The Complexity of Local Proof Search in Linear Logic
نویسندگان
چکیده
منابع مشابه
The Complexity of Local Proof Search in Linear Logic
Proof search in linear logic is known to be diicult: the provability of propositional linear logic formulas is undecidable. Even without the modalities, multiplicative-additive fragment of propositional linear logic, mall, is known to be pspace-complete, and the pure multiplicative fragment, mll, is known to be np-complete. However, this still leaves open the possibility that there might be pro...
متن کاملComplexity of Local Proof Search
Proof search in linear logic is known to be diicult: the provability of propositional linear logic formulas is undecidable. Even without the modalities, multiplicative-additive fragment of propositional linear logic, mall, is known to be pspace-complete, and the pure multiplicative fragment, mll, is known to be np-complete. However, this still leaves open the possibility that there might be pro...
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A class of linear logic proof games is developed, each with a numeric score that depends on the number of preferred axioms used in a complete or partial proof tree. The complexity of these games is analyzed for the np-complete multiplicative fragment (mll) extended with additive constants and the pspace-complete multiplicative, additive fragment (mall) of propositional linear logic. In each cas...
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Linear logic is a refinement of classical logic introduced by J.-Y.Girard to provide means for keeping track of "resources" two assumptions of a formula A are distinguished from a single assumption of A. Although linear logic is not the first attempt for developing "resourceoriented" logics (relevance logic and Lambek calculus being well-known examples), it is by now the mostinvestigated one. S...
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In this paper, we investigate automated proof construction in classical linear logic (CLL) by giving logical foundations for the design of proof search strategies. We propose common theoretical foundations for top-down, bottom-up and mixed proof search procedures with a systematic formalization of strategies construction using the notions of immediate or chaining composition or decomposition, d...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 1996
ISSN: 1571-0661
DOI: 10.1016/s1571-0661(05)80410-4