Generalized matrices in abstract algebraic logic

by Josep Maria Font (University of Barcelona)

In:
V. Hendriks and J. Malinowski (eds.) Trends in Logic: 50 years of Studia Logica
(vol. 21 of Trends in Logic - Studia Logica Library, Kluwer, Dordrecht, 2003) 57--86.

Abstract

The aim of this paper is to survey some work done recently or still in progress that applies generalized matrices (also called abstract logics by some) to the study of sentential logics. My main concern will be to emphasize the links between this line of research and other existing frameworks in Algebraic Logic, either well-established ones (such as the old theory of logical matrices and the younger theories of protoalgebraic logics, of algebraizable logics, and the associated hierarchy) or really new ones (such as the theory of algebraizability of Gentzen systems or the model theory of equality-free logic). I would like to convey the idea that the interaction between these neighbouring fields may be specially fruitful, as it seems to be one of the leading forces in the shaping of this emerging field called Abstract Algebraic Logic.