Interpolative Boolean Logic

Authors:
Dragan Radojević;Aleksandar Perović;Zoran Ognjanović;Miodrag Rašković
Affiliations:
Mihailo Pupin Institute, Belgrade, Serbia 11000;Faculty of Transportation and Traffic Engineering, Belgrade, Serbia 11000;Mathematical Institute SANU, Belgrade, Serbia 11000;Faculty of Transportation and Traffic Engineering, Belgrade, Serbia 11000
Venue:
AIMSA '08 Proceedings of the 13th international conference on Artificial Intelligence: Methodology, Systems, and Applications
Year:
2008

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Abstract

A polyvalent propositional logic $\mathcal L$ is in Boolean frame if the set of all $\mathcal L$-valid formulas coincides with the set of all tautologies. It is well known that the polyvalent logics based on the truth functionality principle are not in the Boolean frame. Interpolative Boolean logic (IBL) is a real-valued propositional logic that is in Boolean frame. The term "interpolative" cames from the fact that semantics of IBL is based on the notion of a generalized Boolean polynomial, where multiplication can be substituted by any continuous t-norm $*:[0,1]^2\longrightarrow [0,1]$ such that $xy\leqslant x* y$. Possible applications are illustrated with several examples.