Proofs and types
Information and Computation
A modal analysis of staged computation
Journal of the ACM (JACM)
A judgmental reconstruction of modal logic
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science
The ILTP Problem Library for Intuitionistic Logic
Journal of Automated Reasoning
ACM Transactions on Computational Logic (TOCL)
Focusing the inverse method for linear logic
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Magically constraining the inverse method using dynamic polarity assignment
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
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We present a multi-context focused sequent calculus whose derivations are in bijective correspondence with normal natural deductions in the propositional fragment of the intuitionistic modal logic IS4. This calculus, suitable for the enumeration of normal proofs, is the starting point for the development of a sequent calculus-based bidirectional decision procedure for propositional IS4. In this system, relevant derived inference rules are constructed in a forward direction prior to proof search, while derivations constructed using these derived rules are searched over in a backward direction. We also present a variant which searches directly over normal natural deductions. Experimental results show that on most problems, the bidirectional prover is competitive with both conventional backward provers using loop-detection and inverse method provers, significantly outperforming them in a number of cases.