to constrain the set of generators of the input/output system, (...) considering only the maximal subsets that do not yield output conflicting with a given input. When inputs are authorised to reappear as outputs, both maxichoice revision in the sense of Alchourr6n/Makinson and the default logic of Poole emerge as special cases, and there is a close relation with Reiter default logic. However, our focus is on the general case where inputs need not be outputs. We show in what contexts the consistency of input with output may be reduced to its consistency with a truth-functional combination of components of generators, and under what conditions constrained output may be obtained by a derivation that is constrained at every step. (shrink)

We revisit a typological puzzle due to Horn (Doctoral Dissertation, UCLA, 1972) regarding the lexicalization of logical operators: in instantiations of the traditional square of opposition across categories and languages, the O corner, corresponding to ‘nand’ (= not and), ‘nevery’ (= not every), etc., is never lexicalized. We discuss Horn’s proposal, which involves the interaction of two economy conditions, one that relies on scalar implicatures and one that relies on markedness. We observe that in order to express markedness and (...) to account for a bigger typological puzzle, namely the absence of lexicalizations of ‘XOR’ (= exclusive or), ‘all-or-none’, and many other imaginable logical operators, one must restrict the basic lexicalizable elements to a small set of primitives. We suggest that an ordering based perspective, following Keenan and Faltz (Boolean semantics for natural language, 1985), makes the stipulated primitives that we arrive at more natural. We also propose a modification to Horn’s proposal, based on recent work on implicatures, in which only the implicature condition is operative and in which markedness is part of the definition of the alternatives for scalar implicatures rather than an independent condition. (shrink)

This collection of current research on logic programming languages presents results from a three-year, ESPRIT-funded effort to explore the integration of the foundational issues of functional, logic, and object-oriented programming. It offers valuable insights into the fast-developing extensions of logic programming with functions, constraints, concurrency, and objects. Chapters are grouped according to the unifying themes of functional programming, constraint, logic programming, and object-oriented programming.

A pioneering look at the fundamental role of logic in optimizationand constraint satisfaction While recent efforts to combine optimization and constraintsatisfaction have received considerable attention, little has beensaid about using logic in optimization as the key to unifying thetwo fields. Logic-Based Methods for Optimization develops for thefirst time a comprehensive conceptual framework for integratingoptimization and constraint satisfaction, then goes a step furtherand shows how extending logical inference to optimization allowsfor more powerful as well as flexible modeling and (...) solutiontechniques. Designed to be easily accessible to industryprofessionals and academics in both operations research andartificial intelligence, the book provides a wealth of examples aswell as elegant techniques and modeling frameworks ready forimplementation. Timely, original, and thought-provoking,Logic-Based Methods for Optimization: * Demonstrates the advantages of combining the techniques inproblem solving * Offers tutorials in constraint satisfaction/constraintprogramming and logical inference * Clearly explains such concepts as relaxation, cutting planes,nonserial dynamic programming, and Bender's decomposition * Reviews the necessary technologies for software developersseeking to combine the two techniques * Features extensive references to important computationalstudies * And much more. (shrink)

Palmer's “isomorphism constraint” presupposes the logical possibility of two qualitatively disparate sets of sensory experiences exhibiting the same relationships. Two arguments are presented to demonstrate that, because such a state of affairs cannot be coherently specified, its occurrence is not logically possible. The prospects for behavioral and biological science are better than Palmer suggests; those for functionalism are worse.

