Journal of Symbolic Computation
Dissolution: making paths vanish
Journal of the ACM (JACM)
A Proof Procedure Using Connection Graphs
Journal of the ACM (JACM)
Resolution Strategies as Decision Procedures
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Completeness, Confluence, and Related Properties of Clause Graph Resolution
Completeness, Confluence, and Related Properties of Clause Graph Resolution
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
The unit preference strategy in theorem proving
AFIPS '64 (Fall, part I) Proceedings of the October 27-29, 1964, fall joint computer conference, part I
An Open Research Problem: Strong Completeness of R. Kowalski's Connection Graph Proof Procedure
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II
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Connection graph resolution (cg-resolution) was introduced by Kowalski as a means of restricting the search space of resolution. Several researchers expected unrestricted connection graph (cg) resolution to be strongly complete until Eisinger proved that it was not. In this paper, ordered resolution is shown to be a special case of cg-resolution, and that relationship is used to prove that ordered cg-resolution is strongly complete. On the other hand, ordered resolution provides little insight about completeness of first order cg-resolution and little about the establishment of strong completeness from completeness. A first order version of Eisinger's cyclic example is presented, illustrating the difficulties with first order cg resolution. But resolution with selection functions does yield a simple proof of strong cg-completeness for the unit-refutable class.