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Game semantics (German: dialogische Logik) is an approach to the semantics of logic that grounds the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player. Paul Lorenzen was the first to introduce a game semantics for logic, doing so in the late 1950s. Since then, a number of different game semantics have been studied in logic. Game semantics has also been applied to the formal semantics of programming languages. The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so conscientious logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. ...
When someone sincerely agrees with an assertion, they are claiming that it is the truth. ...
This article discusses validity in logic, for the term in the social sciences see validity (psychometric). ...
Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ...
Paul Lorenzen (born March 24, 1915 in Kiel, Germany) is a philosopher and mathematician. ...
In theoretical computer science formal semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages and models of computation. ...
The primary motivation for Lorenzen and his student Kuno Lorenz was to find a game-theoretic (their term was "dialogical") semantics for intuitionistic logic. Blass was the first to point out connections between game semantics and linear logic. This line was further developed by Samson Abramsky, Radhakrishnan Jagadeesan, Pasquale Malacaria and independently Martin Hyland and Luke Ong, who placed special emphasis on compositionality, i.e. the definition of strategies inductively on the syntax. Using game semantics, the authors mentioned above have solved the long-standing problem of defining a fully abstract model for the programming languge PCF. Consequently, game semantics has led to fully abstract semantic models for a variety of programming languages and, to new semantic-directed methods of software verification by software model checking. Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ...
In mathematical logic, linear logic is a type of substructural logic that denies the structural rules of weakening and contraction. ...
Samson Abramsky (born 12 March 1953) is a computer scientist. ...
Luke Ong is a Professor of Computer Science at the University of Oxford. ...
The acronym PCF may refer to: Point Coordination Function, a Media Access Control technique used in Wi-Fi Wireless LANs Patrol Craft, Fast, a small, shallow draft water vessel. ...
Model checking is a method to algorithmically verify formal systems. ...
Foundational considerations of game semantics have been more emphasised by Jaakko Hintikka and Gabriel Sandu, especially for Independence-friendly logic (IF logic, more recently Information-friendly logic), a logic with "branching" (or partially ordered) quantifiers. It was thought that the principle of compositionality fails for these logics, so that a Tarskian truth definition could not provide a suitable semantics. To get around this problem, the quantifiers were given a game-theoretic meaning. Specifically, a universal quantifier and existential quantifier represent a choice by a player from the domain. In the universal case, a natural name for the player is "Falsifier"; in the existential, "Verifier". Note that a single counterexample falsifies a universally quantified statement, and a single example suffices to verify an existentially quantified one. Wilfred Hodges has proposed a compositional semantics and proved it equivalent to game semantics for IF-logics. Foundational considerations have motivated the works of others, such as Japaridze's computability logic. Jaakko Hintikka (born January 12, 1929, Vantaa, Finland) is a philosopher and logician. ...
Jaakko Hintikka proposed independence-friendly logic (IF logic) as an alternative to classical first-order logic (FOL). ...
In mathematics, a partially ordered set (or poset for short) is a set equipped with a special binary relation which formalizes the intuitive concept of an ordering. ...
In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. ...
In mathematics, semantics, and philosophy of language, the Principle of Compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. ...
In predicate logic, universal quantification is an attempt to formalise the notion that something (a logical predicate) is true for everything, or every relevant thing. ...
In predicate logic, existential quantification is an attempt to formalize the notion that something (a logical predicate) is true for something, or at least one relevant thing. ...
Domain has several meanings: // General some kind of territory, such as (for example) a demesne or a realm synonymous with field, e. ...
Wilfrid Hodges (born 1941) is a British mathematician, known for his work in model theory. ...
The Principle of Compositionality in semantics is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. ...
Computability logic is a formal theory of computability, introduced by Giorgi Japaridze in 2003. ...
See also
Jaakko Hintikka proposed independence-friendly logic (IF logic) as an alternative to classical first-order logic (FOL). ...
Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ...
In mathematical logic, linear logic is a type of substructural logic that denies the structural rules of weakening and contraction. ...
Computability logic is a formal theory of computability, introduced by Giorgi Japaridze in 2003. ...
Interactive computation involves communication with the external world during the computation. ...
articles - Krabbe, E. C. W., 2001. "Dialogue Foundations: Dialogue Logic Revisited," Supplement to the Proceedings of The Aristotelian Society 75: 33-49.
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