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Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science
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SYSNO ASEP 0488936 Document Type M - Monograph Chapter R&D Document Type Monograph Chapter Title Assertional logics, truth-equational logics, and the hierarchies of abstract algebraic logic Author(s) Albuquerque, H. (ES)
Font, J.M. (ES)
Jansana, R. (ES)
Moraschini, Tommaso (UIVT-O) SAI, RIDSource Title Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science. - Cham : Springer, 2018 / Czelakowski J. - ISSN 2211-2758 - ISBN 978-3-319-74771-2 Pages s. 53-79 Number of pages 27 s. Number of pages 454 Publication form Print - P Language eng - English Country CH - Switzerland Keywords Abstract algebraic logic ; Leibniz hierarchy ; Frege hierarchy ; truth-equational logics ; assertional logics ; Fregean logics ; full generalized models ; unital matrices Subject RIV BA - General Mathematics OECD category Pure mathematics Institutional support UIVT-O - RVO:67985807 DOI 10.1007/978-3-319-74772-9_2 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2019 Electronic address https://link.springer.com/book/10.1007/978-3-319-74772-9
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