MoL-2020-12: Karlsson, Martin (2020) Proofs and Strategies: A Characterization of Classical and Intuitionistic Logic using Games with Explicit Strategies. [Report]
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Abstract
We define two-player perfect information games characterizing classical and intuitionistic first-order validity. In short we enrich the language of first-order logic with two force markers denoting assertion and challenge. A two-player game is then a tree of states representing each players assertions and challenges and whose turn it is to move. A winning strategy for a player is a subtree of a game fulfilling some conditions. In particular we examine one of the players (the proponents) winning strategies for which we define several operations such as parallel, contraction, application, and composition. Using these operations we then establish a correspondence of strategies with derivations in the sequent calculus, giving us soundness and completeness for classical and intuitionistic logic. Additionally a close correspondence between composition and the cut-rule provides us with a method for cut-elimination. The constructive treatment of strategies gives them a computational interpretation which is of general interest for denotational semantics. The techniques developed may also be of use for many similar game-semantics.
| Item Type: | Report |
|---|---|
| Report Nr: | MoL-2020-12 |
| Series Name: | Master of Logic Thesis (MoL) Series |
| Year: | 2020 |
| Subjects: | Computation Logic |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 21 Dec 2020 12:50 |
| Last Modified: | 21 Dec 2020 12:50 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1765 |
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