论文信息 - Sequent calculus proof theory of intuitionistic apartness and order relations

Sequent calculus proof theory of intuitionistic apartness and order relations

Abstract. Contraction-free sequent calculi for intuitionistic theories of apartness and order are given and cut-elimination for the calculi proved. Among the consequences of the result is the disjunction property for these theories. Through methods of proof analysis and permutation of rules, we establish conservativity of the theory of apartness over the theory of equality defined as the negation of apartness, for sequents in which all atomic formulas appear negated. The proof extends to conservativity results for the theories of constructive order over the usual theories of order.

Sara Negri

[1] Roy Dyckhoff,et al. Admissibility of Structural Rules for Contraction-Free Systems of Intuitionistic Logic , 2000, J. Symb. Log..

[2] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.

[3] A. G. Dragálin. Mathematical Intuitionism. Introduction to Proof Theory , 1988 .

[4] R. Statman,et al. Equality in the Presence of Apartness , 1979 .

[5] Lev Gordeev,et al. Basic proof theory , 1998 .

[6] Dana S. Scott. Extending the topological interpretation to intuitionistic analysis , 1968 .

[7] G. Jantzen. 1988 , 1988, The Winning Cars of the Indianapolis 500.

[8] Jan von Plato,et al. From Kripke Models to Algebraic Counter-Valuations , 1998, TABLEAUX.

[9] Craig Smorynski. On Axiomatizing Fragments , 1977, J. Symb. Log..

[10] S. C. Kleene,et al. Introduction to Metamathematics , 1952 .

[11] T. Coquand,et al. The Hahn-Banach Theorem in Type Theory , 1998 .

[12] Dana S. Scott,et al. Extending the Topological Interpretation to Intuitionistic Analysis, II , 1970 .

[13] G. Gentzen. New version of the consistency proof for elementary number theory , 1969 .

[14] Roy Dyckhoff,et al. Contraction-free sequent calculi for intuitionistic logic , 1992, Journal of Symbolic Logic.

[15] Jiirg Hudelmaier,et al. Bounds for cut elimination in intuitionistic propositional logic , 1992, Arch. Math. Log..