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@article{1389554, author = {Chajda, Ivan and Paseka, Jan}, article_location = {PHILADELPHIA}, article_number = {1}, keywords = {De Morgan lattice; De Morgan poset; tense operators; dynamic De Morgan algebra}, language = {eng}, issn = {1542-3980}, journal = {JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING}, title = {De Morgan Algebras with Tense Operators}, volume = {28}, year = {2017} }
TY - JOUR ID - 1389554 AU - Chajda, Ivan - Paseka, Jan PY - 2017 TI - De Morgan Algebras with Tense Operators JF - JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING VL - 28 IS - 1 SP - 29-45 EP - 29-45 PB - OLD CITY PUBLISHING INC SN - 15423980 KW - De Morgan lattice KW - De Morgan poset KW - tense operators KW - dynamic De Morgan algebra N2 - To every propositional logic satisfying double negation law is assigned a De Morgan poset epsilon. Using of axioms for an universal quantifier, we set up axioms for the so-called tense operators G and H on E. The triple D = (epsilon; G, H) is called a (partial) dynamic De Morgan algebra. We solve the following questions: first, if a time frame is given, how to construct tense operators G and H; second, if a (strict) dynamic De Morgan algebra is given, how to find a time frame such that its tense operators G and H can be reached by this construction. In particular, any strict dynamic De Morgan algebra is representable in its Dedekind-MacNeille completion with respect to a suitable countable time frame. ER -
CHAJDA, Ivan a Jan PASEKA. De Morgan Algebras with Tense Operators. \textit{JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING}. PHILADELPHIA: OLD CITY PUBLISHING INC, 2017, roč.~28, č.~1, s.~29-45. ISSN~1542-3980.
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