Game Semantics - Intuitionistic Logic, Denotational Semantics, Linear Logic, Logical Pluralism

Intuitionistic Logic, Denotational Semantics, Linear Logic, Logical Pluralism

The primary motivation for Lorenzen and Kuno Lorenz was to find a game-theoretic (their term was "dialogical" Dialogische Logik) semantics for intuitionistic logic. Andreas 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 language 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.

Shahid Rahman and Helge Rückert extended the dialogical approach to the study of several non-classical logics such as modal logic, relevance logic, free logic and connexive logic. Recently, Rahman and collaborators developed the dialogical approach into a general framework aimed at the discussion of logical pluralism.