Abstract
In 1977, R. B. Angell presented a logic for analytic 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 analytic 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”.
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References
Anderson, A. R., and N. D. Belnap, Entailment: The Logic of Relevance and Necessity, vol I, Princeton University Press, 1975.
Angell, R. B., ‘Three Systems of First Degree Entailment’, Journal of Symbolic Logic 42:147, 1977.
Angell, R. B., ‘Deducibility, Entailment and Analytic Containement’, in J. Norman & R. Sylvan (eds.), Directions in Relevant Logic, Dordrecht: Kluwer Academic Publishers, 1989
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Correia, F. Semantics for Analytic Containment. Studia Logica 77, 87–104 (2004). https://doi.org/10.1023/B:STUD.0000034187.37935.24
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DOI: https://doi.org/10.1023/B:STUD.0000034187.37935.24