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.
Josep Maria Font works in the Department of Probability, Logic and Statistics at the University of Barcelona. Ramon Jansana works in the Department of Logic, History and Philosophy of Science at the University of Barcelona.
Introduction; 1. Generalities on abstract logics and sentential logics; 2. Abstract logics as models of sentential logics; 3. Applications to protoalgebraic and algebraizable logics; 4. Abstract logic as models of Gentzen systems; 5. Applications to particular sentential logics; Bibliography; Symbol index; General index.