Logics of general non-deterministic predicates: semantic aspects

M.S. Nikitchenko, О.S. Shkilniak, S.S. Shkilniak

Abstract


Semantic aspects of a new class of program-oriented logical formalisms – logics of general non-deterministic quasiary predicates (GND-predicates) – are considered. Сlasses of GND-predicates are singled out, their compositions and algebras are investigated. The language of pure first-order logics of GND-predicates is described. The relation of the logical consequence for the sets of formulas is proposed and investigated. The properties of the decomposition of formulas and of quantifier elimination are described.

Problems in programming 2018; 2-3: 031-045


Keywords


logic; algebra; composition; non-deterministic predicate; logical consequence

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References


Abramsky S., Gabbay D. and Maibaum T. (editors). (1993–2000). Handbook of Logic in Computer Science. Oxford University Press.

Nikitchenko M. and Shkilniak S. (2008). Mathematical logic and theory of algorithms. Кyiv: VPC Кyivskyi Universytet (in ukr).

Nikitchenko M. and Shkilniak S. (2013). Applied logic. Кyiv: VPC Кyivskyi Universytet (in ukr).

Nikitchenko M. and Shkilniak S. (2015). Semantic Properties of Logics of Quasiary Predicates. In Workshop on Foundations of Informatics: Proceedings FOI-2015. Chisinau, Moldova. P. 180–197.

Shkilniak O. (2016). Logical consequence relations in logics of quasiary predicates. In Problems in Progamming. № 1. P. 29–43 (in ukr).

Nikitchenko M., Shkilniak O. and Shkilniak S. (2016). Pure first-order logics of quasiary predicates. In Problems in Progamming. N 2–3. P. 73–86 (in ukr).

Nikitchenko M. and Shkilniak S. (2017). Algebras and logics of partial quasiary predicates. In Algebra and Discrete Mathematics. Vol. 23. N 2. P. 263–278.

Avron A. and Zamansky A. (2011). Non-deterministic semantics for logical systems. In Handbook of Philosophical Logic, D.M. Gabbay, F. Guenthner (eds.), 2nd ed., vol. 16, Springer Netherlands. P. 227–304.

Nikitchenko M., Shkilniak O. and Shkilniak S. (2017). Logics of partial non-deterministic predicates. In International conference PDMU-2017: abstracts. Vilnius, Lithuania. P. 94–95.

Nikitchenko M., Shkilniak O. and Shkilniak S. (2018). Algebras of general non-deterministic predicates. In Problems in Progamming. N 1. P. 5–21 (in ukr).


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