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Title: Behavioral algebraization of logics
Author: Caleiro, C.
Gonçalves, R.
Martins, Manuel A.
Keywords: Abstract algebraic logic
Many-sorted behavioral logic
Non-truth- functionality
Issue Date: 2009
Publisher: Springer
Abstract: We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of many-sorted behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability of AAL toward providing a meaningful algebraic counterpart also to logics with a many-sorted language, and possibly including non-truth-functional connectives. The proposed behavioral approach covers logics which are not algebraizable according to the standard approach, while also bringing a new algebraic perspective to logics which are algebraizable using the standard tools of AAL. Furthermore, we pave the way toward a robust behavioral theory of AAL, namely by providing a behavioral version of the Leibniz operator which allows us to generalize the traditional Leibniz hierarchy, as well as several well-known characterization results. A number of meaningful examples will be used to illustrate the novelties and advantages of the approach. © 2009 Springer Science+Business Media B.V.
Peer review: yes
DOI: 10.1007/s11225-009-9163-8
ISSN: 0039-3215
Appears in Collections:DMat - Artigos

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