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Propositions, Propositional Attitudes and Belief RevisionIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 399-418. 1998.
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35Indian Institute of Technology, Kanpur January 14–26, 2008Bulletin of Symbolic Logic 14 (4). 2008.
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48We propose a new relevance sensitive model for representing and revising belief structures, which relies on a notion of partial language splitting and tolerates some amount of inconsistency while retaining classical logic. The model preserves an agent's ability to answer queries in a coherent way using Belnap's four-valued logic. Axioms analogous to the AGM axioms hold for this new model. The distinction between implicit and explicit beliefs is represented and psychologically plausible, computat…Read more
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15From Language Games to Social SoftwareIn Alexander Hieke & Hannes Leitgeb (eds.), Reduction, abstraction, analysis: proceedings of the 31th International Ludwig Wittgenstein-Symposium in Kirchberg, 2008, De Gruyter. pp. 365-376. 2009.
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36Finite information logicAnnals of Pure and Applied Logic 134 (1): 83-93. 2005.We introduce a generalization of Independence Friendly logic in which Eloise is restricted to a finite amount of information about Abelard’s moves. This logic is shown to be equivalent to a sublogic of first-order logic, to have the finite model property, and to be decidable. Moreover, it gives an exponential compression relative to logic
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102The Logic of Knowledge Based ObligationSynthese 149 (2): 311-341. 2006.Deontic Logic goes back to Ernst Mally’s 1926 work, Grundgesetze des Sollens: Elemente der Logik des Willens [Mally. E.: 1926, Grundgesetze des Sollens: Elemente der Logik des Willens, Leuschner & Lubensky, Graz], where he presented axioms for the notion ‘p ought to be the case’. Some difficulties were found in Mally’s axioms, and the field has much developed. Logic of Knowledge goes back to Hintikka’s work Knowledge and Belief [Hintikka, J.: 1962, Knowledge and Belief: An Introduction to the Lo…Read more
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632000-2001 Spring Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 7 (3): 413-419. 2001.
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108Relevance Sensitive Non-Monotonic Inference on Belief SequencesJournal of Applied Non-Classical Logics 11 (1): 131-150. 2001.We present a method for relevance sensitive non-monotonic inference from belief sequences which incorporates insights pertaining to prioritized inference and relevance sensitive, inconsistency tolerant belief revision. Our model uses a finite, logically open sequence of propositional formulas as a representation for beliefs and defines a notion of inference from maxiconsistent subsets of formulas guided by two orderings: a temporal sequencing and an ordering based on relevance relations between …Read more
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20Approximate belief revisionLogic Journal of the IGPL 9 (6): 755-768. 2001.The standard theory for belief revision provides an elegant and powerful framework for reasoning about how a rational agent should change its beliefs when confronted with new information. However, the agents considered are extremely idealized. Some recent models attempt to tackle the problem of plausible belief revision by adding structure to the belief bases and using nonstandard inference operations. One of the key ideas is that not all of an agent's beliefs are relevant for an operation of be…Read more
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20Logic, co-ordination and the envelope of our beliefsLogic Journal of the IGPL 31 (6): 1069-1077. 2023.Each of us has a story which we can think of as a set of beliefs, hopefully consistent. We make our decisions in view of our beliefs which may be probabilistic, in the general case, but simple yes or no as in this paper. Our beliefs are our envelope just as the shell of a tortoise is its envelope. Decision theory—or single agent game theory tells us when to make the best choice in a game of us against nature. But nature has no desire to further or frustrate our efforts. Nature is mysterious but …Read more
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13Proof, Computation and Agency: Logic at the Crossroads (edited book)Springer. 2011.Proof, Computation and Agency: Logic at the Crossroads provides an overview of modern logic and its relationship with other disciplines. As a highlight, several articles pursue an inspiring paradigm called 'social software', which studies patterns of social interaction using techniques from logic and computer science. The book also demonstrates how logic can join forces with game theory and social choice theory. A second main line is the logic-language-cognition connection, where the articles co…Read more
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31Knowledge, behavior, and rationality: rationalizability in epistemic gamesArchive for Mathematical Logic 60 (5): 599-623. 2021.In strategic situations, agents base actions on knowledge and beliefs. This includes knowledge about others’ strategies and preferences over strategy profiles, but also about other external factors. Bernheim and Pearce in 1984 independently defined the game theoretic solution concept of rationalizability, which is built on the premise that rational agents will only take actions that are the best response to some situation that they consider possible. This accounts for other agents’ rationality a…Read more
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62On knowledge and obligationEpisteme 9 (2): 171-188. 2012.This article provides a brief overview of several formal frameworks concerning the relation between knowledge on the one hand, and obligation on the other. We discuss the paradox of the knower, knowledge based obligation, knowingly doing, deontic dynamic epistemology, descriptive obligations, and responsibilities as dynamic epistemology.