These are the proceedings of the First International Conference on Compu- tional Logic (CL 2000) which was held at Imperial College in London from 24th to 28th July, 2000. The theme of the conference covered all aspects of the theory, implementation, and application of computational logic, where computational logic is to be understood broadly as the use of logic in computer science. The conference was collocated with the following events: { 6th International Conference on Rules and Objects in Databases (DOOD (...) 2000) { 10th International Workshop on Logic-based Program Synthesis and Tra- formation (LOPSTR 2000) { 10th International Conference on Inductive Logic Programming (ILP 2000). CL 2000 consisted of seven streams: { Program Development (LOPSTR 2000) { Logic Programming: Theory and Extensions { Constraints { Automated Deduction: Putting Theory into Practice { Knowledge Representation and Non-monotonic Reasoning { Database Systems (DOOD 2000) { Logic Programming: Implementations and Applications. The LOPSTR 2000 workshop constituted the program development stream and the DOOD 2000 conference constituted the database systems stream. Each stream had its own chair and program committee, which autonomously selected the papers in the area of the stream. Overall, 176 papers were submitted, of which 86 were selected to be presented at the conference and appear in these proceedings. The acceptance rate was uniform across the streams. In addition, LOPSTR 2000 accepted about 15 extended abstracts to be presented at the conference in the program development stream. (shrink)

Sport occupies a significant role in modern society and has a wide following. In his Leftist Theories of Sport, Morgan examines what he considers to be a degradation of modern sport and the lack of proper critical theory to address this challenge. In the latter part of LTS, Morgan presents a reconstructed critical theory with ‘a liberal twist’ in terms of an analysis of what he sees as the internal ‘gratuitous’ logic of sport, and a call for critical deliberation in (...) sporting practice communities. I depart from Morgan’s ideas of the ‘gratuitous’ logic of sport which, I believe, has significant potential and operative force. I interpret the logic of sport as forms of self-imposed constraints at three levels: in the logic of the rules, in norms for fair play, and in a particular interpretation of sporting excellence as a form of human excellence. Using the practical case of performance-enhancing drugs, I demonstrate how this interpretation can exert operative power. I conclude by pointing to th... (shrink)

In their brief online presentation "Qu'est-ce que l'Oulipo?", Jacques Roubaud and Marcel Bénabou explain how Oulipians proceed in the exploration of the lipo, littérature potentielle: "Certes, MAIS COMMENT?", they ask, before replying: "En inventant des contraintes. Des contraintes nouvelles et anciennes, difficiles et moins diiffficiles et trop diiffiiciiiles. La Littérature Oulipienne est une LITTÉRATURE SOUS CONTRAINTES." The vigorous tone conveyed by spelling and typography points to the distinct challenge posed by Oulipian writing, which relies on the difficulty of the (...) class='Hi'>constraint in its effort to reach as far as possible into the uncharted territory of potential literature.... (shrink)

In this paper I discuss a prevailing view by which logical terms determine forms of sentences and arguments and therefore the logical validity of arguments. This view is common to those who hold that there is a principled distinction between logical and nonlogical terms and those holding relativistic accounts. I adopt the Tarskian tradition by which logical validity is determined by form, but reject the centrality of logical terms. I propose an alternative framework for logic (...) where logical terms no longer play a distinctive role. This account employs a new notion of semantic. (shrink)

Unlike statutory law, which relies on the explicit formulation of rules, common law is thought to emerge from a complex doctrine of precedential constraint, according to which decisions in earlier cases constrain later courts while still allowing these courts the freedom to address new situations in creative ways. Although this doctrine is applied by legal practitioners on a daily basis, it has proved to be considerably more difficult to develop an adequate theoretical account of the doctrine itself. Drawing on (...) recent work in legal theory, as well as AI and law, this book develops a new account of precedential constraint and the balance achieved in the common law between constraint and freedom. This account, which involves construction of a group priority ordering among reasons, is then applied to other topics including the semantics of open-textured predicates and the practice of making exceptions to general rules. (shrink)

