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619A Simple Logic of ConceptsJournal of Philosophical Logic 52 (3): 705-730. 2022.In Pietroski ( 2018 ) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“ Some_not ”) eludes expression. We then study a seemingly sm…Read more
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143Logics for epistemic programsSynthese 139 (2). 2004.We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dynamic logic, and indeed our languages are not significantly more complicated than dynamic logics. But the semantics is more complicated. In general,…Read more
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127Logics for the relational syllogisticReview of Symbolic Logic 2 (4): 647-683. 2009.The Aristotelian syllogistic cannot account for the validity of certain inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to th…Read more
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68Editors' Introduction: The Third Life of Quantum Logic: Quantum Logic Inspired by Quantum Computing (review)Journal of Philosophical Logic 42 (3): 443-459. 2013.
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56Modal correspondence for modelsJournal of Philosophical Logic 27 (3): 275-294. 1998.This paper considers the correspondence theory from modal logic and obtains correspondence results for models as opposed to frames. The key ideas are to consider infinitary modal logic, to phrase correspondence results in terms of substitution instances of a given modal formula, and to identify bisimilar model-world pairs
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55Special Issue on the Occasion of Johan van Benthem’s 60th Birthday—EditorialJournal of Philosophical Logic 38 (6): 587-588. 2009.
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54The logic of recursive equationsJournal of Symbolic Logic 63 (2): 451-478. 1998.We study logical systems for reasoning about equations involving recursive definitions. In particular, we are interested in "propositional" fragments of the functional language of recursion FLR [18, 17], i.e., without the value passing or abstraction allowed in FLR. The "pure," propositional fragment FLR 0 turns out to coincide with the iteration theories of [1]. Our main focus here concerns the sharp contrast between the simple class of valid identities and the very complex consequence relation…Read more
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48Grammar formalisms viewed as evolving algebrasLinguistics and Philosophy 17 (6). 1994.We consider the use ofevolving algebra methods of specifying grammars for natural languages. We are especially interested in distributed evolving algebras. We provide the motivation for doing this, and we give a reconstruction of some classic grammar formalisms in directly dynamic terms. Finally, we consider some technical questions arising from the use of direct dynamism in grammar formalisms.
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47Syllogistic Logic with Comparative AdjectivesJournal of Logic, Language and Information 20 (3): 397-417. 2011.This paper adds comparative adjectives to two systems of syllogistic logic. The comparatives are interpreted by transitive and irreflexive relations on the underlying domain. The main point is to obtain sound and complete axiomatizations of the valid formulas in the logics
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43Finite models constructed from canonical formulasJournal of Philosophical Logic 36 (6). 2007.This paper obtains the weak completeness and decidability results for standard systems of modal logic using models built from formulas themselves. This line of work began with Fine (Notre Dame J. Form. Log. 16:229-237, 1975). There are two ways in which our work advances on that paper: First, the definition of our models is mainly based on the relation Kozen and Parikh used in their proof of the completeness of PDL, see (Theor. Comp. Sci. 113-118, 1981). The point is to develop a general model-c…Read more
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432000-2001 Spring Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 7 (3): 413-419. 2001.
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39Topological reasoning and the logic of knowledgeAnnals of Pure and Applied Logic 78 (1-3): 73-110. 1996.We present a bimodal logic suitable for formalizing reasoning about points and sets, and also states of the world and views about them. The most natural interpretation of the logic is in subset spaces , and we obtain complete axiomatizations for the sentences which hold in these interpretations. In addition, we axiomatize the validities of the smaller class of topological spaces in a system we call topologic . We also prove decidability for these two systems. Our results on topologic relate earl…Read more
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38Dynamic interpretations of constraint-based grammar formalismsJournal of Logic, Language and Information 4 (1): 61-79. 1995.We present a rendering of some common grammatical formalisms in terms of evolving algebras. Though our main concern in this paper is on constraint-based formalisms, we also discuss the more basic case of context-free grammars. Our aim throughout is to highlight the use of evolving algebras as a specification tool to obtain grammar formalisms.
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37Exploring logical dynamics, Johan Van BenthemJournal of Logic, Language and Information 9 (2): 261-263. 2000.
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36The Undecidability of Iterated Modal RelativizationStudia Logica 79 (3): 373-407. 2005.In dynamic epistemic logic and other fields, it is natural to consider relativization as an operator taking sentences to sentences. When using the ideas and methods of dynamic logic, one would like to iterate operators. This leads to iterated relativization. We are also concerned with the transitive closure operation, due to its connection to common knowledge. We show that for three fragments of the logic of iterated relativization and transitive closure, the satisfiability problems are fi1 11–c…Read more
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36Syllogistic Logic with Cardinality Comparisons, on Infinite SetsReview of Symbolic Logic 13 (1): 1-22. 2020.This article enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: Allxareyand Somexarey, There are at least as manyxasy, and There are morexthany. Herexandyrange over subsets (not elements) of a giveninfiniteset. Moreover,xandymay appear complemented (i.e., as$\bar{x}$and$\bar{y}$), with the natural meaning. We formulate a logic for our language that is based on th…Read more
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34Rohit Parikh on Logic, Language and Society (edited book)Springer Verlag. 2017.This book discusses major milestones in Rohit Jivanlal Parikh’s scholarly work. Highlighting the transition in Parikh’s interest from formal languages to natural languages, and how he approached Wittgenstein’s philosophy of language, it traces the academic trajectory of a brilliant scholar whose work opened up various new avenues in research. This volume is part of Springer’s book series Outstanding Contributions to Logic, and honours Rohit Parikh and his works in many ways. Parikh is a leader i…Read more
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34Barbara H. Partee, Alice ter Meulen, and Robert E. Wall. Mathematical methods in linguistics. Studies in linguistics and philosophy, vol. 30. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1990, xx + 663 pp (review)Journal of Symbolic Logic 57 (1): 271-272. 1992.
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302010 north american annual meeting of the association for symbolic logicBulletin of Symbolic Logic 17 (1): 127-154. 2011.
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27New Orleans Marriott and Sheraton New Orleans Hotels New Orleans, LA January 8–9, 2011Bulletin of Symbolic Logic 18 (1). 2012.
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27The Soundness of Internalized Polarity MarkingStudia Logica 100 (4): 683-704. 2012.This paper provides a foundation for the polarity marking technique introduced by David Dowty [3] in connection with monotonicity reasoning in natural language and in linguistic analyses of negative polarity items based on categorial grammar. Dowty's work is an alternative to the better-known algorithmic approach first proposed by Johan van Benthem [11], and elaborated by Víctor Sánchez Valencia [10]. Dowty's system internalized the monotonicity/polarity markings by generating strings using a ca…Read more
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26On the Foundations of CorecursionLogic Journal of the IGPL 5 (2): 231-257. 1997.We consider foundational questions related to the definition of functions by corecursion. This method is especially suited to functions into the greatest fixed point of some monotone operator, and it is most applicable in the context of non-wellfounded sets. We review the work on the Special Final Coalgebra Theorem of Aczel [1] and the Corecursion Theorem of Barwise and Moss [4]. We offer a condition weaker than Aczel's condition of uniformity on maps, and then we prove a result relating the ope…Read more
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25Exploring Logical Dynamics, Johan van Benthem (review)Journal of Logic, Language and Information 9 (2): 261-263. 2000.
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Indiana UniversityProfessor
Areas of Specialization
Science, Logic, and Mathematics |
Areas of Interest
Science, Logic, and Mathematics |