Editing Game semantics (section)

== 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 logic|''dialogical'']], in German {{ill|Dialogische Logik|de}}) semantics for [[intuitionistic logic]]. [[Andreas Blass]]<ref>[http://www.math.lsa.umich.edu/~ablass/ Andreas R. Blass<!-- Bot generated title -->]</ref> 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 [[Programming language for Computable Functions|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]].

{{ill|Shahid Rahman|fr}} and Helge Rückert extended the [[Dialogical logic|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.