Studia Logica 101 (4):713-747 (2013)

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Abstract
This paper is a contribution to the study of the rôle of disjunction inAlgebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize the multitude of notions of disjunction (both those already considered in the literature and those introduced in this paper), and to show several interesting applications allowed by the presence of a suitable disjunction in a given logic
Keywords Abstract Algebraic Logic  Generalized disjunction  Proof by cases properties  Consequence relations  Filter-distributive logics  Protoalgebraic logics
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DOI 10.1007/s11225-013-9496-1
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References found in this work BETA

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
A Survey of Abstract Algebraic Logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
A Propositional Calculus with Denumerable Matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Selfextensional Logics with a Conjunction.Ramon Jansana - 2006 - Studia Logica 84 (1):63-104.

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Citations of this work BETA

A Study of Truth Predicates in Matrix Semantics.Tommaso Moraschini - 2018 - Review of Symbolic Logic 11 (4):780-804.

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