A Heuristic Program that Solves Symbolic Integration Problems in Freshman Calculus
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Efficiency and Completeness of the Set of Support Strategy in Theorem Proving
Journal of the ACM (JACM)
Automatic Theorem Proving With Renamable and Semantic Resolution
Journal of the ACM (JACM)
Experiments With a Multipurpose, Theorem-Proving Heuristic Program
Journal of the ACM (JACM)
Experiments in automatic learning for a multipurpose hueristic program
Communications of the ACM
Experiments with a deductive question-answering program
Communications of the ACM
Computers and Thought
The use of theorem-proving techniques in question-answering systems
ACM '68 Proceedings of the 1968 23rd ACM national conference
Empirical explorations of the geometry theorem machine
IRE-AIEE-ACM '60 (Western) Papers presented at the May 3-5, 1960, western joint IRE-AIEE-ACM computer conference
The unit preference strategy in theorem proving
AFIPS '64 (Fall, part I) Proceedings of the October 27-29, 1964, fall joint computer conference, part I
A chess mating combinations program
AFIPS '66 (Spring) Proceedings of the April 26-28, 1966, Spring joint computer conference
Concepts and methods for heuristic search
IJCAI'69 Proceedings of the 1st international joint conference on Artificial intelligence
PROW: a step toward automatic program writing
IJCAI'69 Proceedings of the 1st international joint conference on Artificial intelligence
Completeness theorems for semantic resolution in consequence-finding
IJCAI'69 Proceedings of the 1st international joint conference on Artificial intelligence
Completeness of Linear Refutation for Theories with Equality
Journal of the ACM (JACM)
A Definition-Driven Theorem Prover
IEEE Transactions on Computers
Semantic Resolution for Horn Sets
IEEE Transactions on Computers
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The Proving Program, PP (part of the MULTIPLE program), has found resolution principle proofs of theorems in first order predicate calculus with functions and individual constants. Finding proofs in predicate calculus is an important domain because it can conveniently represent many forms of mathematical and everyday reasoning and because a proof-finding program can be easily extended to become a deductive question-answering program. Completeness theorems are proved which show that an implicit AND/OR goal tree is suitable for representing the problem of finding a resolution principle proof for an important part of predicate calculus. Since PP searches such trees, it can now work on such problems. In addition, PP has been given the ability to utilize duplicate goals on the tree. Some problems in group theory, geometry, chemistry, and neurophysiology have been formalized in predicate calculus and solved by the program.