Game-Theoretical Semantics

Hintikka, Jaakko; Sandu, Gabriel

doi:10.1016/b0-08-044854-2/01000-2

Cited by 18 publications

(22 citation statements)

References 8 publications

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“…Some extensive surveys of the subject can be found in (Abramsky & McCusker, 1999;A. Pietarinen & Sandu, 2000;A.-V. Pietarinen, 2003;Hintikka & Sandu, 1997). An overview of the field and its relation to various epistemic and scientific topics was discussed in (A.-V. Pietarinen, 2003).…”

Section: Non-classical Logics and Game Theoretical Semantics: A Briefmentioning

confidence: 99%

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Game theoretical semantics for some non-classical logics

Baskent

2016

Journal of Applied Non-Classical Logics

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Section: Non-classical Logics and Game Theoretical Semantics: A Briefmentioning

confidence: 99%

“…Pietarinen, 2000;A.-V. Pietarinen, 2004;Sandu & Pietarinen, 2001). Hintikka and Sandu discussed non-classicality in GTS also without specifically offering any insight on paraconsistency (Hintikka & Sandu, 1997;A. Pietarinen & Sandu, 2000).…”

Section: Non-classical Logics and Game Theoretical Semantics: A Briefmentioning

confidence: 99%

Game theoretical semantics for some non-classical logics

Baskent

2016

Journal of Applied Non-Classical Logics

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“…Second, as we stressed in §2, even when the rules are changed, the focus in all of these games is the maintenance of (some level of) consistency. Obligational disputations thus differ in a crucial way from modern game or dialogue approaches to logic (à la Lorenzen [22] and Hintikka [13]) in that they are not intended to give semantic meaning to the logical connectives, or to demonstrate the validity of a proposition. Instead, the rules of inference for reasoning must be known in advance by both the Opponent and the Respondent, and an obligational disputation about 53 Yrjönsuuri also believes that "medieval authors did not generally accept the idea of employing counterfactual reasoning in the rules of obligations" [40, p. 72], and he says this is one reason why Kilvington's theory, with its markedly counterfactual language for evaluating irrelevant propositions, was not widely accepted.…”

Section: Cooperative and Uncooperative Gamesmentioning

confidence: 98%

Interactive logic in the middle ages

Uckelman

2013

LLP

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Recently logic has shifted emphasis from static systems developed for purely theoretical reasons to dynamic systems designed for application to real world situations. The emphasis on the applied aspects of logic and reasoning means that logic has become a pragmatic tool, to be judged against the backdrop of a particular application. This shift in emphasis is, however, not new. A similar shift towards "interactive logic" occurred in the high Middle Ages. We provide a number of different examples of "interactive logic" in the Middle Ages, all species of the disputation game obligatio. These games display a recognition of the importance of interaction in logical contexts and the way that interactive logic differs from single-agent inference.

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“…In this paper we introduce a game semantics for the validity of inferences in System P. The study of logical systems with game-theoretic methods was initiated independently by Lorenzen and Lorenz [11] and Hintikka [6]. Hintikka's approach, known as game theoretic semantics, uses a game to establish the truth of a formula in a given model.…”

Section: Introductionmentioning

confidence: 99%

A Game Semantics for System P

Marti

Pinosio

2016

Stud Logica

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In this paper we introduce a game semantics for System P, one of the most studied axiomatic systems for non-monotonic reasoning, conditional logic and belief revision. We prove soundness and completeness of the game semantics with respect to the rules of System P, and show that an inference is valid with respect to the game semantics if and only if it is valid with respect to the standard order semantics of System P. Combining these two results leads to a new completeness proof for System P with respect to its order semantics. Our approach allows us to construct for every inference either a concrete proof of the inference from the rules in System P or a countermodel in the order semantics. Our results rely on the notion of a witnessing set for an inference, whose existence is a concise, necessary and sufficient condition for validity of an inferences in System P. We also introduce an infinitary variant of System P and use the game semantics to show its completeness for the restricted class of well-founded orders.

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Game-Theoretical Semantics

Cited by 18 publications

References 8 publications

Game theoretical semantics for some non-classical logics

Game theoretical semantics for some non-classical logics

Interactive logic in the middle ages

A Game Semantics for System P

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