Superposition as a logical glue

Andrea Asperti
(University of Bologna)
Enrico Tassi
(Microsoft Research - INRIA Joint Centre)

The typical mathematical language systematically exploits notational and logical abuses whose resolution requires not just the knowledge of domain specific notation and conventions, but not trivial skills in the given mathematical discipline. A large part of this background knowledge is expressed in form of equalities and isomorphisms, allowing mathematicians to freely move between different incarnations of the same entity without even mentioning the transformation. Providing ITP-systems with similar capabilities seems to be a major way to improve their intelligence, and to ease the communication between the user and the machine. The present paper discusses our experience of integration of a superposition calculus within the Matita interactive prover, providing in particular a very flexible, "smart" application tactic, and a simple, innovative approach to automation.

In Tom Hirschowitz: Proceedings Types for Proofs and Programs, Revised Selected Papers (TYPES 2009), Aussois, France, 12-15th May 2009, Electronic Proceedings in Theoretical Computer Science 53, pp. 1–15.
Published: 16th March 2011.

ArXived at: https://dx.doi.org/10.4204/EPTCS.53.1 bibtex PDF
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