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Interpolative Boolean logic. (English) Zbl 1169.03344
Dochev, Danail (ed.) et al., Artificial intelligence: Methodology, systems, and applications. 13th international conference, AIMSA 2008, Varna, Bulgaria, September 4–6, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-85775-4/pbk). Lecture Notes in Computer Science 5253. Lecture Notes in Artificial Intelligence, 209-219 (2008).
Summary: A polyvalent propositional logic $$\mathcal L$$ is in the 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 the 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.
For the entire collection see [Zbl 1147.68004].

##### MSC:
 03B52 Fuzzy logic; logic of vagueness
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