Assertional logics, truth-equational logics, and the hierarchies of abstract algebraic logic

Autoři: Tommaso Moraschini
Rok vydání: 2018
Typ publikace: Kapitola v monografii
Periodikum: Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science
Bibliografická citace: ALBUQUERQUE, H., FONT, J.M., JANSANA, R., MORASCHINI, Tommaso. Assertional logics, truth-equational logics, and the hierarchies of abstract algebraic logic. In: CZELAKOWSKI, J., ed. Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science. Cham: Springer, 2018, S. 53-79. Outstanding Contributions to Logic, 16. ISBN 978-3-319-74771-2
Dostupné z: doi:10.1007/978-3-319-74772-9_2.
DOI: 10.1007/978-3-319-74772-9_2
ID: 488936
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Abstrakt

We establish some relations between the class of truth-equational logics, the class of assertional logics, other classes in the Leibniz hierarchy, and the classes in the Frege hierarchy. We argue that the class of assertional logics belongs properly in the Leibniz hierarchy. We give two new characterizations of truth-equational logics in terms of their full generalized models, and use them to obtain further results on the internal structure of the Frege hierarchy and on the relations between the two hierarchies. Some of these results and several counter examples contribute to answer a few open problems in abstract algebraic logic, and open a new one.