Journal of Automated Reasoning
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Automated Theory Formation in Pure Mathematics
Automated Theory Formation in Pure Mathematics
Vampire 1.1 (System Description)
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
The IJCAR-2004 automated theorem proving competition
AI Communications
Mathematical applications of inductive logic programming
Machine Learning
Applying SAT Solving in Classification of Finite Algebras
Journal of Automated Reasoning
AI Communications - CASC
Cooperating reasoning processes: more than just the sum of their parts
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Automatic construction and verification of isotopy invariants
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Automatic invention of fitness functions with application to scene generation
Evo'08 Proceedings of the 2008 conference on Applications of evolutionary computing
European collaboration on automated reasoning
AI Communications - ECAI 2012 Turing and Anniversary Track
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We extend our previous study of the automatic construction of isomorphic classification theorems for algebraic domains by considering the isotopy equivalence relation. Isotopism is an important generalisation of isomorphism, and is studied by mathematicians in domains such as loop theory. This extension was not straightforward, and we had to solve two major technical problems, namely, generating and verifying isotopy invariants. Concentrating on the domain of loop theory, we have developed three novel techniques for generating isotopic invariants, by using the notion of universal identities and by using constructions based on subblocks. In addition, given the complexity of the theorems that verify that a conjunction of the invariants form an isotopy class, we have developed ways of simplifying the problem of proving these theorems. Our techniques employ an interplay of computer algebra, model generation, theorem proving, and satisfiability-solving methods. To demonstrate the power of the approach, we generate isotopic classification theorems for loops of size 6 and 7, which extend the previously known enumeration results. This work was previously beyond the capabilities of automated reasoning techniques.