论文信息 - Indexed systems of sequents and cut-elimination

Indexed systems of sequents and cut-elimination

Cut reductions are defined for a Kripke-style formulation of modal logic in terms of indexed systems of sequents. A detailed proof of the normalization (cut-elimination) theorem is given. The proof is uniform for the propositional modal systems with all combinations of reflexivity, symmetry and transitivity for the accessibility relation. Some new transformations of derivations (compared to standard sequent formulations) are needed, and some additional properties are to be checked. The display formulations of the systems considered can be presented as encodings of Kripke-style formulations.

Grigori Mints | G. Mints

[1] Saul A. Kripke,et al. Semantical Analysis of Intuitionistic Logic I , 1965 .

[2] G. Mints. A Short Introduction to Modal Logic , 1992 .

[3] Lincoln A. Wallen,et al. Automated deduction in nonclassical logics , 1990 .

[4] Grigori Mints,et al. Selected papers in proof theory , 1992 .

[5] M. Fitting. Proof Methods for Modal and Intuitionistic Logics , 1983 .

[6] G. Gentzen. Untersuchungen über das logische Schließen. I , 1935 .

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

[8] Stephen Cole Kleene,et al. Two papers on the predicate calculus , 1952 .

[9] Max J. Cresswell,et al. A New Introduction to Modal Logic , 1998 .

[10] Saul A. Kripke,et al. Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi , 1963 .

[11] Hans Jürgen Ohlbach,et al. Semantics-Based Translation Methods for Modal Logics , 1991, J. Log. Comput..

[12] Heinrich Wansing,et al. Sequent Calculi for Normal Modal Proposisional Logics , 1994, J. Log. Comput..