On Skolemization And Proof Complexity

Authors:
Matthias Baaz;Alexander Leitsch
Affiliations:
Institut für Algebra und Diskrete Mathematik, Technische Universität Wien, Wiedner Hauptstraβe 8-10, A-1040 Wien, Austria;Institut für Computersprachen, Technische Universität Wien, Resselgasse 3, A-1040 Wien, Austria, email, leitsch@csdecl.twwien.ac.at
Venue:
Fundamenta Informaticae
Year:
1994

Citing 4
Cited 5

Inference with path resolution and semantic graphs

Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle

Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving

Symbolic Logic and Mechanical Theorem Proving
Automated theorem proving: A logical basis (Fundamental studies in computer science)

Automated theorem proving: A logical basis (Fundamental studies in computer science)

CERES: An analysis of Fürstenberg's proof of the infinity of primes

Theoretical Computer Science
Translation of resolution proofs into short first-order proofs without choice axioms

Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Towards a clausal analysis of cut-elimination

Journal of Symbolic Computation
On the elimination of quantifier-free cuts

Theoretical Computer Science
On Definitional Transformations To Normal Form For Intuitionistic Logic

Fundamenta Informaticae

Quantified Score

Hi-index	0.00

Visualization

Abstract

The impact of Skolemization on the complexity of proofs in the sequent calculus is investigated. It is shown that prefix Skolemization may result in a nonelementary increase of Herbrand complexity (i. e. the minimal number of constituents in a Herbrand disjunction) versus structural Skolemization. Moreover it is shown that restricting the range of quantifiers never increases Herbrand complexity. The results provide a general mathematical justification for minimizing the range of quantifiers (by means of shifting) before Skolemization of formulas.