Towards a Behavioral Algebraic Theory of Logical Valuations

Authors:
Carlos Caleiro;Ricardo Gonçalves
Affiliations:
SQIG - Instituto de Telecomunicações and Dept. Mathematics, IST, TU Lisbon, Portugal. caleiro@gmail.com;(Correspd.) CENTRIA, FCT-UNL, Portugal. rjrg@fct.unl.pt
Venue:
Fundamenta Informaticae - Logic, Language, Information and Computation
Year:
2011

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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.