A Variant to Turing's Theory of Computing Machines
Journal of the ACM (JACM)
FME '02 Proceedings of the International Symposium of Formal Methods Europe on Formal Methods - Getting IT Right
Trends in Artificial Intelligence
IEEE Transactions on Computers
A Semantically Guided Deductive System for Automatic Theorem Proving
IEEE Transactions on Computers
System for Automated Deduction (SAD): A Tool for Proof Verification
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Early History and Perspectives of Automated Deduction
KI '07 Proceedings of the 30th annual German conference on Advances in Artificial Intelligence
Pursuing the Goal of Language Understanding
ICCS '08 Proceedings of the 16th international conference on Conceptual Structures: Knowledge Visualization and Reasoning
On Correctness of Mathematical Texts from a Logical and Practical Point of View
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Query Learning and Certificates in Lattices
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Computer proofs of limit theorems
IJCAI'71 Proceedings of the 2nd international joint conference on Artificial intelligence
A new method for proving certain Presburger formulas
IJCAI'75 Proceedings of the 4th international joint conference on Artificial intelligence - Volume 1
Towards the automation of set theory and its logic
Artificial Intelligence
Theorem proving with variable-constrained resolution
Information Sciences: an International Journal
A short survey of automated reasoning
AB'07 Proceedings of the 2nd international conference on Algebraic biology
Canonical horn representations and query learning
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Agent-oriented programming: from prolog to guarded definite clauses
Agent-oriented programming: from prolog to guarded definite clauses
Evidence algorithm and system for automated deduction: a retrospective view
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Artificial Intelligence
The strategy challenge in SMT solving
Automated Reasoning and Mathematics
Cybernetics and Systems Analysis
Unifying Rough Set Theories via Large Scaled Granular Computing
Fundamenta Informaticae - To Andrzej Skowron on His 70th Birthday
| Hi-index | 0.01 |
Results are reported here of a rather successful attempt at proving all theorems, totalling near 400, of Principia Mathematica which are strictly in the realm of logic, viz., the restricted predicate calculus with equality. A number of other problems of the same type are discussed. It is suggested that the time is ripe for a new branch of applied logic which may be called "inferential" analysis, which treats proofs as numerical analysis does calculations. This discipline seems capable, in the not too remote future, of leading to machine proofs of difficult new theorems. An easier preparatory task is to use machines to formalize proofs of known theorems. This line of work may also lead to mechanical checks of new mathematical results comparable to the debugging of a program.