By David A. Plaisted

ISBN-10: 332293862X

ISBN-13: 9783322938626

ISBN-10: 352805574X

ISBN-13: 9783528055745

Inhalt

Bereitstellung asymptotischer Schranken f?r die Gr??e von Suchfeldern der von vielen gebr?uchlichen Beweisstrategien erzeugten Suchr?ume - Gewinnung eines theoretischen Verst?ndnisses der Effizienz unterschiedlicher Beweisverfahren - Effizienzvergleich von Beweisstrategien Asymptotic bounds at the sizes of the quest areas generated by means of many universal theorem proving options - gaining a theoretical realizing of the efficiencies of many various theorem proving tools - a comparative learn of theorem proving strategies

Zielgruppe

Studierende und Forscher der Informatik und Mathematik mit Schwerpunkten im Bereich des automatischen Theorembeweisens, der mathematischen Logik, bzw. der Logik K?nstlicher Intelligenz

?ber den Autor/Hrsg

David A. Plaisted ist seit 1984 Professor am Fachbereich Informatik der college of North Carolina. Seine gegenw?rtigen Forschungen umfassen automatisches Theorembeweisen, Termersetzungssysteme sowie funktionale und Logikprogrammierung. Yunshan Zhu ist Mitarbeiter am selben Fachbereich der UNC. Sein Forschungsinteresse gilt dem automatischen Theorembeweisen, formalen Methoden und logikbasierten Methoden der K?nstlichen Intelligenz. due to the fact 1984 David A. Plaisted is professor within the division of machine technology on the college of North Carolina. His present pursuits comprise theorem proving, term-rewriting structures and common sense and practical programming. Yunshan Zhu is also a member of the dep. of computing device technology on the college of North Carolina. Zhu's present examine pursuits contain theorem proving, formal equipment and logical ways of synthetic Intelligence.

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**Additional resources for The Efficiency of Theorem Proving Strategies: A Comparative and Asymptotic Analysis**

**Sample text**

A-ordering does not behave exactly like PI-deduction or like allnegative resolution with ordering. One would think that by choosing a suitable ordering we could simulate these, but it does not appear in general to be possible. We would have to make the unit clauses maximal in the ordering to simulate PI deduction, but because these unit clauses may also appear elsewhere, some non-PI deductions may occur. For example, we could have a clause set containing, among other clauses, of Theorem Proving Strategies 25 {-,Q, P}, {P}, and {-'P, R}.

Also, the same analysis applies to hyperresolution enhanced with any literal ordering method (ordering of the positive literals), since in the Horn case each clause has at most one positive literal. 3 PI deduction Pi-deduction is the strategy that resolves two clauses only if one of them is positive [Rob65a]. For Horn clauses, as in hyper-resolution, this produces a clause that subsumes its parent. For example, if we resolve P (which is positive) and {-,P, -'Q, R} we obtain {-,Q, R}, which subsumes {-'P, -'Q, R}.

We show an exponential lower bound even with them deleted, which implies an exponential lower bound if they are retained. 16 for individual clauses. 18 Suppose Al for PI and A2 for P 2 are two clusters, of heights hi and h2' respectively, where hi + h2 :::; n. Suppose that there is a frontier position a of A2 which is also the distinguished position of AI' Suppose that Po: or Qo: is the maximal predicate symbol in both clusters, in an ordering < on predicate symbols. Then in one round of breadth-first A -ordering resolution using this ordering, we can l'esolve on Po: or Qo: and generate a cluster A of height hi + h2 - 1.

### The Efficiency of Theorem Proving Strategies: A Comparative and Asymptotic Analysis by David A. Plaisted

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