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2Justified True Belief: Plato, Gettier, and TuringIn Alisa Bokulich & Juliet Floyd (eds.), Philosophical Explorations of the Legacy of Alan Turing, Springer Verlag. 2017.
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Propositions, Propositional Attitudes and Belief RevisionIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 399-418. 1998.
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30Review of Epistemology, A Contemporary Introduction to the Theory of Knowledge, by Robert Audi (review)Essays in Philosophy 9 (2): 261-262. 2008.
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6Review of If P, then Q; Conditionals and the Foundations of Reasoning, by David H. Sanford (review)Essays in Philosophy 7 (1): 122-125. 2006.
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30Georg Kreisel and William W. Tait. Finite definability of number-theoretic functions and parametric completeness of equational calculi. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 7 , pp. 28–38 (review)Journal of Symbolic Logic 32 (2): 270-271. 1967.
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35Sheila Greibach. A new normal-form theorem for context-free phrase structure grammars. Journal of the Association for Computing Machinery, vol. 12 (1965), pp. 42–52 (review)Journal of Symbolic Logic 34 (4): 658-658. 1970.
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63Ronald Fagin, Joseph Y. Halpern, Yoram Moses, and Moshe Y. Vardi. Reasoning about knowledge. MIT Press, Cambridge, Mass., and London1995, xiii + 477 pp (review)Journal of Symbolic Logic 62 (4): 1484-1487. 1997.
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The Complete Bibliography of Rohit ParikhIn Ramaswamy Ramanujam, Lawrence Moss & Can Başkent (eds.), Rohit Parikh on Logic, Language and Society, Springer Verlag. 2017.
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37Some Generalisations of the Notion of Well OrderingMathematical Logic Quarterly 12 (1): 333-340. 1966.
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63Obituary: Horacio Arló-costaEpisteme 9 (2): 89-89. 2012.Editorial Rohit Parikh, Jeffrey Helzner, Episteme, FirstView Article
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'Abolition of the Fregean Axiom', in: Logic Colloquium, Symposium on Logic Held at Boston, 1972-73Erkenntnis 12 (3): 369-380. 1978.
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55Completeness of Certain Bimodal Logics for Subset SpacesStudia Logica 71 (1): 1-30. 2002.Subset Spaces were introduced by L. Moss and R. Parikh in [8]. These spaces model the reasoning about knowledge of changing states.In [2] a kind of subset space called intersection space was considered and the question about the existence of a set of axioms that is complete for the logic of intersection spaces was addressed. In [9] the first author introduced the class of directed spaces and proved that any set of axioms for directed frames also characterizes intersection spaces.We give here a c…Read more
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147Conditional Probability and Defeasible InferenceJournal of Philosophical Logic 34 (1). 2005.We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey-Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of nonmonotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).'Expectation' is a term of art in these models, which should not be confused with the notion of expected utility. The exp…Read more
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53Topological 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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36Vague Predicates and Language GamesTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 11 (3): 97-107. 1996.Attempts to give a Logic or Semantics for vague predicates and to defuse the Sorites paradoxes have been largely a failure. We point out yet another problem with these predicates which has not been remarked on before,namely that different people do and must use these predicates in individually different ways. Thus even if there were a semantics for vague predicates, people would not be able to share it. To explain the occurrence nonetheless of these troublesome predicates in language, we propose…Read more
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Some Reminiscences of KreiselIn Piergiorgio Odifreddi (ed.), Kreiseliana: About and Around Georg Kreisel, A K Peters. pp. 89. 1996.
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Logic and Philosophy of Logic |