Merging logic and mathematics in deductive inference-an innovative, cutting-edge approach. Optimization methods for logical inference? Absolutely, say Vijay Chandru and John Hooker, two major contributors to this rapidly expanding field. And even though "solving logical inference problems with optimization methods may seem a bit like eating sauerkraut with chopsticks... it is the mathematical structure of a problem that determines whether an optimization model can help solve it, not the context in which the problem occurs." Presenting powerful, proven optimization (...) techniques for logic inference problems, Chandru and Hooker show how optimization models can be used not only to solve problems in artificial intelligence and mathematical programming, but also have tremendous application in complex systems in general. They survey most of the recent research from the past decade in logic/optimization interfaces, incorporate some of their own results, and emphasize the types of logic most receptive to optimization methods-propositional logic, first order predicate logic, probabilistic and related logics, logics that combine evidence such as Dempster-Shafer theory, rule systems with confidence factors, and constraint logic programming systems. Requiring no background in logic and clearly explaining all topics from the ground up, Optimization Methods for Logical Inference is an invaluable guide for scientists and students in diverse fields, including operations research, computer science, artificial intelligence, decision support systems, and engineering. (shrink)

Constraint programming is the fruit of several decades of research carried out in mathematical logic, automated deduction, operations research and arti?cial intelligence. The tools and programming languages arising from this research?eldhaveenjoyedrealsuccessintheindustrialworldastheycontributetosolving hard combinatorial problems in diverse domains such as production planning, communication networks, robotics and bioinformatics. This volume contains the extended and reviewed versions of a selection of papers presented at the Joint ERCIM/CoLogNET International Workshop on Constraint Solving and Constraint Logic Programming, which was held from June (...) 30 to July 2, 2003. The venue chosen for the seventh edition of this annual workshop was the Computer and Automation Research Institute of the Hungarian Academy of Sciences in Budapest, Hungary. This institute is one of the 20 members of the Working Group on Constraints of the European Research Consortium for Informatics and Mathematics. For many participants this workshop provided the?rst opportunity to visit their ERCIM partner in Budapest. CoLogNET is the European-funded network of excellence dedicated to s- porting and enhancing cooperation and research on all areas of computational logic, and continues the work done previously by the Compulog Net. In part- ular, the aim of the logic and constraint logic programming area of CoLogNET is to foster and support all research activities related to logic programming and constraint logic programming. The editors would like to take the opportunity and thank all the authors who submitted papers to this volume, as well as the reviewers for their helpful work. (shrink)

Logic arguably plays a role in the normativity of reasoning. In particular, there are plausible norms of belief/disbelief whose antecedents are constituted by claims about what follows from what. But is logic also relevant to the normativity of agnostic attitudes? The question here is whether logical entailment also puts constraints on what kinds of things one can suspend judgment about. In this paper I address that question and I give a positive answer to it. In particular, I advance two (...) logical norms of agnosticism, where the first one allows us to assess situations in which the subject is agnostic about the conclusion of a valid argument and the second one allows us to assess situations in which the subject is agnostic about one of the premises of a valid argument. (shrink)

The article presents several adaptive fuzzy hedge logics . These logics are designed to perform a specific kind of hedge detection. Given a premise set Γ that represents a series of communicated statements, the logics can check whether some predicate occurring in Γ may be interpreted as being (implicitly) hedged by technically , strictly speaking or loosely speaking , or simply non-hedged. The logics take into account both the logical constraints of the premise set as well as conceptual information (...) concerning the meaning of potentially hedged predicates (stored in the memory of the interpreter in question). The proof theory of the logics is non-monotonic in order to enable the logics to deal with possible non-monotonic interpretation dynamics (this is illustrated by means of several concrete proofs). All the adaptive fuzzy hedge logics are also sound and strongly complete with respect to their [0,1]-semantics. (shrink)

A natural suggestion and increasingly popular account of how to revise our logical beliefs treats revision of logic analogously to the revision of scientific theories. I investigate this approach and argue that simple applications of abductive methodology to logic result in revision-cycles, developing a detailed case study of an actual dispute with this property. This is problematic if we take abductive methodology to provide justification for revising our logical framework. I then generalize the case study, pointing to similarities (...) with more recent and popular heterodox logics such as naïve logics of truth. I use this discussion to motivate a constraint—logical partisanhood—on the uses of such methodology: roughly: both the proposed alternative and our actual background logic must be able to agree that moving to the alternative logic is no worse than staying put. (shrink)

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model- theoretic probabilistic reasoning and to default reasoning in System . In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default reasoning in System (...) . That is, we provide a new probabilistic semantics for System , which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System , and they give new insight into default reasoning with conditional objects. (shrink)

