A Logic of Sequentiality
- Cite this paper as:
- Churchill M., Laird J. (2010) A Logic of Sequentiality. In: Dawar A., Veith H. (eds) Computer Science Logic. CSL 2010. Lecture Notes in Computer Science, vol 6247. Springer, Berlin, Heidelberg
Game semantics has been used to interpret both proofs and functional programs: an important further development on the programming side has been to model higher-order programs with state by allowing strategies with ”history-sensitive” behaviour. In this paper, we develop a detailed analysis of the structure of these strategies from a logical perspective by showing that they correspond to proofs in a new kind of affine logic.
We describe the semantics of our logic formally by giving a notion of categorical model and an instance based on a simple category of games. Using further categorical properties of this model, we prove a full completeness result: each total strategy is the semantics of a unique cut-free core proof in the system. We then use this result to derive an explicit cut-elimination procedure.
KeywordsGame semantics sequentiality full completeness
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