Sequent calculi of first-order logics of partial predicates with extended renominations and composition of predicate complement

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

Abstract


We study new classes of program-oriented logical formalisms – pure first-order logics of quasiary predicates with extended renominations and a composition of predicate complement. For these logics, various logical consequence relations are specified and corresponding calculi of sequent type are constructed. We define basic sequent forms for the specified calculi and closeness conditions. The soundness, completeness, and counter-model existence theorems are proved for the introduced calculi.

Problems in programming 2020; 2-3: 182-197


Keywords


logic; partial predicate; logical consequence; sequent calculus; soundness; completeness

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References


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

University Press.

Kleene S. (1967) Mathematical Logic. New York.

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

Shkilniak S. (2013). Spectrum of sequent calculi of first-order composition-nominative logics. Problems in Progamming. N 3.

P. 22–37 (in ukr).

Nikitchenko M., Shkilniak O. and Shkilniak S. (2014). First-order composition-nominative logics with generalized renominations.

Problems in Progamming. N 2–3. P. 17–28 (in ukr).

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

P. 73–86 (in ukr).

Hoare C. (1969). An axiomatic basis for computer programming, Comm. ACM 12(10). P. 576–580.

Apt K. (1981). Ten years of Hoare’s lo¬gic: a survey – part I, ACM Trans. Program. Lang. Syst. 3(4). P. 431–483

Nikitchenko M., Shkilniak O., Shkilniak S. and Mamedov T. (2019). Propositional logics of partial predicates with composition of predicate complement. Prob¬lems in Progamming. N 1. P. 3–13 (in ukr).

Nikitchenko M., Shkilniak O. and Shkilniak S. (2019). Program Logics of Renominative Level with the Composition of Predicate Complement. Proceedings of the 15th International Conference on ICT. CEUR Workshop, Kherson, Ukraine. Vol. 2393. P. 603–616.

Nikitchenko M., Shkilniak O., Shkilniak S. and Mamedov T. (2019). Completeness of the First-Order Logic of Partial Quasiary Predicates with the Complement Composition. Computer Science Journal of Moldova, Vol. 27, N 2 (80). P.162–187.

Shkilniak O. (2019). Relations of logical consequence of logics of partial predicates with composition of predicate complement. Problems in Progamming. N 3. P. 11–27 (in ukr).


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