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Paolo Mancosu - One of the best experts on this subject based on the ideXlab platform.
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Fixed‐ versus Variable‐domain Interpretations of Tarski’s Account of Logical Consequence
Philosophy Compass, 2010Co-Authors: Paolo MancosuAbstract:In this article I describe and evaluate the debate that surrounds the proper interpretation of Tarski’s account of Logical Consequence given in his classic 1936 article ‘On the concept of Logical Consequence’. In the late 1980s Etchemendy argued that the familiar model theoretic account of Logical Consequence is not to be found in Tarski’s original article. Whereas the contemporary account of Logical Consequence is a variable-domain conception – in that it calls for a reinterpretation of the domain of variation of the quantifiers when evaluating Logical Consequence –, no such reinterpretation is found in Tarski’s original account, which was rather based on a ‘fixed-domain’ conception. Etchemendy’s claims have sparked a debate on Tarski’s conception of Logical Consequence with important contributions by, among others, Bach, Bays, Corcoran, Gomez-Torrente, Mancosu, Ray, Saguillo, and Sher.
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fixed versus variable domain interpretations of tarski s account of Logical Consequence
Philosophy Compass, 2010Co-Authors: Paolo MancosuAbstract:In this article I describe and evaluate the debate that surrounds the proper interpretation of Tarski’s account of Logical Consequence given in his classic 1936 article ‘On the concept of Logical Consequence’. In the late 1980s Etchemendy argued that the familiar model theoretic account of Logical Consequence is not to be found in Tarski’s original article. Whereas the contemporary account of Logical Consequence is a variable-domain conception – in that it calls for a reinterpretation of the domain of variation of the quantifiers when evaluating Logical Consequence –, no such reinterpretation is found in Tarski’s original account, which was rather based on a ‘fixed-domain’ conception. Etchemendy’s claims have sparked a debate on Tarski’s conception of Logical Consequence with important contributions by, among others, Bach, Bays, Corcoran, Gomez-Torrente, Mancosu, Ray, Saguillo, and Sher.
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Tarski on models and Logical Consequence
2006Co-Authors: Paolo MancosuAbstract:An essential notion in semantics is that of Logical Consequence. A sentence P is a Logical Consequence of a set of sentences S if and only if it is not possible for the sentences in S to be true and the sentence P to be false at the same time. This is basically the definition (although given in the more abstract terminology of models) that Tarski gave of Logical Consequence in 1936. In the last twenty years there has been a heated debate on the exact nature of Tarski's theory of Logical Consequence. This debate has important Consequences for the philosophical problem of giving an exact characterization of this central notion in philosophy. Moreover, the intense focus on the original publication by Tarski has led to several disagreements with respect to important interpretative issues related to Tarski's contribution. This chapter provides evidence to show that in 1936 (and 1940) Tarski defended a notion of Logical Consequence (based on a fixed domain conception) that is at odds with the model-theoretic one common today. The addendum to the chapter defends the interpretation against recent criticism by Gomez-Torrente.
William H. Hanson - One of the best experts on this subject based on the ideXlab platform.
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The Formal-Structural View of Logical Consequence: A Reply to Gila Sher
Philosophical Review, 2002Co-Authors: William H. HansonAbstract:In a recent discussion article in thisjournal, Gila Sher (2001) responds to some of my criticisms of her work on what she calls the formal-structural account of Logical Consequence.1 In the present paper I reply and attempt to advance the discussion in a constructive way. Unfortunately, Sher seems to have not fully understood my 1997. Several of the defenses she mounts in her 2001 are aimed at views I do not hold and
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Ray on Tarski on Logical Consequence
Journal of Philosophical Logic, 1999Co-Authors: William H. HansonAbstract:In “Logical Consequence: A defense of Tarski” (Journal of Philosophical Logic, vol. 25, 1996, pp. 617–677), Greg Ray defends Tarski"s account of Logical Consequence against the criticisms of John Etchemendy. While Ray"s defense of Tarski is largely successful, his attempt to give a general proof that Tarskian Consequence preserves truth fails. Analysis of this failure shows that de facto truth preservation is a very weak criterion of adequacy for a theory of Logical Consequence and should be replaced by a stronger absence-of-counterexamples criterion. It is argued that the latter criterion reflects the modal character of our intuitive concept of Logical Consequence, and it is shown that Tarskian Consequence can be proved to satisfy this criterion for certain choices of Logical constants. Finally, an apparent inconsistency in Ray"s interpretation of Tarski"s position on the modal status of the Consequence relation is noted.
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The Concept of Logical Consequence
The Philosophical Review, 1997Co-Authors: William H. HansonAbstract:There is broad agreement among logicians about the technical definition of the notion of Logical Consequence, especially as it applies to extensional first-order languages. The definition most logicians accept is the familiar one framed in terms of assignments of truth values to sentence letters, denotations to individual constants, and extensions to predicates, these assignments being relative to some nonempty set of objects. There is less agreement, however, on the pre-theoretic notion this technical definition is supposed to represent, and very little discussion of whether it actually does represent it adequately.' This paper will be concerned with the latter two points, primarily as they arise in the context of extensional first-order languages. In the first section, I consider what several logicians say informally about the notion of Logical Consequence. There is significant variation among these accounts, they are sometimes poorly explained, and some of them are clearly at odds with the usual technical definition. In the second section, I first argue (subsection 2. 1) that a certain kind of informal account-one that includes elements of necessity, generality, and apriority-is approximately correct. Next (subsection 2.2) I refine this account and consider several important questions about it, including the appropriate characterization of necessity, the criterion for selecting Logical constants, and the exact role of apriority. I argue, among other things, that there is no need to recognize a special Logical sense of necessity and that the selection of terms to serve as Logical constants is ultimately a pragmatic matter. (Subsection 2.2.1 contains my fully developed account of the informal notion of Logical Consequence; subsection 2.2.2 includes criticism of recent work by Sher and Etchemendy.) In the third section, I consider whether the informal
Jeff Heflin - One of the best experts on this subject based on the ideXlab platform.
