Relevancy Based Use of Lemmas in Connection Tableau Calculi

Automated deduction is a fundamental research area in the field of artificial intelligence. The aim of an automated deduction system is to find a formal proof for a given goal based on given axioms. Essentially automated deduction can be viewed as a search problem which spans huge search spaces. One main thrust of research in automated deduction is the development of techniques for achieving a reduction of the search space. A particularly promising approach for search space reduction...
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Automated deduction is a fundamental research area in the field of artificial intelligence. The aim of an automated deduction system is to find a formal proof for a given goal based on given axioms. Essentially automated deduction can be viewed as a search problem which spans huge search spaces. One main thrust of research in automated deduction is the development of techniques for achieving a reduction of the search space. A particularly promising approach for search space reduction relies on the integration of top-down and bottom-up reasoning. A possible approach employs bottom-up generated lemmas in top-down systems. Lemma use offers the possibility to shorten proofs and to overcome weaknesses of top-down systems like poor redundancy control. In spite of the possible advantages of lemma use, however, naive approaches for lemma integration even tend to slow down top-down systems. The main problem is the increased indeterminism in the search process. In this thesis important contributions for a successful application of lemmas in top-down deduction systems based on connection tableau calculi are made. New methods for lemma generation and for the estimation of the relevancy of lemmas are developed. As a practical contribution, the implementation of the new techniques leads to a powerful system for automated deduction which demonstrates the high potential of the new techniques.