Converting Non-Classical Matrix Proofs into Sequent-Style Systems.

Stephan Schmitt, Christoph Kreitz.

In M. McRobbie & J. Slaney eds., 13th International Conference on Automated Deduction (CADE-13),
LNCS 1104, pp. 418-432, Springer Verlag, 1996.


We present a uniform algorithm for transforming matrix proofs in classical, constructive, and modal logics into sequent style proofs. Making use of a similarity between matrix methods and Fitting's prefixed tableaus we first develop a procedure for extracting a prefixed sequent proof from a given matrix proof. By considering the additional restrictions on the order of rule applications we then extend this procedure into an algorithm which generates a conventional sequent proof.
Our algorithm is based on unified representations of matrix characterizations for various logics as well as of prefixed and usual sequent calculi. The peculiarities of a logic are encoded by certain parameters which are summarized in tables to be consulted by the algorithm.

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@InProceedings{inp:SchmittKreitz96a, author = "Stephan Schmitt and Christoph Kreitz", title = "Converting Non-Classical Matrix Proofs into Sequent-Style Systems", booktitle = "13$^{th}$ International Conference on Automated Deduction", year = 1996, editor = "M. McRobbie and J. Slaney", volume = 1104, series = "Lecture Notes in Artificial Intelligence", pages = "418--432", publisher = "Springer Verlag" }