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).
Work partially supported by project NOCoST (ANR, JC05_43380).
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Boudes, P. (2009). Thick Subtrees, Games and Experiments. In: Curien, PL. (eds) Typed Lambda Calculi and Applications. TLCA 2009. Lecture Notes in Computer Science, vol 5608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02273-9_7
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DOI: https://doi.org/10.1007/978-3-642-02273-9_7
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