Semantics for analytic containment

Studia Logica 77 (1):87 - 104 (2004)
Abstract
In 1977, R. B. Angell presented a logic for <span class='Hi'>analytic</span> containment, a notion of relevant implication stronger than Anderson and Belnap's entailment. In this paper I provide for the first time the logic of first degree <span class='Hi'>analytic</span> containment, as presented in [2] and [3], with a semantical characterization—leaving higher degree systems for future investigations. The semantical framework I introduce for this purpose involves a special sort of truth-predicates, which apply to pairs of collections of formulas instead of individual formulas, and which behave in some respects like Gentzen's sequents. This semantics captures very general properties of the truth-functional connectives, and for that reason it may be used to model a vast range of logics. I briefly illustrate the point with classical consequence and Anderson and Belnap's tautological entailments.
Keywords analytic containment  relevant implication  R. B. Angell
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