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Towards a Behavioral Algebraic Theory of Logical Valuations
January 2011
rgon:11
Logical matrices are widely accepted as the semantic structures that most naturally fit the traditional approach to algebraic logic. The behavioral approach to the algebraization of logics extends the applicability of the traditional methods of algebraic logic to a wider range of logical systems, possibly encompassing many-sorted languages and non-truth-functional phenomena. However, as one needs to work with behavioral congruences, matrix semantics are unsuited to the behavioral setting. In [5], a promising version of algebraic valuation semantics was proposed in order to fill in this gap. Herein, we define the class of valuations that should be canonically associated to a logic, and we show, by means of new meaningful bridge results, how it is related to the behaviorally equivalent algebraic semantics of a behaviorally algebraizable logic.
Journal
R. Gonçalves, C. Caleiro
Fundamenta Informaticae
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106
2-4
191-209
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R. Gonçalves and C. Caleiro, Towards a Behavioral Algebraic Theory of Logical Valuations, Fundamenta Informaticae, Vol. 106, No. 2-4, Pag. 191-209, January 2011.
<b><a href="/people/members/view.php?code=855d4cc45b6396858cd0838dd42db58f" class="author">R. Gonçalves</a> and C. Caleiro</b>, <u>Towards a Behavioral Algebraic Theory of Logical Valuations</u>, Fundamenta Informaticae, Vol. 106, No. 2-4, Pag. 191-209, January 2011.
@article {rgon:11, author = {R. Gon\c{c}alves and C. Caleiro}, title = {Towards a Behavioral Algebraic Theory of Logical Valuations}, journal = {Fundamenta Informaticae}, volume = {106}, number = {2-4}, pages = {191-209}, abstract = {Logical matrices are widely accepted as the semantic structures that most naturally fit the traditional approach to algebraic logic. The behavioral approach to the algebraization of logics extends the applicability of the traditional methods of algebraic logic to a wider range of logical systems, possibly encompassing many-sorted languages and non-truth-functional phenomena. However, as one needs to work with behavioral congruences, matrix semantics are unsuited to the behavioral setting. In [5], a promising version of algebraic valuation semantics was proposed in order to fill in this gap. Herein, we define the class of valuations that should be canonically associated to a logic, and we show, by means of new meaningful bridge results, how it is related to the behaviorally equivalent algebraic semantics of a behaviorally algebraizable logic.}, month = {January}, year = {2011}, }
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