Hyper-chaining and knowledge-based theorem proving

Hines, Larry

doi:10.1007/bfb0012850

Cited by 4 publications

(2 citation statements)

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“…The improvements are not only of theoretical significance, as experimental evidence indicates that equational inference mechanisms, such as superposition and demodulation, are preferable to explicit axiomatizations of equality. Some form of equational reasoning appears to be used in the provers described by Bledsoe and Hines (1980), Hines (1988) and Hines (1990), and inference systems with equational reasoning capabilities may provide a better approximation to actual implementation practice than other chaining systems.…”

Section: Discussionmentioning

confidence: 99%

“…Completeness results for particular such systems of restricted chaining are proved by Bledsoe, Kunen and Shostak (1985) and Hines (1992). Theorem provers developed from these theoretical investigations have performed successfully in proving theorems such as the continuity of the sum of two continuous functions or the intermediate value theorem; see Bledsoe and Hines (1980), Hines (1988) or Hines (1990).…”

Section: Introductionmentioning

confidence: 99%

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Ordered chaining for total orderings

Bachmair

Ganzinger

1994

Automated Deduction — CADE-12

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We design new inference systems for total orderings by applying rewrite techniques to chaining calculi. Equality relations may either be specified axiomatically or built into the deductive calculus via paramodulation or superposition. We demonstrate that our inference systems are compatible with a concept of (global) redundancy for clauses and inferences that covers such widely used simplification techniques as tautology deletion, subsumption, and demodulation. A key to the practicality of chaining techniques is the extent to which so-called variable chainings can be restricted. Syntactic ordering restrictions on terms and the rewrite techniques which account for their completeness considerably restrict variable chaining. We show that variable elimination is an admissible simplification techniques within our redundancy framework, and that consequently for dense total orderings without endpoints no variable chaining is needed at all.

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Section: Discussionmentioning

confidence: 99%