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18The 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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20Editors' 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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12Topological 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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12Modal 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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15Logics 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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3Special Issue on the Occasion of Johan van Benthem’s 60th Birthday—EditorialJournal of Philosophical Logic 38 (6): 587-588. 2009.
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680A 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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1025th Workshop on Logic, Language, Information and Computation: WoLLIC 2018Journal of Logic, Language and Information 31 (4): 525-527. 2022.
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36Rohit 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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Syllogistic Logic with Cardinality ComparisonsIn Katalin Bimbó (ed.), J. Michael Dunn on Information Based Logics, Springer. 2016.
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2625th Workshop on Logic, Language, Information and ComputationLogic Journal of the IGPL 27 (5): 766-776. 2019.
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3On 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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6The 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 relati…Read more
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2Special Issue on the Occasion of Johan van Benthem’s 60th Birthday—EditorialJournal of Philosophical Logic 38 (6): 587-588. 2009.
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72000-2001 Spring Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 7 (3): 413-419. 2001.
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8New Orleans Marriott and Sheraton New Orleans Hotels New Orleans, LA January 8–9, 2011Bulletin of Symbolic Logic 18 (1). 2012.
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Indiana UniversityProfessor
Areas of Specialization
Science, Logic, and Mathematics |
Areas of Interest
Science, Logic, and Mathematics |