### 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.

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.

Original language | English |
---|---|

Title of host publication | Computer Science Logic (Lecture Notes in Computer Science) |

Editors | A Dawar, H Veith |

Publisher | Springer |

Pages | 215-229 |

Number of pages | 15 |

Volume | 6247/2 |

DOIs | |

Publication status | Published - 24 Aug 2010 |

### Publication series

Name | Lecture Notes in Computer Science |
---|---|

Publisher | Springer Verlag |

### Keywords

- full completeness
- sequentiality
- Game semantics

## Fingerprint Dive into the research topics of 'A logic of sequentiality'. Together they form a unique fingerprint.

## 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