Editing Game semantics (section)

== Computability logic == 
[[Giorgi Japaridze|Japaridze]]’s [[computability logic]] is a game-semantical approach to logic in an extreme sense, treating games as targets to be serviced by logic rather than as technical or foundational means for studying or justifying logic. Its starting philosophical point is that logic is meant to be a universal, general-utility intellectual tool for ‘navigating the real world’ and, as such, it should be construed semantically rather than syntactically, because it is semantics that serves as a bridge between real world and otherwise meaningless formal systems (syntax). Syntax is thus secondary, interesting only as much as it services the underlying semantics. From this standpoint, Japaridze has repeatedly criticized the often followed practice of adjusting semantics to some already existing target syntactic constructions, with [[Paul Lorenzen|Lorenzen]]’s approach to intuitionistic logic being an example. This line of thought then proceeds to argue that the semantics, in turn, should be a game semantics, because games “offer the most comprehensive, coherent, natural, adequate and convenient mathematical models for the very essence of all ‘navigational’ activities of agents: their interactions with the surrounding world”.<ref>[[Giorgi Japaridze|G. Japaridze]], “[https://link.springer.com/chapter/10.1007%2F978-1-4020-9374-6_11 In the beginning was game semantics]”. In: [https://www.springer.com/book/9781402093739 Games: Unifying Logic, Language and Philosophy]. O. Majer, A.-V. Pietarinen and T. Tulenheimo, eds. Springer  2009, pp.249-350.  [https://arxiv.org/abs/cs/0507045%7CPreprint]</ref> Accordingly, the logic-building paradigm adopted by computability logic is to identify the most natural and basic operations on games, treat those operators as logical operations, and then look for sound and complete axiomatizations of the sets of game-semantically valid formulas. On this path a host of familiar or unfamiliar logical operators have emerged in the open-ended language of computability logic, with several sorts of negations, conjunctions, disjunctions, implications, quantifiers and modalities. 

Games are played between two agents: a machine and its environment, where the machine is required to follow only [[computable]] strategies. This way, games are seen as interactive computational problems, and the machine's winning strategies for them as solutions to those problems.  It has been established that computability logic is robust with respect to reasonable variations in the complexity of allowed strategies, which can be brought down as low as [[logarithmic space]] and [[polynomial time]] (one does not imply the other in interactive computations) without affecting the logic. All this explains the name “computability logic” and determines applicability in various areas of computer science. [[Classical logic]], [[independence-friendly logic]] and certain extensions of [[Linear logic|linear]] and [[Intuitionistic logic|intuitionistic]] logics turn out to be special fragments of computability logic, obtained merely by disallowing certain groups of operators or atoms.