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Behavioral Algebraization of Logics

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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.

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Authors and Affiliations

  1. SQIG-Instituto de Telecomunicações and Department of Mathematics, IST, TU Lisbon, Portugal

    Carlos Caleiro & Ricardo Gonçalves

  2. Department of Mathematics, U Aveiro, Aveiro, Portugal

    Manuel Martins

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  1. Carlos Caleiro
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  2. Ricardo Gonçalves
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  3. Manuel Martins
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Correspondence to Carlos Caleiro.

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Caleiro, C., Gonçalves, R. & Martins, M. Behavioral Algebraization of Logics. Stud Logica 91, 63–111 (2009). https://doi.org/10.1007/s11225-009-9163-8

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