Title: On the intuitionistic force of classical search (Extended abstract)
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.
Publication Year: 1996
Publication Date: 1996-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
Access and Citation
Cited By Count: 6
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