﻿ Semantic properties of five-valued logics | Nikitchenko | PROBLEMS IN PROGRAMMING

DOI: https://doi.org/10.15407/pp2018.01.022

### Semantic properties of five-valued logics

M.S. Nikitchenko, E.V. Shyshatska

#### Abstract

A new class of program-oriented logical formalisms – propositional five-valued logics and five-valued logics of quasiary predicates is proposed and studied in the article. The quasiarity of predicates means that their arity is not fixed. A special feature of such five-valued logics is the use of special truth values, indicating errors or uncertainties in various systems, in particular, software systems. The article gives an ontological justification of five-valued logics and examines their examples. For the propositional level, an algebra of truth values is constructed and its semantic properties are studied. For the predicate level, the five-valued logic of quasiary predicates is constructed, its semantic properties are studied, the relation of equivalence of formulas and the relation of logical consequence are introduced, the principle of duality is proved and various normal forms are considered. Further research is focused on constructing algorithms for checking satisfiability and refutability of formulas and constructing various types of calculi for the introduced logics.

Problems in programming 2018; 1: 22-35

#### Keywords

program system; five-valued function; five-valued predicate; algebra; logic

PDF (Russian)

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DOI: https://doi.org/10.15407/pp2018.01.022

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