We present two approaches to investigate the validity of connexive principles and related formulas and properties within coherence-based probability logic. Connexive logic emerged from the intuition that conditionals of the formif not-A,thenA, should not hold, since the conditional’s antecedentnot-Acontradicts its consequentA. Our approaches cover this intuition by observing that the only coherent probability assessment on the conditional event$${A| \overline{A}}$$A|A¯is$${p(A| \overline{A})=0}$$p(A|A¯)=0. In the first approach we investigate connexive principles within coherence-based probabilistic default reasoning, by interpreting defaults and negated defaults in terms (...) of suitable probabilistic constraints on conditional events. In the second approach we study connexivity within the coherence framework of compound conditionals, by interpreting connexive principles in terms of suitable conditional random quantities. After developing notions of validity in each approach, we analyze the following connexive principles:Aristotle’s theses,Aristotle’s Second Thesis,Abelard’s First Principle, andBoethius’ theses. We also deepen and generalize some principles and investigate further properties related to connexive logic (likenon-symmetry). Both approaches satisfyminimalrequirements for a connexive logic. Finally, we compare both approaches conceptually. (shrink)

We present an overview of linear-time temporal logics with Presburger constraints whose models are sequences of tuples of integers. Such formal specification languages are well-designed to specify and verify systems that can be modelled with counter systems. The paper recalls the general framework of LTL over concrete domains and presents the main decidability and complexity results related to fragments of Presburger LTL. Related formalisms are also briefly presented.

In this paper we present an executable approach to model interactions between agents that involve sensitive, privacy-related information. The approach is formal and based on deontic, epistemic and action logic. It is conceptually related to the Belief-Desire-Intention model of Bratman. Our approach uses the concept of sphere as developed by Waltzer to capture the notion that information is provided mostly with restrictions regarding its application. We use software agent technology to create an executable approach. Our agents hold beliefs about the (...) world, have goals and commitment to the goals. They have the capacity to reason about different courses of action, and communicate with one another. The main new ingredient of our approach is the idea to model information itself as an intentional agent whose main goal it is to preserve the integrity of the information and regulate its dissemination. We demonstrate our approach by applying it to an important process in the insurance industry: applying for a life insurance.In this paper we will: (1) describe the challenge organizational complexity poses in moral reasoning about informational relationships; (2) propose an executable approach, using software agents with reasoning capacities grounded in modal logic, in which moral constraints on informational relatio nships can be modeled and investigated; (3) describe the details of our approach, in which information itself is modeled as an intentional agent in its own right; (4) test and validate it by applying it to a concrete ‘hard case’ from the insurance industry; and (5) conclude that our approach upholds and offers potential for both research and practical application. (shrink)

This volume presents a collection of refereed papers reflecting the state of the art in the area of over-constrained systems. Besides 11 revised full papers, selected from the 24 submissions to the OCS workshop held in conjunction with the First International Conference on Principles and Practice of Constraint Programming, CP '95, held in Marseilles in September 1995, the book includes three comprehensive background papers of central importance for the workshop papers and the whole field. Also included is an introduction (...) by one of the volume editors together with a bibliography listing 243 entries. All in all this is a very useful reference book relevant for all researchers and practitioners interested in hierarchical, partial, and over-constrained systems. (shrink)

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology (...) is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance. (shrink)

K. R. Popper distinguished between two main uses of logic, the demonstrational one, in mathematical proofs, and the derivational one, in the empirical sciences. These two uses are governed by the following methodological constraints: in mathematical proofs one ought to use minimal logical means (logical minimalism), while in the empirical sciences one ought to use the strongest available logic (logical maximalism). In this paper I discuss whether Popper’s critical rationalism is compatible with a revision of logic in (...) the empirical sciences, given the condition of logical maximalism. Apparently, if one ought to use the strongest logic in the empirical sciences, logic would remain immune to criticism and, thus, non-revisable. I will show that critical rationalism is theoretically compatible with a revision of logic in the empirical sciences. However, a question that remains to be clarified by the critical rationalists is what kind of evidence would lead them to revise the system of logic that underlies a physical theory, such as quantum mechanics? Popper’s falsificationist methodology will be compared with the recently advocated extension of the abductive methodology from the empirical sciences to logic by T. Williamson, since both of them arrive at the same conclusion concerning the status of classical logic. (shrink)

Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe, then another perspective emerges: the theses of relevance logic, specifically the system R, may also be seen as the output of a conservative extension of the relation of classical consequence. We describe two ways in which this may be done. One is by defining a suitable closure relation out (...) of the set of theses of relevance logic; the other is by adding to the usual natural deduction system for it further rules with ‘projective constraints’, whose application restricts the subsequent application of other rules. The significance of the two constructions is also discussed. (shrink)

Monists say that the nature of truth is invariant, whichever sentence you consider; pluralists say that the nature of truth varies between different sets of sentences. The orthodoxy is that logic and logical form favour monism: there must be a single property that is preserved in any valid inference; and any truth-functional complex must be true in the same way as its components. The orthodoxy, I argue, is mistaken. Logic and logical form impose only structural constraints on a (...) metaphysics of truth. Monistic theories are not guaranteed to satisfy these constraints, and there is a pluralistic theory that does so. (shrink)

"Philosophical logic" describes two distinct areas: the investigation of the fundamental concepts of logic, the formal investigation of alternatives and extensions to classical logic. The first is a philosophical discipline, concerned with notions like truth, propositions, necessity, logical consequence, vagueness, and reasoning. The second is a technical discipline, devoted to developing formal logical systems-modal logics, second-order logics, intuitionistic logics, relevance logics, logics of vagueness and conditionals-and proving things about them. Most texts in philosophical logic focus on one of (...) these areas, but in this book John MacFarlane treats them together in an integrated way, showing how philosophical considerations motivate the technical projects, and how the constraints revealed by the technical projects illuminate the philosophical issues. Topics covered include quantifiers, modal logic, indicative conditionals, model-theoretic and proof-theoretic characterizations of logical consequence, intuitionistic logic, fundamental logical disagreement, relevance logic, the relation of logic and reasoning, and vagueness. Each chapter is organized around suggested readings and includes exercises. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Written by a leading authority on logicism and logical form and a successful expositor and teacher Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter. (shrink)

The problems that surround iterated contractions and expansions of beliefs are approached by studying hypertheories, a generalisation of Adam Grove's notion of systems of spheres. By using a language with dynamic and doxastic operators different ideas about the basic nature of belief change are axiomatised. It is shown that by imposing quite natural constraints on how hypertheories may change, the basic logics for belief change can be strengthened considerably to bring one closer to a theory of iterated belief change. It (...) is then argued that the logic of expansion, in particular, cannot without loss of generality be strengthened any further to allow for a full logic of iterated belief change. To remedy this situation a notion of directed expansion is introduced that allows for a full logic of iterated belief change. The new operation is given an axiomatisation that is complete for linear hypertheories. (shrink)

Is logic normative for reasoning? In the wake of work by Gilbert Harman and John MacFarlane, this question has been reduced to: are there any adequate bridge principles which link logical facts to normative constraints on reasoning? Hitherto, defenders of the normativity of logic have exclusively focussed on identifying adequate validity bridge principles: principles linking validity facts—facts of the form 'gamma entails phi'—to normative constraints on reasoning. This paper argues for two claims. First, for the time being at least, (...) Harman’s challenge cannot be surmounted by articulating validity bridge principles. Second, Harman’s challenge can be met by articulating invalidity bridge principles: principles linking invalidity facts of the form 'gamma does not entail phi' to normative constraints on reasoning. In doing so, I provide a novel defence of the normativity of logic. (shrink)

