# A logic of sequentiality

Martin Churchill, James Laird

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Citations (Scopus)

### Abstract

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 \emph{core} proof in the system. We then use this result to derive an explicit cut-elimination procedure.
Language English Computer Science Logic (Lecture Notes in Computer Science) A Dawar, H Veith Springer 215-229 15 6247/2 10.1007/978-3-642-15205-4_19 Published - 24 Aug 2010

### Publication series

Name Lecture Notes in Computer Science Springer Verlag

Logic
Categorical
Game Semantics
Cut-elimination
Completeness
Programming
Model
Game
Higher Order
Strategy
Semantics
History

### Keywords

• full completeness
• sequentiality
• Game semantics

### Cite this

Churchill, M., & Laird, J. (2010). A logic of sequentiality. In A. Dawar, & H. Veith (Eds.), Computer Science Logic (Lecture Notes in Computer Science) (Vol. 6247/2, pp. 215-229). (Lecture Notes in Computer Science). Springer. https://doi.org/10.1007/978-3-642-15205-4_19

A logic of sequentiality. / Churchill, Martin; Laird, James.

Computer Science Logic (Lecture Notes in Computer Science). ed. / A Dawar; H Veith. Vol. 6247/2 Springer, 2010. p. 215-229 (Lecture Notes in Computer Science).

Research output: Chapter in Book/Report/Conference proceedingChapter

Churchill, M & Laird, J 2010, A logic of sequentiality. in A Dawar & H Veith (eds), Computer Science Logic (Lecture Notes in Computer Science). vol. 6247/2, Lecture Notes in Computer Science, Springer, pp. 215-229. https://doi.org/10.1007/978-3-642-15205-4_19
Churchill M, Laird J. A logic of sequentiality. In Dawar A, Veith H, editors, Computer Science Logic (Lecture Notes in Computer Science). Vol. 6247/2. Springer. 2010. p. 215-229. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-642-15205-4_19
Churchill, Martin ; Laird, James. / A logic of sequentiality. Computer Science Logic (Lecture Notes in Computer Science). editor / A Dawar ; H Veith. Vol. 6247/2 Springer, 2010. pp. 215-229 (Lecture Notes in Computer Science).
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