Selfextensional logics with a conjunction

Studia Logica 84 (1):63 - 104 (2006)
Abstract
A logic is selfextensional if its interderivability (or mutual consequence) relation is a congruence relation on the algebra of formulas. In the paper we characterize the selfextensional logics with a conjunction as the logics that can be defined using the semilattice order induced by the interpretation of the conjunction in the algebras of their algebraic counterpart. Using the charactrization we provide simpler proofs of several results on selfextensional logics with a conjunction obtained in [13] using Gentzen systems. We also obtain some results on Fregean logics with conjunction.
Keywords algebraic logic  selfextensional logic  Fregan logic  algebraizable logic  generalized matrix  full generalized model  fully adequate Gentzen system
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