A Machine-Oriented Logic Based on the Resolution Principle

Robinson, John A.

doi:10.1145/321250.321253

Cited by 2,934 publications

(338 citation statements)

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“…Automatic theorem proving in first-order logic is a significant field in its own right; one of its main achievements, though 20 years ago, is the solution of the Robbins conjecture [20]. Incidentally, two early titans of computational logic-Hilary Putnam [21] and Alan Robinson [22]-were trained as philosophers, and Putnam is chiefly remembered for his essays.…”

Section: Mechanized Logic: the Lcf Traditionmentioning

confidence: 99%

Computational logic: its origins and applications

Paulson¹

2018

Proc. R. Soc. A.

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Computational logic is the use of computers to establish facts in a logical formalism. Originating in nineteenth century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms, techniques and technologies. One strand of work follows the ‘logic for computable functions (LCF) approach’ pioneered by Robin Milner, where proofs can be constructed interactively or with the help of users’ code (which does not compromise correctness). A refinement of LCF, called Isabelle, retains these advantages while providing flexibility in the choice of logical formalism and much stronger automation. The main application of these techniques has been to prove the correctness of hardware and software systems, but increasingly researchers have been applying them to mathematics itself.

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Section: Mechanized Logic: the Lcf Traditionmentioning

confidence: 99%

Computational logic: its origins and applications

Paulson¹

2018

Proc. R. Soc. A.

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“…Among these, resolution R is probably one of the most investigated and perhaps the best known. This calculus is popularly credited to Robinson [32] but it was already contained in Blake's thesis [5] and is also an immediate consequence of Davis and Putnam's work [10].…”

Section: Propositional Logic Preliminaries: Interpolation and Feasiblmentioning

confidence: 99%

Some applications of propositional logic to cellular automata

Cavagnetto¹

2009

Mathematical Logic Qtrly

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In this paper we give a new proof of Richardson's theorem [31]: a global function G A of a cellular automaton A is injective if and only if the inverse of G A is a global function of a cellular automaton. Moreover, we show a way how to construct the inverse cellular automaton using the method of feasible interpolation from [20]. We also solve two problems regarding complexity of cellular automata formulated by Durand [12].

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“…We crib from various sources in so doing, but especially from Robinson's [25]. (Readers who know all this stuff should jump immediately to Section 5, referring back if they wish to align their preferred terminology with ours.…”

Section: T Unifiers and Most General Unifersmentioning

confidence: 99%

Implementing the ‘Fool's model’ of combinatory logic

1991

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This paper studies "Fool's models" of combmatory logic, and relates them to Hmdley's 'Dcompleteness" problem. A "fool's model' is a family of sets of ~ formulas, closed under condensed detachment. Alternatively, Jt is a 'model" of CL in naive set theory. We examine Resoluhon; and the P-W problem A sequel shows T~ is D-complete: also, its extensions We close wllh an lmplementaUon FMO of these ideas.

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A Machine-Oriented Logic Based on the Resolution Principle

Cited by 2,934 publications

References 3 publications

Computational logic: its origins and applications

Computational logic: its origins and applications

Some applications of propositional logic to cellular automata

Implementing the ‘Fool's model’ of combinatory logic

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