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The Properties of Sets of Temporal Logic Subformulas

Mariusz Giero (2012)

Formalized Mathematics

This is a second preliminary article to prove the completeness theorem of an extension of basic propositional temporal logic. We base it on the proof of completeness for basic propositional temporal logic given in [17]. We introduce two modified definitions of a subformula. In the former one we treat until-formula as indivisible. In the latter one, we extend the set of subformulas of until-formulas by a special disjunctive formula. This is needed to construct a temporal model. We also define an...

The study on semicopula based implications

Zuming Peng (2020)

Kybernetika

Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula...

Theories of orders on the set of words

Dietrich Kuske (2006)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

It is shown that small fragments of the first-order theory of the subword order, the (partial) lexicographic path ordering on words, the homomorphism preorder, and the infix order are undecidable. This is in contrast to the decidability of the monadic second-order theory of the prefix order [M.O. Rabin, Trans. Amer. Math. Soc., 1969] and of the theory of the total lexicographic path ordering [P. Narendran and M. Rusinowitch, Lect. Notes Artificial Intelligence, 2000] and, in case of the subword...

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