Semantics for analytic containment

Studia Logica 77 (1):87-104 (2004)


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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Fabrice Correia
University of Geneva

References found in this work

Three Systems of First Degree Entailment.Richard Bradshaw Angell - 1977 - Journal of Symbolic Logic 42 (1):147.
Deducibility, Entailment and Analytic Containment.Richard Bradshaw Angell - 1989 - In Jean Norman & Richard Sylvan (eds.), Directions in Relevant Logic. Kluwer Academic Publishers. pp. 119-143.

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Citations of this work

Angellic Content.Kit Fine - 2016 - Journal of Philosophical Logic 45 (2):199-226.
Aboutness in Imagination.Franz Berto - 2018 - Philosophical Studies 175 (8):1871-1886.
Grounding and Truth-Functions.Fabrice Correia - 2010 - Logique Et Analyse 53 (211):251-279.
Laws of Nature, Explanation, and Semantic Circularity.Erica Shumener - 2019 - British Journal for the Philosophy of Science 70 (3):787-815.
On the Logic of Factual Equivalence.Fabrice Correia - 2016 - Review of Symbolic Logic 9 (1):103-122.

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