15-815 Automated Theorem Proving
Lecture 19: Matrix Methods

In labeled sequent calculus or tableaux, we still have to make non-deterministic choices during proof search because the right rule for implication introduces a label parameter that may be needed by a left rule for implication. In matrix methods this non-determinism is removed by always full decomposing the proposition, applying label unification for initial sequents, and then verifying that the left and right implication inferences can be done in some order.

We further show how to generalize labeled sequent calculus and then the matrix methods to the first order case. Again, we fully decompose the proposition, unify the terms for initial sequents, and then verify that the inference can be carried out in a proper order.

[W01] Arild Waaler.
Connections in nonclassical logics.
Handbook of Automated Reasoning, Vol.2, pp.1487-1578, Elsevier Science and MIT Press, 2001.
[KS00] Christoph Kreitz and Stephan Schmitt.
A Uniform Procedure for Converting Matrix Proofs into Sequent-Style Systems.
Information & Computation 162(1-2), pp.226-254, 2000.
[W90] Lincoln Wallen.
Automated Proof Search in Non-Classical Logics.
MIT Press, 1990.

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Frank Pfenning