Chains of structurally complete predicate logics with the application of Prucnal's substitution

• Autorzy: Dzik W.
• Języki publikacji: EN

Abstrakty

EN

A logical systems is structurally complete (or smooth) if structural and admissible rules are derivable in it. It is shown that if some peculiar "omitting" rules are neglected then classical predicate logic L2 is structurally complete. A unique structural and structurally complete extension of L2 is described. Next, it is shown that among negation-free intermediate predicate logics, there are chains of type ? ? + 1 of such logics (extension of Gödel-Dummett logic) which are hereditarily structurally complete. This is in contrast with the case of prepositional logics.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2004
• Tom: Nr 38
• Strony: 37--48

Twórcy

autor

Dzik W.

• Institute of Mathematics, Silesian University, Katowice, Poland

Bibliografia

• [1] E. Casari, P. Minari, Negation-Free Intermediate Predicate Logics, Bolletino Unione Matematica Italiana (6) 2B (1993), 499-536.
• [2] W. Dzik, A. Wroński, Structural completeness of Godel and Dummett’s propositional calculi, Studia Logica 32, 1973, pp. 69-73.
• [3] W. Dzik, On Structural completeness of some nonclassical predicate calculi, Reports on Mathematical Logic 5, 1975, pp. 19-26.
• [4] E. Mendelson, Introduction to Mathematical Logic, D. van Norstrand Co., Princeton New Jersey, 1964.
• [5] P. Minari, Kripke definable ordinals, Atti degli incontri di Logica Matematica Universita di Siena, vol.2, 1985, pp. 185-188.
• [6] S.C. Kleene, Disjunction and existence under implication in elementary intuitionistic formalism, JSL 27, 1962, pp. 11-18.
• [7] W.A. Pogorzelski, Structural completeness of the propositional calculus, Bulletin Acad. Polon. Sci. Ser. Sci. Math, vol.19, No.5. 1971, pp.349-351.
• [8] W.A. Pogorzelski, T. Prucnal, Structural completeness of the first-order predicate calculus, Zeitschrift f. Math. Log. und Grundl. der Math., Bd 21, 1975.
• [9] T. Prucnal, Structural completeness of some pure implicational propositional calculi, Studia Logica 30, 1972, pp. 45-51.
• [10] H. Rasiowa, R. Sikorski, The Mathematics of Metamathematics, PWN, Warszawa, 1970.
• [11] V.V. Rybakov, Hereditarily structurally complete modal logics, JSL vol 60, 1995, pp. 266-288.
• [12] D.P. Skvortsov, On axiomatizability of some intermediate logics, Reports on Mathematical Logic 22, 1988, pp. 115-116.