Results 1  10
of
17
Equations and rewrite rules: a survey
 In Formal Language Theory: Perspectives and Open Problems
, 1980
"... bY ..."
The Applications of Theorem Proving to QuestionAnswering Systems
, 1969
"... This paper shows how a questionanswering system can use firstorder logic as its language and an automatic theorem prover, based upon the resolution inference principle, as its deductive mechanism. The resolution proof procedure is extended to a constructive proof procedure. An answer construction ..."
Abstract

Cited by 28 (0 self)
 Add to MetaCart
This paper shows how a questionanswering system can use firstorder logic as its language and an automatic theorem prover, based upon the resolution inference principle, as its deductive mechanism. The resolution proof procedure is extended to a constructive proof procedure. An answer construction algorithm is given whereby the system is able not only to produce yes or no answers but also to find or construct an object satisfying a specified condition. A working computer program, QA3, based on these ideas, is described. The performance of the program, illustrated by extended examples, compares favorably with several other questionanswering programs. Methods are presented for solving state transformation problems. In addition to questionanswering, the program can do automatic programming
Formalized mathematics
 TURKU CENTRE FOR COMPUTER SCIENCE
, 1996
"... It is generally accepted that in principle it’s possible to formalize completely almost all of presentday mathematics. The practicability of actually doing so is widely doubted, as is the value of the result. But in the computer age we believe that such formalization is possible and desirable. In c ..."
Abstract

Cited by 27 (0 self)
 Add to MetaCart
It is generally accepted that in principle it’s possible to formalize completely almost all of presentday mathematics. The practicability of actually doing so is widely doubted, as is the value of the result. But in the computer age we believe that such formalization is possible and desirable. In contrast to the QED Manifesto however, we do not offer polemics in support of such a project. We merely try to place the formalization of mathematics in its historical perspective, as well as looking at existing praxis and identifying what we regard as the most interesting issues, theoretical and practical.
AssociativeCommutative Deduction with Constraints
, 1993
"... Associativecommutative equational reasoning is known to be highly complex for theorem proving. Hence, it is very important to focus deduction by adding constraints, such as unification and ordering, and to define efficient strategies, such as the basic requirements `a la Hullot. Constraints are f ..."
Abstract

Cited by 18 (3 self)
 Add to MetaCart
Associativecommutative equational reasoning is known to be highly complex for theorem proving. Hence, it is very important to focus deduction by adding constraints, such as unification and ordering, and to define efficient strategies, such as the basic requirements `a la Hullot. Constraints are formulas used for pruning the set of ground instances of clauses deduced by a theorem prover. We propose here an extension of ACparamodulation and ACsuperposition with these constraint mechanisms ; we do not need to compute ACunifiers anymore. The method is proved to be refutationally complete, even with simplification. The power of this approach is exemplified by a very short proof of the equational version of SAM's Lemma using DATAC, our implementation of the strategy.
HOL Light Tutorial (for version 2.20)
, 2007
"... The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, aimed at teaching basic use of the system quickly by means of a graded set of examples. Some readers may find it easier to absorb; those who do not are referred after all to the standard manual. “Shouldn’t we read the instructions?”
Using Rippling for Equational Reasoning
 In Proceedings 20th German Annual Conference on Artificial Intelligence KI96
, 1996
"... . This paper presents techniques to guide equational reasoning in a goal directed way. Suggested by rippling methods developed in the field of inductive theorem proving we use annotated terms to represent syntactical differences of formulas. Based on these annotations and on hierarchies of function ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
. This paper presents techniques to guide equational reasoning in a goal directed way. Suggested by rippling methods developed in the field of inductive theorem proving we use annotated terms to represent syntactical differences of formulas. Based on these annotations and on hierarchies of function symbols we define different abstractions of formulas which are used for planning of proofs. Rippling techniques are used to refine single planning steps, e.g. the application of a bridge lemma, on a next planning level. Fachbeitrag. Keywords: Automated reasoning, Theorem Proving, Rippling 1 Introduction Heuristics for judging similarities between formulas and subsequently reducing differences have been applied to automated deduction since the 1950s, when Newell, Shaw, and Simon built their first "logic machine" [NSS63]. Since the later 60s, a similar theme of difference identification and reduction appears in the field of resolution theorem proving [Mor69], [Dig85], [BS88]. Partial unifica...
Automated Reasoning and Bledsoe's Dream for the Field
"... In one sense, this article is a personal tribute to Woody Bledsoe. As such, the style will in general be that of private correspondence. However, since this article is also a compendium of experiments with an automated reasoning program, researchers interested in automated reasoning, mathematics, an ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
In one sense, this article is a personal tribute to Woody Bledsoe. As such, the style will in general be that of private correspondence. However, since this article is also a compendium of experiments with an automated reasoning program, researchers interested in automated reasoning, mathematics, and logic will find pertinent material here. The results of those experiments strongly suggest that research frequently benefits greatly from the use of an automated reasoning program. As evidence, I select from those results some proofs that are better than one can find in the literature, and focus on some theorems that, until now, had never been proved with an automated reasoning program, theorems that Hilbert, Church, and various logicians thought significant. To add spice to the article, I present challenges for reasoning programs, including questions that are still open. 1 This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Depa...
Equalizing Terms by Difference Reduction Techniques
 In Proceedings Gramlich, B., Kirchner, H. (Eds.) Workshop on Strategies in Automated Deduction
, 1997
"... In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling / coloring terms and there is considerable evidence of ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling / coloring terms and there is considerable evidence of its success on practical examples. For equality reasoning we use these annotated terms to represent syntactical differences of formulas. Based on these annotations and on hierarchies of function symbols we define different abstractions of formulas which are used for a hierarchical planning of proofs. Also rippling techniques are used to refine single planning steps, e.g. the application of a bridge lemma, on a next planning level. 1 Introduction In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling ...