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An introduction to substructural logics
, 2000
"... Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1 ..."
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Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1
The ProofTheory and Semantics of Intuitionistic Modal Logic
, 1994
"... Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpret ..."
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Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpreted in an intuitionistic metatheory then the induced modal logics no longer satisfy certain intuitionistically invalid principles. This thesis investigates the intuitionistic modal logics that arise in this way. Natural deduction systems for various intuitionistic modal logics are presented. From one point of view, these systems are selfjustifying in that a possible world interpretation of the modalities can be read off directly from the inference rules. A technical justification is given by the faithfulness of translations into intuitionistic firstorder logic. It is also established that, in many cases, the natural deduction systems induce wellknown intuitionistic modal logics, previously given by Hilbertstyle axiomatizations. The main benefit of the natural deduction systems over axiomatizations is their
Ontological Semantics
, 2004
"... This book introduces ontological semantics, a comprehensive approach to the treatment of text meaning by computer. Ontological semantics is an integrated complex of theories, methodologies, descriptions and implementations. In ontological semantics, a theory is viewed as a set of statements determin ..."
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Cited by 126 (37 self)
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This book introduces ontological semantics, a comprehensive approach to the treatment of text meaning by computer. Ontological semantics is an integrated complex of theories, methodologies, descriptions and implementations. In ontological semantics, a theory is viewed as a set of statements determining the format of descriptions of the phenomena with which the theory deals. A theory is associated with a methodology used to obtain the descriptions. Implementations are computer systems that use the descriptions to solve specific problems in text processing. Implementations of ontological semantics are combined with other processing systems to produce applications, such as information extraction or machine translation. The theory of ontological semantics is built as a society of microtheories covering such diverse ground as specific language phenomena, world knowledge organization, processing heuristics and issues relating to knowledge representation and implementation system architecture. The theory briefly sketched above is a toplevel microtheory, the ontological semantics theory per se. Descriptions in ontological semantics include text meaning representations, lexical entries, ontological concepts and instances as well as procedures for manipulating texts and their meanings. Methodologies in ontological semantics are sets of techniques and instructions for acquiring and
Pattern matching with dependent types
 In the Proceedings of the Workshop on Types for Proofs and Programs
, 1992
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Rationality, meaning and the analysis of delusion
 Philosophy, Psychiatry, & Psychology
, 2001
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Multiple conclusions
 In 12th International Congress on Logic, Methodology and Philosophy of Science
, 2005
"... Abstract: I argue for the following four theses. (1) Denial is not to be analysed as the assertion of a negation. (2) Given the concepts of assertion and denial, we have the resources to analyse logical consequence as relating arguments with multiple premises and multiple conclusions. Gentzen’s mult ..."
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Abstract: I argue for the following four theses. (1) Denial is not to be analysed as the assertion of a negation. (2) Given the concepts of assertion and denial, we have the resources to analyse logical consequence as relating arguments with multiple premises and multiple conclusions. Gentzen’s multiple conclusion calculus can be understood in a straightforward, motivated, nonquestionbegging way. (3) If a broadly antirealist or inferentialist justification of a logical system works, it works just as well for classical logic as it does for intuitionistic logic. The special case for an antirealist justification of intuitionistic logic over and above a justification of classical logic relies on an unjustified assumption about the shape of proofs. Finally, (4) this picture of logical consequence provides a relatively neutral shared vocabulary which can help us understand and adjudicate debates between proponents of classical and nonclassical logics. Our topic is the notion of logical consequence: the link between premises and conclusions, the glue that holds together deductively valid argument. How can we understand this relation between premises and conclusions? It seems that any account begs questions. Painting with very broad brushtrokes, we can sketch the landscape
Bruno de Finetti and the Logic of Conditional Events
"... This article begins by outlining some of the history—beginning with brief remarks of Quine's—of work on conditional assertions and conditional events. The upshot of the historical narrative is that diverse works from various starting points have circled around a nexus of ideas without convincin ..."
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This article begins by outlining some of the history—beginning with brief remarks of Quine's—of work on conditional assertions and conditional events. The upshot of the historical narrative is that diverse works from various starting points have circled around a nexus of ideas without convincingly tying them together. Section 3 shows how ideas contained in a neglected article of de Finetti's lead to a unified treatment of the topics based on the identification of conditional events as the objects of conditional bets. The penultimate section explores some of the consequences of the resulting logic
What does it mean to say that logic is formal
, 2000
"... Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and ..."
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Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal? Three things: logic is said to be formal (or “topicneutral”) (1) in the sense that it provides constitutive norms for thought as such, (2) in the sense that it is indifferent to the particular identities of objects, and (3) in the sense that it abstracts entirely from the semantic content of thought. Though these three notions of formality are by no means equivalent, they are frequently run together. The reason, I argue, is that modern talk of the formality of logic has its source in Kant, and these three notions come together in the context of Kant’s transcendental philosophy. Outside of this context (e.g., in Frege), they can come apart. Attending to this
Modal logic and invariance
 Journal of Applied NonClassical Logics
, 2008
"... Abstract. This paper deals with the problem of giving a principled characterization of the class of logical constants. According to the socalled Tarski–Sher thesis, an operation is logical iff it is invariant under permutation. In the modeltheoretic tradition, this criterion has been widely accept ..."
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Abstract. This paper deals with the problem of giving a principled characterization of the class of logical constants. According to the socalled Tarski–Sher thesis, an operation is logical iff it is invariant under permutation. In the modeltheoretic tradition, this criterion has been widely accepted as giving a necessary condition for an operation to be logical. But it has been also widely criticized on the account that it counts too many operations as logical, failing thus to provide a sufficient condition. Our aim is to solve this problem of overgeneration by modifying the invariance criterion. We introduce a general notion of invariance under a similarity relation and present the connection between similarity relations and classes of invariant operations. The next task is to isolate a similarity relation wellsuited for a definition of logicality. We argue that the standard arguments in favor of invariance under permutation, which rely on the generality and the formality of logic, should be modified. The revised arguments are shown to support an alternative to Tarski’s criterion, according to which an operation is logical iff it is invariant under potential isomorphism. On the traditional semantic account of logical consequence, a sentenceφ is
Validity concepts in prooftheoretic semantics
 ProofTheoretic Semantics. Special issue of Synthese
"... Abstract. The standard approach to what I call “prooftheoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of prooftheoretic semantics, this paper investigates in det ..."
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Abstract. The standard approach to what I call “prooftheoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of prooftheoretic semantics, this paper investigates in detail various notions of prooftheoretic validity and offers certain improvements of the definitions given by Prawitz. Particular emphasis is placed on the relationship between semantic validity concepts and validity concepts used in normalization theory. It is argued that these two sorts of concepts must be kept strictly apart. 1. Introduction: Prooftheoretic