Algebras of general non-deterministic predicates

• Дата: 2018
• Автори: Nikitchenko, M.S., Shkilniak, O.S., Shkilniak, S.S.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: PROBLEMS IN PROGRAMMING 2018
• Теми: logic; algebra; non-deterministic predicate; logical consequence; UDC 004.42:510.69
• Онлайн доступ: https://pp.isofts.kiev.ua/index.php/ojs1/article/view/227
• Назва журналу: Problems in programming

Logics of general nondeterministic qua-siary predicates, called GND-predicates, are defined and investigated. These logics are program-oriented logical for-malisms that reflect such properties of programs as partiality, nondeterminism, and non-fixed arity. GND-predicates generalize partial predicates of the rela-tional type. The main attention is paid to the construction of composition algebras of GND-predicates. Compositions of GND-predicates are described, their properties are formulated. For these predicates, such important laws of tradi-tional logic as the law of absorption and the law of distributivity for for and are not valid. Various types of GND-predicates are identified. GND-predicates can be modeled as 7-value total deter-ministic predicates (TD7-predicates). A 7-element algebra of truth values of TD7-predicates is defined and all of its subalgebras are described. Each such subalgebra induces a corresponding al-gebra of TD7-predicates, which then in-duces the algebra of GND-predicates. This makes possible to identify a number of important composition algebras of general nondeterministic predicates. The languages of pure first-order logics of GND-predicates and their interpretations are described. The relations of a logical G-consequence and a logical G-equivalence are introduced. The relation of the logical G-consequence is mono-tonic, reflexive, and transitive; for it the properties of the decomposition of for-mulas are satisfied. On the basis of these properties, it is planned to construct cal-culi of sequential type for the logic of GND-predicates.Problems in programming 2018; 1: 05-21