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Selfextensional Logics with a Conjunction

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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.

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Authors and Affiliations

  1. Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Montalegre, 608001, Barcelona, Spain

    Ramon Jansana

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  1. Ramon Jansana
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Correspondence to Ramon Jansana.

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This paper is a version of the invited talk at the conference Trends in Logic III, dedicated to the memory of A. MOSTOWSKI, H. RASIOWA and C. RRAUSZER, and held in Warsaw and Ruciane-Nida from 23rd to 25th September 2005.

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Jansana, R. Selfextensional Logics with a Conjunction. Stud Logica 84, 63–104 (2006). https://doi.org/10.1007/s11225-006-9003-z

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  • DOI: https://doi.org/10.1007/s11225-006-9003-z

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