NDLI: Behavioral Algebraization of Logics

Content Provider	Springer Nature Link
Author	Caleiro, Carlos Gonçalves, Ricardo Martins, Manuel
Copyright Year	2009
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.
Starting Page	63
Ending Page	111
Page Count	49
File Format	PDF
ISSN	00393215
Journal	Studia Logica
Volume Number	91
Issue Number	1
e-ISSN	15728730
Language	English
Publisher	Springer Netherlands
Publisher Date	2009-01-23
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Abstract algebraic logic many-sorted behavioral logic non-truth-functionality Computational Linguistics Mathematical Logic and Foundations Logic
Content Type	Text
Resource Type	Article
Subject	Logic History and Philosophy of Science

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