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20Partiality and games: propositional logicLogic Journal of the IGPL 9 (1): 101-121. 2001.We study partiality in propositional logics containing formulas with either undefined or over-defined truth-values. Undefined values are created by adding a four-place connective W termed transjunction to complete models which, together with the usual Boolean connectives is shown to be functionally complete for all partial functions. Transjunction is seen to be motivated from a game-theoretic perspective, emerging from a two-stage extensive form semantic game of imperfect information between two…Read more
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Game-Theoretic SemanticsIn Benthem & Meulen (eds.), Handbook of Logic and Language, Mit Press. 1997.The paper presents an application of game-theoretical ideas to the semantics of natural language, especially the analysis of quantifiers and anaphora. The paper also introduces the idea of games of imperfect information and connects to partial logics.
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17numbers as in the following example ♦1,1♦1,2 2,3 5,4p We denote the set of formulas of this modal language by M L(k). For each modality type i, there will be an accessibility relation Ri. That is, an k-ary modal structure for the modal propositional language L will have the form..
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11The logic of informational independence and finite modelsLogic Journal of the IGPL 5 (1): 79-95. 1997.In this paper we relax the assumption that the logical constants of ordinary first-order logic be linearly ordered. As a consequence, we shall have formulas involving not only partially ordered quantifiers, but also partially ordered connectives. The resulting language, called the language of informational independence will be given an interpretation in terms of games of imperfect information. The II-logic will be seen to have some interesting properties: It is very natural to define in this log…Read more
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16Entre logique et langageVrin. 2009.Linguistique et philosophie logique du langage: deux traditions de pensee que bien des choses opposent. La premiere est plutot mentaliste, et orientee vers l'etude de la syntaxe; la seconde, plus preoccupee de semantique, cherche volontiers le sens dans les conditions de verite des phrases. Ce portrait n'est pas faux, mais il est incomplet: entre logique et linguistique, les relations n'ont pas ete, ne sont pas que d'opposition. Dans cet ouvrage, les auteurs proposent une sorte d'histoire concep…Read more
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78Henkin quantifiers and the definability of truthJournal of Philosophical Logic 29 (5): 507-527. 2000.Henkin quantifiers have been introduced in Henkin (1961). Walkoe (1970) studied basic model-theoretical properties of an extension $L_{*}^{1}$ (H) of ordinary first-order languages in which every sentence is a first-order sentence prefixed with a Henkin quantifier. In this paper we consider a generalization of Walkoe's languages: we close $L_{*}^{1}$ (H) with respect to Boolean operations, and obtain the language L¹(H). At the next level, we consider an extension $L_{*}^{2}$ (H) of L¹(H) in whic…Read more
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163The fallacies of the new theory of referenceSynthese 104 (2). 1995.The so-called New Theory of Reference (Marcus, Kripke etc.) is inspired by the insight that in modal and intensional contexts quantifiers presuppose nondescriptive unanalyzable identity criteria which do not reduce to any descriptive conditions. From this valid insight the New Theorists fallaciously move to the idea that free singular terms can exhibit a built-in direct reference and that there is even a special class of singular terms (proper names) necessarily exhibiting direct reference. This…Read more
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11There is a line of argument which aims to show that certain ontological claims are harmless by making use of conservativity results. The argument goes back to Hilbert who set its general frame. Hilbert’s concern was with certain abstract (ideal) entities in mathematics but the argument has been applied without discrimination to avoid ontological commitment to abstract entities in physics (Field) or to avoid ontological commitment to semantical properties like truth (Shapiro).
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Independence-friendly logic: A game-theoretic approach. LMS Lecture Notes, vol. 386Bulletin of Symbolic Logic 18 (2): 272-273. 2012.
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114Some aspects of negation in EnglishSynthese 99 (3). 1994.I introduce a formal language called the language of informational independence (IL-language, for short) that extends an ordinary first-order language in a natural way. This language is interpreted in terms of semantical games of imperfect information. In this language, one can define two negations: (i) strong or dual negation, and (ii) weak or contradictory negation. The latter negation, unlike the former, can occur only sentence-initially. Then I argue that, to a certain extent, the two negati…Read more
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64Uses and Misuses of Frege’s IdeasThe Monist 77 (3): 278-293. 1994.Frege has one magnificent achievement to his credit, viz. the creation of modern formal logic. As a philosopher and as a theoretical logician, he was nevertheless as parochial as he was, geographically speaking. Hence Frege’s concepts and problems offer singularly unfortunate starting points for constructive work in the foundations of logic and mathematics. Even if he is right in some of his views, they depend on severely restrictive assumptions that have to be noted and eliminated. These restri…Read more
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22Probabilistic IF LogicIn Kamal Lodaya (ed.), Logic and its Applications, Springer. pp. 69--79. 2013.
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14Partially ordered connectives and finite graphsIn M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation, Kluwer Academic Publishers. pp. 79--88. 1995.
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68Logic and semantics in the twentieth centuryIn Leila Haaparanta (ed.), The Development of Modern Logic, Oxford University Press. pp. 562. 2008.This chapter explores logical semantics, that is, the structural meaning of logical expressions like connectives, quantifiers, and modalities. It focuses on truth-theoretical semantics for formalized languages, a tradition emerging from Carnap's and Tarski's work in the first half of the last century that specifies the meaning of these expressions in terms of the truth-conditions of the sentences in which they occur. It considers Tarski-style definitions of the semantics of a given language in a…Read more
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105If-logic and truth-definitionJournal of Philosophical Logic 27 (2): 143-164. 1998.In this paper we show that first-order languages extended with partially ordered connectives and partially ordered quantifiers define, under a certain interpretation, their own truth-predicate. The interpretation in question is in terms of games of imperfect information. This result is compared with those of Kripke and Feferman
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36Equilibrium semantics of languages of imperfect informationAnnals of Pure and Applied Logic 161 (5): 618-631. 2010.In this paper, we introduce a new approach to independent quantifiers, as originally introduced in Informational independence as a semantic phenomenon by Hintikka and Sandu [9] under the header of independence-friendly languages. Unlike other approaches, which rely heavily on compositional methods, we shall analyze independent quantifiers via equilibriums in strategic games. In this approach, coined equilibrium semantics, the value of an IF sentence on a particular structure is determined by the…Read more
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100Aspects of compositionalityJournal of Logic, Language and Information 10 (1): 49-61. 2001.We introduce several senses of the principle ofcompositionality. We illustrate the difference between them with thehelp of some recent results obtained by Cameron and Hodges oncompositional semantics for languages of imperfect information.
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University of HelsinkiDepartment of Philosophy (Theoretical Philosophy, Practical Philosophy, Philosophy in Swedish)Retired faculty
Areas of Specialization
Philosophy of Language |
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Science, Logic, and Mathematics |