Proof Theory for Casari's Comparative Logics

Comparative logics were introduced by Casari in the 1980s to treat aspects of comparative reasoning occurring in natural language. In this article Gentzen systems are defined for these logics by means of a special mix rule that combines calculi for various substructural logics with a hypersequent calculus for Meyer and Slaney's Abelian logic. Cut-elimination is established for all these systems, and as a consequence, a positive answer is given to an open problem on the decidability of the basic comparative logic.

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