## 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 |
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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 |
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Publisher | Springer Verlag |

## Keywords

- full completeness
- sequentiality
- Game semantics