Open AccessPure first-order logics of quasiary predicates
Author(s) -
Mykola S. Nikitchenko,
Oksana Shkilniak,
S.S. Shkilniak
Publication year - 2016
Publication title -
problemy programmirovaniâ
Language(s) - English
Resource type - Journals
ISSN - 1727-4907
DOI - 10.15407/pp2016.02-03.073
Subject(s) - sequent , closure (psychology) , interpretation (philosophy) , sequent calculus , mathematics , quantifier (linguistics) , first order , order (exchange) , monoidal t norm logic , quantifier elimination , t norm fuzzy logics , type (biology) , discrete mathematics , algebra over a field , computer science , pure mathematics , programming language , artificial intelligence , law , fuzzy logic , ecology , membership function , biology , geometry , political science , fuzzy set , fuzzy number , mathematical proof , finance , economics
Pure first-order logics of partial and total, single-valued and multi-valued quasiary predicates are investigated. For these logics we describe semantic models and languages, giving special attention in our research to composition algebras of predicates and interpretation classes (sematics), and logical consequence relations for sets of formulas. For the defined relations a number of sequent type calculi is constructed; their characteristic features are extended conditions for sequent closure and original forms for quantifier elimination.