A Machine-Oriented Logic Based on the Resolution Principle

  title={A Machine-Oriented Logic Based on the Resolution Principle},
  author={John Alan Robinson},
  journal={J. ACM},
:tb.~tract. [] Key Method The theory of the resolution process is presented in the form of a system of first<~rder logic with .just one inference principle (the resolution principle). The completeness of the system is proved; the simplest proof-procedure based oil the system is then the direct implementation of the proof of completeness. Howew~r, this procedure is quite inefficient, ~nd the paper concludes with a discussion of several principles (called search principles) which are applicable to the design…

Theorem-Proving for Computers: Some Results on Resolution and Renaming

A considerable step forward in the development of theorem-proving by machine was taken by Robinson (1965) with the introduction of the resolution method, which shows that the original set is unsatisfiable if and only if an empty clause can be generated.

Note on theorem proving strategies for resolution counterparts of non-classical logics

Two of the more powerful speed-up techniques available for classical first-order logic, namely the set of support and the polarity strategies can be formulated and applied to resolution proof systems for non-classical logics are shown.

A pragmatic approach to resolution-based theorem proving

  • Judy A. Townley
  • Computer Science
    International Journal of Computer & Information Sciences
  • 2004
i-resolution does not preserve completeness; it does define a means for approaching completeness efficiently and systematically, and attempts to provide a pragmatic approach to mechanical theorem proving.

Proof Procedure based on Modified Analytic Tableaux

The modified analytic tableaux is a variant of the "analytic tableaux" of Smullyan and is compatible with the resolu- tion method, which forms the basis for probably all contemporary theorem- provers for predicate calculus.

Investigations into the complexity of some propositional calculi

It is shown that KE, though being ‘close’ to the tableau method and sharing all its desirable features, is essentially more efficient, owing to the fact that KE establishes a closer connection with the intended (classical, bivalent) semantics.

Computer-Oriented Calculi of Sequent Trees

The problem of construction of a computer-oriented technique for inference search based on a certain sequent formalism for first-order classical logic with equality is solved. For this, special

Completeness of Resolution for Definite Answers

The A-resolution calculus is complete in the following sense: if such a deenite substitution exists, then the A-calculus derives a clause giving such a substitution, and the result is strengthened by allowing the usage of liftable criterias R of a certain type, prohibiting the derivation of the substitution terms t for which R(t) fails.

SETHEO: A high-performance theorem prover

A sound and complete theorem prover for first-order logic is presented, which is based on the connection method, and incorporates a powerful preprocessing module for a reduction of the input formula.

Completeness results for e-resolution

The purpose of this paper is to define E-resolution in terms of paramodulation and resolution and to prove the completeness ofE-resolution and several modifications of E- resolution.

Automatic Theorem Proving With Renamable and Semantic Resolution

The theory of J. A. Robinson's resolution principle, an inference rule for first-order predicate calculus, is unified and extended. A theorem-proving computer program based on the new theory is



Theorem-Proving on the Computer

The paper discusses the "combinatorial explosion" difficulties encountered by computer programs embodying proof-construction procedures, and a program developed at Argonne National Laboratory is described in which these difficulties are somewhat alleviated in two ways.

A Computing Procedure for Quantification Theory

In the present paper, a uniform proof procedure for quantification theory is given which is feasible for use with some rather complicated formulas and which does not ordinarily lead to exponentiation.

A Proof Method for Quantification Theory: Its Justification and Realization

A program is described which can provide a computer with quick logical facility for syllogisms and moderately more complicated sentences. The program realizes a method for proving that a sentence of

A Semi-Decision Procedure for the Functional Calculus

Algorithms by which decision procedures for the functional calculus can be applied mechanically and it is proved that the method provides a solution to the decision problem in the sense that the given expression is a theorem if and only if M* is tautologous.

A note on the Entscheidungsproblem

  • A. Church
  • Mathematics
    Journal of Symbolic Logic
  • 1936
It is shown that the general case of the Entscheidungsproblem is unsolvable in any system of symbolic logic which is adequate to a certain portion of arithmetic and is ω-consistent.