Abstract
The combinatorics of proof-search in classical propositional logic lies at the heart of most efficient proof procedures because the logic admits least-commitment search. The key to extending such methods to quantifiers and non-classical connectives is the problem of recovering this least-commitment principle in the context of the non-classical/non-propositional logic; i.e., characterizing when a least-commitment (classical) search yields sufficient evidence for provability in the (non-classical) logic.
In this paper, we present such a characterization for the (⊃, ∧)-fragment of intuitionistic logic using the λμ-calculus: a system of realizers for classical free deduction (cf. natural deduction) due to Parigot.
We show how this characterization can be used to define a notion of uniform proof, and a corresponding proof procedure, which extends that of Miller et al. to multiple-conclusioned sequent systems. The procedure is sound and complete for the fragment of intuitionistic logic considered and enjoys the combinatorial advantages of search in classical logic.
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Ritter, E., Pym, D., Wallen, L. (1996). On the intuitionistic force of classical search (Extended abstract). In: Miglioli, P., Moscato, U., Mundici, D., Ornaghi, M. (eds) Theorem Proving with Analytic Tableaux and Related Methods. TABLEAUX 1996. Lecture Notes in Computer Science, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61208-4_19
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