The SRL of King is a sound, complete and decidable logic designed specifically to support formalisms for the HPSG of Pollard and Sag. The SRL notion of modellability in a signature is particularly important for HPSG, and the present paper modifies an elegant method due to Blackburn and Spaan in order to prove that – modellability in each computable signature is 1 0 – modellability in some finite signature is 1 0 -hard, and – modellability in some finite signature is (...) decidable. (shrink)

The current resurgence of interest in cognition and in the nature of cognitive processing has brought with it also a renewed interest in the early work of Husserl, which contains one of the most sustained attempts to come to grips with the problems of logic from a cognitive point of view. Logic, for Husserl, is a theory of science; but it is a theory which takes seriously the idea that scientific theories are constituted by the mental acts of cognitive subjects. (...) The present essay begins with an exposition of Husserl's act-based conception of what a science is, and goes on to consider his account of the role of linguistic meanings, of the ontology of scientific objects, and of evidence and truth. The essay concentrates almost exclusively on the Logical Investigations of 1900/01. This is not only because this work, which is surely Husserl's single most important masterpiece, has been overshadowed first of all by his Ideas I and then later by the Crisis. It is also because the Investigations contain, in a peculiarly clear and pregnant form, a whole panoply of ideas on logic and cognitive theory which either simply disappeared in Husserl's own later writings or became obfuscated by an admixture of that great mystery which is 'transcendental phenomenology'. (shrink)

The article presents several adaptive fuzzy hedge logics. These logics are designed to perform a specific kind of hedge detection. Given a premise set Γ that represents a series of communicated statements, the logics can check whether some predicate occurring in Γ may be interpreted as being (implicitly) hedged by technically, strictly speaking or loosely speaking, or simply non-hedged. The logics take into account both the logical constraints of the premise set as well as conceptual information concerning the meaning (...) of potentially hedged predicates (stored in the memory of the interpreter in question). The proof theory of the logics is non-monotonic in order to enable the logics to deal with possible non-monotonic interpretation dynamics (this is illustrated by means of several concrete proofs). All the adaptive fuzzy hedge logics are also sound and strongly complete with respect to their [0,1]-semantics. (shrink)

This book constitutes the refereed proceedings of the 20th International Conference on Logic Programming, ICLP 2004, held in Saint-Malo, France in September 2004. The 28 revised full papers and 16 poster papers presented together with 2 invited papers were carefully reviewed and selected from 70 submissions. The papers are organized in topical sections on program analysis, constraints, alternative programming paradigms, answer set programming, and implementation.

Donald Davidson contributed to the discussion of logical form in two ways. On the one hand, he made several influential suggestions on how to give the logical forms of certain constructions of natural language. His account of adverbial modification and so called action-sentences is nowadays, in some form or other, widely employed in linguistics (Harman (forthcoming) calls it "the standard view"). Davidson's approaches to indirect discourse and quotation, while not as influential, also still attract attention today. On the (...) other hand, Davidson provided a general account of what logical form is. This paper is concerned with this general account. Its foremost aim is to give a faithful and detailed picture of what, according to Davidson, it means to give the logical form of a sentence. The structure of the paper is as follows. (1) I will first informally introduce a notion of logical form as the form that matters in certain kinds of entailments, and indicate why philosophers have taken an interest in such a notion. (2) The second section develops constraints that we should arguably abide by in giving an account of logical form. (3) I then turn to Davidson’s view of what is involved in giving such an account. To this end, I will try to reconstruct Davidson’s view of the connection between an assignment of logical forms, a truth theory and a meaning theory. (4) Finally, I will briefly discuss possible problems of Davidson’s account as developed in this paper. (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)

I develop a non-representationalist account of mathematical thought, on which the point of mathematical theorizing is to provide us with the conceptual capacity to structure and articulate information about the physical world in an epistemically useful way. On my view, accepting a mathematical theory is not a matter of having a belief about some subject matter; it is rather a matter of structuring logical space, in a sense to be made precise. This provides an elegant account of the cognitive (...) utility of mathematics. Further, it makes explicit how the brand of non-representationalism I develop is compatible with there being substantive rationality constraints on our mathematical theorizing. (shrink)