On Constructive Connectives and Systems

Details On Constructive Connectives and Systems On Constructive Connectives and Systems

2010-11-19

arxiv.org/abs/1011.4384v2

LMCS 6 (4:12) 2010

Computer Science

Logic in Computer Science

Scientific paper

10.2168/LMCS-6(4:12)2010

Canonical inference rules and canonical systems are defined in the framework of non-strict single-conclusion sequent systems, in which the succeedents of sequents can be empty. Important properties of this framework are investigated, and a general non-deterministic Kripke-style semantics is provided. This general semantics is then used to provide a constructive (and very natural), sufficient and necessary coherence criterion for the validity of the strong cut-elimination theorem in such a system. These results suggest new syntactic and semantic characterizations of basic constructive connectives.

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