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on Logical Consequence for collections of owl documents
International Semantic Web Conference, 2005Co-Authors: Yuanbo Guo, Jeff HeflinAbstract:In this paper, we investigate the (in)dependence among OWL documents with respect to the Logical Consequence when they are combined, in particular the inference of concept and role assertions about individuals. On the one hand, we present a systematic approach to identifying those documents that affect the inference of a given fact. On the other hand, we consider ways for fast detection of independence. First, we demonstrate several special cases in which two documents are independent of each other. Secondly, we introduce an algorithm for checking the independence in the general case. In addition, we describe two applications in which the above results have allowed us to develop novel approaches to overcome some difficulties in reasoning with large scale OWL data. Both applications demonstrate the usefulness of this work for improving the scalability of a practical Semantic Web system that relies on the reasoning about individuals.
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International Semantic Web Conference - On Logical Consequence for collections of OWL documents
The Semantic Web – ISWC 2005, 2005Co-Authors: Yuanbo Guo, Jeff HeflinAbstract:In this paper, we investigate the (in)dependence among OWL documents with respect to the Logical Consequence when they are combined, in particular the inference of concept and role assertions about individuals. On the one hand, we present a systematic approach to identifying those documents that affect the inference of a given fact. On the other hand, we consider ways for fast detection of independence. First, we demonstrate several special cases in which two documents are independent of each other. Secondly, we introduce an algorithm for checking the independence in the general case. In addition, we describe two applications in which the above results have allowed us to develop novel approaches to overcome some difficulties in reasoning with large scale OWL data. Both applications demonstrate the usefulness of this work for improving the scalability of a practical Semantic Web system that relies on the reasoning about individuals.
Simone Pascucci - One of the best experts on this subject based on the ideXlab platform.
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the Logical Consequence role in lpnmr a parameterized computation approach
International Conference on Logic Programming, 2009Co-Authors: Mauricio Osorio Galindo, Simone PascucciAbstract:We present results about the Logical Consequence test under classical logic w.r.t. the Theory of Parameterized Complexity and Computation [1]. We show how a normal logic program P can partitioned in subset of clauses such that we can define an algorithm proving sets of atoms which complexity is bounded by a relation exponential in terms of a fixed parameter k and polynomial on the original size of the problem, namely the size of P . As example of application we study the model checking problem w.r.t. the P-Stable semantics.
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LPNMR - The Logical Consequence Role in LPNMR: A Parameterized Computation Approach
Logic Programming and Nonmonotonic Reasoning, 2009Co-Authors: Mauricio Osorio Galindo, Simone PascucciAbstract:We present results about the Logical Consequence test under classical logic w.r.t. the Theory of Parameterized Complexity and Computation [1]. We show how a normal logic program P can partitioned in subset of clauses such that we can define an algorithm proving sets of atoms which complexity is bounded by a relation exponential in terms of a fixed parameter k and polynomial on the original size of the problem, namely the size of P . As example of application we study the model checking problem w.r.t. the P-Stable semantics.
Yuanbo Guo - One of the best experts on this subject based on the ideXlab platform.
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on Logical Consequence for collections of owl documents
International Semantic Web Conference, 2005Co-Authors: Yuanbo Guo, Jeff HeflinAbstract:In this paper, we investigate the (in)dependence among OWL documents with respect to the Logical Consequence when they are combined, in particular the inference of concept and role assertions about individuals. On the one hand, we present a systematic approach to identifying those documents that affect the inference of a given fact. On the other hand, we consider ways for fast detection of independence. First, we demonstrate several special cases in which two documents are independent of each other. Secondly, we introduce an algorithm for checking the independence in the general case. In addition, we describe two applications in which the above results have allowed us to develop novel approaches to overcome some difficulties in reasoning with large scale OWL data. Both applications demonstrate the usefulness of this work for improving the scalability of a practical Semantic Web system that relies on the reasoning about individuals.
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International Semantic Web Conference - On Logical Consequence for collections of OWL documents
The Semantic Web – ISWC 2005, 2005Co-Authors: Yuanbo Guo, Jeff HeflinAbstract:In this paper, we investigate the (in)dependence among OWL documents with respect to the Logical Consequence when they are combined, in particular the inference of concept and role assertions about individuals. On the one hand, we present a systematic approach to identifying those documents that affect the inference of a given fact. On the other hand, we consider ways for fast detection of independence. First, we demonstrate several special cases in which two documents are independent of each other. Secondly, we introduce an algorithm for checking the independence in the general case. In addition, we describe two applications in which the above results have allowed us to develop novel approaches to overcome some difficulties in reasoning with large scale OWL data. Both applications demonstrate the usefulness of this work for improving the scalability of a practical Semantic Web system that relies on the reasoning about individuals.
