•  111
    Conditional Probability and Defeasible Inference
    Journal 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
  •  109
  •  108
    Game Logic - An Overview
    with Marc Pauly
    Studia Logica 75 (2): 165-182. 2003.
    Game Logic is a modal logic which extends Propositional Dynamic Logic by generalising its semantics and adding a new operator to the language. The logic can be used to reason about determined 2-player games. We present an overview of meta-theoretic results regarding this logic, also covering the algebraic version of the logic known as Game Algebra.
  •  103
    Sentences, belief and logical omniscience, or what does deduction tell us?
    Review of Symbolic Logic 1 (4): 459-476. 2008.
    We propose a model for belief which is free of presuppositions. Current models for belief suffer from two difficulties. One is the well known problem of logical omniscience which tends to follow from most models. But a more important one is the fact that most models do not even attempt to answer the question what it means for someone to believe something, and just what it is that is believed. We provide a flexible model which allows us to give meaning to beliefs in general contexts, including th…Read more
  •  91
    Vagueness and utility: The semantics of common nouns (review)
    Linguistics and Philosophy 17 (6). 1994.
    A utility-based approach to the understanding of vague predicates (VPs) is proposed. It is argued that assignment of truth values to propositions containing VPs entails unjustifiable assumptions of consensus; two models of VP semantics are criticized on this basis: (1) the super-truth theory of Kit Fine (1975), which requires an unlikely consensus on base points; (2) the fuzzy logic of Lotfi Zadeh (1975), on fuzzy truth values of sentences. Pragmatism is held to provide a key: successful behavio…Read more
  •  76
    Vague predicates and language games
    Theoria 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
  •  76
    Existence and feasibility in arithmetic
    Journal of Symbolic Logic 36 (3): 494-508. 1971.
  •  60
    The Logic of Knowledge Based Obligation
    with Eric Pacuit and Eva Cogan
    Synthese 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
  •  55
    Social Software
    Synthese 132 (3): 187-211. 2002.
    We suggest that the issue of constructing and verifying social procedures, which we suggestively call "social software", be pursued as systematically as computer software is pursued by computer scientists. Certain complications do arise with social software which do not arise with computer software, but the similarities are nonetheless strong, and tools already exist which would enable us to start work on this important project. We give a variety of suggestive examples and indicate some theoreti…Read more
  •  50
    Logic in India—Editorial Introduction
    with Hans van Ditmarsch and Ramaswamy Ramanujam
    Journal of Philosophical Logic 40 (5): 557-561. 2011.
  •  46
    A knowledge based semantics of messages
    with Ramaswamy Ramanujam
    Journal of Logic, Language and Information 12 (4): 453-467. 2003.
    We investigate the semantics of messages, and argue that the meaning ofa message is naturally and usefully given in terms of how it affects theknowledge of the agents involved in the communication. We note thatthis semantics depends on the protocol used by the agents, and thus not only the message itself, but also the protocol appears as a parameter in the meaning. Understanding this dependence allows us to give formal explanations of a wide variety of notions including language dependence, impl…Read more
  •  46
    Probabilistic conditionals are almost monotonic
    Review of Symbolic Logic 1 (1): 73-80. 2008.
    One interpretation of the conditional If P then Q is as saying that the probability of Q given P is high. This is an interpretation suggested by Adams (1966) and pursued more recently by Edgington (1995). Of course, this probabilistic conditional is nonmonotonic, that is, if the probability of Q given P is high, and R implies P, it need not follow that the probability of Q given R is high. If we were confident of concluding Q from the fact that we knew P, and we have stronger information R, we c…Read more
  •  32
    Length and structure of proofs
    Synthese 114 (1): 41-48. 1998.
  •  32
    On knowledge and obligation
    with Can Başķent and Loes Olde Loohuis
    Episteme 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.
  •  31
    Both the Beth definability theorem and Craig's lemma (interpolation theorem from now on) deal with the issue of the entanglement of one language L1 with another language L2, that is to say, information transfer—or the lack of such transfer—between the two languages. The notion of splitting we study below looks into this issue. We briefly relate our own results in this area as well as the results of other researchers like Kourousias and Makinson, and Peppas, Chopra and Foo.Section 3 does contain …Read more
  •  30
    Completeness of Certain Bimodal Logics for Subset Spaces
    with M. Angela Weiss
    Studia 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…Read more
  •  26
    Some Generalisations of the Notion of Well Ordering
    Mathematical Logic Quarterly 12 (1): 333-340. 1966.
  •  25
  •  23
    Topological reasoning and the logic of knowledge
    with Andrew Dabrowski and Lawrence S. Moss
    Annals 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
  •  22
    It is a sunny autumn day, and our protagonists have taken their meals outside, to enjoy the mild rays of the September sun. The NIAS cook Paul Nolte, as always glowing with pride while serving out his delicious food, has prepared a traditional Dutch meal today with sausage, red cabbage and pieces of apple
  •  22
    Semantical Considerations on Floyd-Hoare Logic
    with Vaughan R. Pratt, Michael J. Fischer, Richard E. Ladner, Krister Segerberg, and Tadeuz Traczyk
    Journal of Symbolic Logic 51 (1): 225-227. 1986.
  •  21
    Vague Predicates and Language Games
    Theoria: 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
  •  20
    Obituary: Horacio Arló-costa
    Episteme 9 (2): 89-89. 2012.
    Editorial Rohit Parikh, Jeffrey Helzner, Episteme, FirstView Article
  •  20
    Editorial introduction
    with Marc Pauly
    Studia Logica 75 (2): 163-164. 2003.
  •  19
    How Far Can We Formalize Language Games?
    Vienna Circle Institute Yearbook 3 89-100. 1995.
    I want to start by giving some quotes from Wittgenstein. It is part of his conception of what the foundations of Mathematics are about, a conception which many people have found peculiar and one of my defects is that I am not able to find it peculiar anymore, but find it perfectly sensible