Encoding transition systems in sequent calculus

  • Authors:

  • Raymond McDowell;Dale Miller;Catuscia Palamidessi

  • Affiliations:

  • Department of Mathematics and Computer Science, Kalamazoo College, 1200 Academy Street, Kalamazoo, MI;Department of Computer Science and Engineering, The Pennsylvania State University, 220 Pond Laboratory, University Park, PA;Department of Computer Science and Engineering, The Pennsylvania State University, 220 Pond Laboratory, University Park, PA

  • Venue:
  • Theoretical Computer Science - Linear logic
  • Year:
  • 2003

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Abstract

Intuitionistic and linear logics can be used to specify the operational semantics of transition systems in various ways. We consider here two encodings: one uses linear logic and maps states of the transition system into formulas, and the other uses intuitionistic logic and maps states into terms. In both cases, it is possible to relate transition paths to proofs in sequent calculus. In neither encoding, however, does it seem possible to capture properties, such as simulation and bisimulation, that need to consider all possible transitions or all possible computation paths. We consider augmenting both intuitionistic and linear logics with a proof theoretical treatment of definitions. In both cases, this addition allows proving various judgments concerning simulation and bisimulation (especially for noetherian transition systems). We also explore the use of infinite proofs to reason about infinite sequences of transitions. Finally, combining definitions and induction into sequent calculus proofs makes it possible to reason more richly about properties of transition systems completely within the formal setting of sequent calculus.