Thick Subtrees, Games and Experiments

Authors:
Pierre Boudes
Affiliations:
Laboratoire d'Informatique de l'université Paris-Nord UMR CNRS 7030 Institut Galilée, Université Paris-Nord, Villetaneuse, France 93430
Venue:
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Year:
2009

Citing 5
Cited 1

Linear logic

Theoretical Computer Science
Timeless Games

CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Abstract Böhm trees

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Syntax vs. semantics: a polarized approach

Theoretical Computer Science - Game theory meets theoretical computer science
Sequential algorithms and strongly stable functions

Theoretical Computer Science - Game theory meets theoretical computer science

Compressing Polarized Boxes

LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science

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Abstract

We relate the dynamic semantics (games, dealing with interactions) and the static semantics (dealing with results of interactions) of linear logic with polarities, in the spirit of Timeless Games [1]. The polarized game semantics is full and faithfull for polarized proof-nets [2]. We detail the correspondence between cut free proof-nets and innocent strategies, in a framework related to abstract Böhm trees. A notion of thick subtree allows us to reveal a deep relation between plays in games and Girard's experiments on proof-nets. We then define a desequentializing operation, forgetting time in games which coincides with the usual way of computing a result of interaction from an experiment. We then obtain our main result: desequentializing the game interpretation of a polarized proof-net yields its standard relational model interpretation (static semantics).