A General Algebraic Semantics for Sentential Logics

An exposition of the approach to the algebraization of sentential logics developed by the Barcelona logic group.

This monograph is an exposition of the very general approach to the algebraization of sentential logics developed by the Barcelona logic group in the 1970s. It shows the results of this approach on a number of particular logics, and relates it to those developed by Blok, Czelakowski, Pigozzi and others.Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the seventh publication in the Lecture Notes in Logic series, Font and Jansana develop a very general approach to the algebraization of sentential logics and present its results on a number of particular logics. The authors compare their approach, which uses abstract logics, to the classical approach based on logical matrices and the equational consequence developed by Blok, Czelakowski, Pigozzi and others. This monograph presents a systematized account of some of the work on the algebraic study of sentential logics carried out by the logic group in Barcelona in the 1970s.