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Sequent calculi for logics of free-quantifier functional levels
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UDC: 004.42:510.69
Publication Language: Ukrainian
Stuc. intelekt. 2016; 21(4):50-62
Abstract: In this paper we specify sequent calculi for free-quantifier functional logics and their variants with weak and strong equality. The introduced calculi formalize irrefutability, truth, falsity and strong logical consequence relations. For the proposed calculi we prove the soundness and completeness theorems. On the base of the completeness theorems we obtain an algorithmic solvability of problems of existence of logical consequence for finite sets of formulas, irrefutability problems and identically truth problems for formulas.
Keywords: logic, free-quantifier functional level, sequent calculus, completeness
References:
- Handbook of Logic in Computer Science / Edited by S. Abramsky, Dov M. Gabbay and T. S. E. Maibaum. – Oxford University Press, Vol. 1–5, 1993–2000.
- Nikitchenko M.S. Matematychna logika ta teoria algorytmiv / M.S. Nikitchenko, S.S. Shkilniak. – К.: VPC Kyivskyi universytet, 2008. – 278 s.
- Shkilniak S.S. Bezkvantorno-funkcionalni logiky chastkovyh kvaziarnyh predykativ / S.S. Shkilniak, D.B. Volkovyts'kyy // Visnyk Kyivskoho universytetu imeni Tarasa Shechenka. Ser.: phiz.-mat. nauky. – 2015. – Vyp. 3. – S. 148–154.
- Shkilniak S.S. Kompozycijno-nominatyvni logiky bezkvantornyh rivniv / S.S. Shkilniak, D.B. Volkovyts'kyy // Problemy programuvannia. – 2016. – # 2–3 – S. 48–62.
- Nikitchenko M.S. Chysti pershoporiadkovi logiky kvaziarnyh predykativ / M.S. Nikitchenko, S.S. Shkilniak // Problemy programuvannia. – 2016. – # 2–3. – S. 73–86.