2009
DOI: 10.1007/s11225-009-9163-8
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Behavioral Algebraization of Logics

Abstract: 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 towards providing a meaningful algebraic counterpart also to logics with a manysorted language, and possibly including non-truth-functional connectives. The proposed behavioral approach covers logics which are not algebraizable according to the st… Show more

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Cited by 13 publications
(35 citation statements)
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“…The idea was to associate to C 1 not a class of algebras over the signature of C 1 , but rather a class of algebras over a two-sorted signature of formulas and truth-values, where the valuation map is an operation between the two sorts. This work actually inspired a novel behavioral approach to AAL, as introduced in (Caleiro et al, 2007), whose main aim was extending the range of applicability of the usual tools of AAL towards providing a meaningful algebraic counterpart also to logics that, as C 1 , include non-truth-functional connectives and which are not algebraizable according to the traditional theory. The key idea of the behavioral approach to AAL is to substitute the role played by unsorted equational logic (Eqn) by a suitable many-sorted behavioral equational logic (BEqn).…”
Section: Behavioral Algebraizationmentioning
confidence: 99%
See 4 more Smart Citations
“…The idea was to associate to C 1 not a class of algebras over the signature of C 1 , but rather a class of algebras over a two-sorted signature of formulas and truth-values, where the valuation map is an operation between the two sorts. This work actually inspired a novel behavioral approach to AAL, as introduced in (Caleiro et al, 2007), whose main aim was extending the range of applicability of the usual tools of AAL towards providing a meaningful algebraic counterpart also to logics that, as C 1 , include non-truth-functional connectives and which are not algebraizable according to the traditional theory. The key idea of the behavioral approach to AAL is to substitute the role played by unsorted equational logic (Eqn) by a suitable many-sorted behavioral equational logic (BEqn).…”
Section: Behavioral Algebraizationmentioning
confidence: 99%
“…The interested reader can find all the details in (Caleiro et al, 2007;Gonçalves, 2008). We can say, informally, that a propositional logic is behaviorally algebraizable if it is equivalent to the behavioral equational theory of a class of two-sorted algebras.…”
Section: Behavioral Algebraizationmentioning
confidence: 99%
See 3 more Smart Citations