Journal ArticleDOI
A Linear Format for Resolution With Merging and a New Technique for Establishing Completeness
Robert Anderson,W. W. Bledsoe +1 more
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The main new result obtained is that a linear format for resolution with merging and set of support and with several further restrictions is a complete deductive system for the first-order predicate calculus.Abstract:
A new technique is given for establishing the completeness of resolution-based deductive systems for first-order logic (with or without equality) and several new completeness results are proved using this technique. The technique leads to very simple and clear completeness proofs and can be used to establish the completeness of most resolution-based deductive systems reported in the literature. The main new result obtained by means of this technique is that a linear format for resolution with merging and set of support and with several further restrictions is a complete deductive system for the first-order predicate calculus.read more
Citations
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Journal ArticleDOI
Logical foundations of object-oriented and frame-based languages
TL;DR: A novel formalism, called Frame Logic (abbr., F-logic), is proposed, that accounts in a clean and declarative fashion for most of the structural aspects of object-oriented and frame-based languages.
Book ChapterDOI
Linear Resolution with Selection Function
TL;DR: Linear resolution with selection function (SL-resolution) as mentioned in this paper is a restricted form of linear resolution with a selection function which chooses from each clause a single literal to be resolved upon in that clause.
Journal ArticleDOI
Automated deduction by theory resolution
Mark E. Stickel,Mark E. Stickel +1 more
TL;DR: Theoretical resolution as mentioned in this paper is a set of complete procedures for incorporating theories into a resolution theorem-proving program, thereby making it unnecessary to resolve directly upon axioms of the theory.
Book
The Resolution Calculus
TL;DR: This is a completely new presentation of resolution as a logical calculus and as a basis for computational algorithms and decision procedures and a systematic treatment of recent research topics.
Journal ArticleDOI
Partition-based logical reasoning for first-order and propositional theories
Eyal Amir,Sheila A. McIlraith +1 more
TL;DR: It is shown how tree decomposition can be applied to reasoning with first-order and propositional logic theories and a greedy algorithm is provided that automatically decomposes a set of logical axioms into partitions, following this analysis.
References
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Journal ArticleDOI
A Machine-Oriented Logic Based on the Resolution Principle
TL;DR: The paper concludes with a discussion of several principles which are applicable to the design of efficient proof-procedures employing resolution as the basle logical process.
Journal ArticleDOI
Efficiency and Completeness of the Set of Support Strategy in Theorem Proving
TL;DR: Evidence of the efficiency of the set of support strategy is presented, and a theorem giving sufficient conditions for its logical completeness is proved.
Book ChapterDOI
A Linear Format for Resolution
TL;DR: The Resolution procedure of J. A. Robinson is shown to remain a complete proof procedure when the refutations permitted are restricted so that clauses C and D and resolvent R of clauses c and D meet the following conditions: (1) C is the resolver immediately preceding R in the refutation if any resolver precedes R, (2) either D is a member of the given set S of clauses or D precedes C in this article.
Book ChapterDOI
E-resolution: extension of resolution to include the equality relation
TL;DR: The E-Resolution inference principle is a single-inference logic system for the first-order predicate calculus with equality, where special axioms for equality are not required to be added to the original set of clauses.
Book ChapterDOI
Refinement Theorems in Resolution Theory
TL;DR: It is proved that two of the refinements of the Resolution Principle preserve the logical completeness of the proof procedure when used separately, but not when used in conjunction.