Computability logic

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Published in James A. Momoh, Adaptive Stochastic Optimization Techniques with Applications, 2015

Game theory has come to play an increasingly important role in logic and in computer science. Several logical theories have a basis in game semantics. And computer scientists have used games to model interactive computations. Computability logic attempts to develop a comprehensive formal theory of interactive computational tasks and resources, formalizing these entities as games between a computing agent and its environment [12].

Non-commutative propositional logic with short-circuit evaluation

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Published in Journal of Applied Non-Classical Logics, 2021

Jan A. Bergstra, Alban Ponse, Daan J. C. Staudt

Boolean connectives that prescribe short-circuit evaluation often have specific names or notations, for example, Dijkstra's cand (conditional conjunction) and cor used in the three-valued setting with (see Dijkstra, 1976; Gries, 1981), or the short-circuited connectives && and || as used in programming languages such as C, Go, Java, and Perl. Short-circuit evaluation in C is discussed in e.g. Zimmermann and Dold (2003). Other notations for the sequential connectives and with memorising interpretation are ▵ and from computability logic (see, e.g. Japaridze, 2008), and ⊗ and ⊕ from transaction logic (see, e.g. Basseda & Kifer, 2015, there called serial connectives). However, is just a part of both these logics and it is questionable whether its axiomatisation or semantics are of any relevance.

Computability logic

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Non-commutative propositional logic with short-circuit evaluation