We present the theoretical foundations of the many-valued generalization of a technique for simplifying large non-clausal formulas in propositional logic, that is called removal of anti-links. Possible applications include computation of prime implicates of large non-clausal formulas as required, for example, in diagnosis. With the anti-link technique, one does not compute any normal form of a ...

We introduce a suitable notion of bisimulation for the family of Heyting-valued modal logics introduced by M. Fitting. In this family of logics, each modal language is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language which is interpreted on relational frames with an H-valued accessibility relation. We prove that for...

Logical systems with classical negation and means for sentential or propositional self-reference involve, in some way, paradoxical statements such as the liar. However, the paradox disappears if one replaces classical by an appropriate non-classical negation such as a paraconsistent one (no paradox arises if the liar is both true and false). We consider a non-Fregean logic which is a revised an...

After Zadeh has introduced his theory, many-valued logic began to have a new interest. Especially, Łukasiewicz logic was enclosed quite closely in fuzzy sets. There is a strong opinion that Łukasiewicz infinite-valued logic has the role as the logic of fuzzy sets, similarly as classical logic has the role as the logic of crisp sets. But actually, it seems that Kleene’s 3-valued logic was the cl...

In this paper we discuss some generalizations of Ulam’s game with lies: some of them are simply probabilistic variants of it, some others differ from it by the presence of more than one number to guess. In the last part of the paper, we also discuss the relationship between such variants and many-valued logic. This paper is just a survey of known results, but in its last part it also contains s...

Description: The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to ...

ion in Formal Specification

The issue of rewarding partially correct answers has been addressed by many authors (Guzman, E. & Conejo, R., 2004, Gardner-Medwin, A.R. 1995, Huffman, D, Goldberg, F., & Michlin, M. 2003). Intelligent systems have been designed to assign scores related to the importance of missing or incorrect part of an answer. Such systems are meant to facilitate the process of knowledge assessment. While tr...

In this paper we present the theorem prover SBR3 for equational logic and its application in the many-valued logic of Lukasiewicz. We give a new equational axiomatization of many-valued logic and we prove by SBR3 that it is equivalent to the classical equational presentation of such logic given by Wajsberg. We feel that our equational axiomatization of Wajsberg algebras is more suited for autom...