DOI : 10.14738/tmlai.71.6187 Publication Date: 23 rd February, 2019 URL: http://dx.doi.org/10.14738/tmlai.71.6187 Volume 7 No. 1 Investigation of the Proof Complexity Measures of Strongly Equal K-Tautologies in Some Proof Systems Anahit Chubaryan, Artur Khamisyan, Garik Petrosyan Department of Informatics and Applied Mathematics Yerevan State University achubaryan@ysu.am, Artur.Khamisyan@gmail.com, garik.petrosyan.1@gmail.com ABSTRACT Here we generalize the notions of determinative conjunct and strongly equal tautologies formany-valued logic (MVL) and compare the proof complexity measures of strongly equal many-valued tautologies in some proof systems of MVL. It is proved that in some “weak” proof system the strongly equal many- valued tautologies have the same proof complexities, while in the “strong” proof systems the measures of proof complexities for strongly equal tautologies can essentially differ from each other. Keywords: many-valued logic, determinative conjunct, strongly equal tautologies, proof complexity characteristics. 1 Introduction In the mean time many interesting applications of many-valued logic (MVL) were found in such fields as Logic, Mathematics, Formal Verification, Artificial Intelligence, Operations Research, Computational Biology, Cryptography, Data Mining, Machine Learning, Hardware Design etc., therefore the investigations of proof complexity for different systems of MVL are very important. The traditional assumption that all tautologies as Boolean functions are equal to each other is not fine- grained enough to support a sharp distinction among tautologies. The authors of [1] have provided a different picture of equality for classical tautologies. They have introduced the notion of strong equality of 2-valued tautologies on the basis of determinative conjunct notion. The idea to revise the notion of equivalence between tautologies in such way that is takes into account an appropriate measure of their “complexity”. It was proved in [2,3] that in “weak” proof systems the strongly equal 2-valued tautologies have the same proof complexities, while in the “strong” proof systems the measures of proof complexities for strongly equal tautologies can essentially differ from each other. Here we generalize the notions of determinative conjunct and strongly equal tautologies for MVL and compare the proof complexity measures of strongly equal many-valued tautologies in some proof systems of MVL.