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Constructive Game Logic

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12075)

Abstract

Game Logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in response to the opponent’s actions. We thus develop Constructive Game Logic, which extends Parikh’s Game Logic (GL) with constructivity and with first-order programs à la Pratt’s first-order dynamic logic (DL). Our major contributions include: 1. a novel realizability semantics capturing the adversarial dynamics of games, 2. a natural deduction calculus and operational semantics describing the computational meaning of strategies via proof-terms, and 3. theoretical results including soundness of the proof calculus w.r.t. realizability semantics, progress and preservation of the operational semantics of proofs, and Existential Properties on support of the extraction of computational artifacts from game proofs. Together, these results provide the most general account of a Curry-Howard interpretation for any program logic to date, and the first at all for Game Logic.

Keywords

  • Game Logic
  • Constructive Logic
  • Natural Deduction
  • Proof Terms

This research was sponsored by the AFOSR under grant number FA9550-16-1-0288. The authors were also funded by the NDSEG Fellowship and Alexander von Humboldt Foundation, respectively.

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Bohrer, R., Platzer, A. (2020). Constructive Game Logic. In: Müller, P. (eds) Programming Languages and Systems. ESOP 2020. Lecture Notes in Computer Science(), vol 12075. Springer, Cham. https://doi.org/10.1007/978-3-030-44914-8_4

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