Categorical Abstract Algebraic Logic: More on Protoalgebraicity

Voutsadakis, George

Notre Dame J. Formal Logic, Tome 47 (2006) no. 1, p. 487-514 / Harvested from Project Euclid

Résumé

Protoalgebraic logics are characterized by the monotonicity of the Leibniz operator on their theory lattices and are at the lower end of the Leibniz hierarchy of abstract algebraic logic. They have been shown to be the most primitive among those logics with a strong enough algebraic character to be amenable to algebraic study techniques. Protoalgebraic π-institutions were introduced recently as an analog of protoalgebraic sentential logics with the goal of extending the Leibniz hierarchy from the sentential framework to the π-institution framework. Many properties of protoalgebraic logics, studied in the sentential logic framework by Blok and Pigozzi, Czelakowski, and Font and Jansana, among others, have already been adapted in previous work by the author to the categorical level. This work aims at further advancing that study by exploring in this new level some more properties of protoalgebraic sentential logics.

Détail

Publié le : 2006-10-14
Classification:  algebraic logic,  equivalent deductive systems,  equivalent institutions,  protoalgebraic logics,  equivalential logics,  algebraizable deductive systems,  adjunctions,  equivalent categories,  algebraizable institutions,  Leibniz operator,  Tarski operator,  Leibniz hierarchy,  03G99,  18C15,  68N30