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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 5

An Integration of Resolution and Natural Deduction Theorem Proving

February 1, 2023

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Authors

Dale Miller

Amy Felty

DOI:


Abstract:

We present a high-level approach to the integration of such different theorem proving technologies as resolution and natural deduction. This system represents natural deduction proofs as X-terms and resolution refutations as the types of such X-terms. These type structures, called expansion trees, are essentially formulas in which substitution terms are attached to quantifiers. As such, this approach to proofs and their types extends the formulas-as-type notion found in proof theory. The LCF notion of tactics and tacticals can also be extended to incorporate proofs as typed X-terms. Such extended tacticals can be used to program different interactive and automatic natural deduction theorem provers. Explicit representation of proofs as typed values within a programming language provides several capabilities not generally found in other theorem proving systems. For example, it is possible to write a tactic which can take the type specified by a resolution refutation and automatically construct a complete natural deduction proof. Such a capability can be of use in the development of user oriented explanation facilities.

Topics: AAAI

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Dale Miller|| Amy Felty An Integration of Resolution and Natural Deduction Theorem Proving Proceedings of the AAAI Conference on Artificial Intelligence, 5 (1986) 198.

Dale Miller|| Amy Felty An Integration of Resolution and Natural Deduction Theorem Proving AAAI 1986, 198.

Dale Miller|| Amy Felty (1986). An Integration of Resolution and Natural Deduction Theorem Proving. Proceedings of the AAAI Conference on Artificial Intelligence, 5, 198.

Dale Miller|| Amy Felty. An Integration of Resolution and Natural Deduction Theorem Proving. Proceedings of the AAAI Conference on Artificial Intelligence, 5 1986 p.198.

Dale Miller|| Amy Felty. 1986. An Integration of Resolution and Natural Deduction Theorem Proving. "Proceedings of the AAAI Conference on Artificial Intelligence, 5". 198.

Dale Miller|| Amy Felty. (1986) "An Integration of Resolution and Natural Deduction Theorem Proving", Proceedings of the AAAI Conference on Artificial Intelligence, 5, p.198

Dale Miller|| Amy Felty, "An Integration of Resolution and Natural Deduction Theorem Proving", AAAI, p.198, 1986.

Dale Miller|| Amy Felty. "An Integration of Resolution and Natural Deduction Theorem Proving". Proceedings of the AAAI Conference on Artificial Intelligence, 5, 1986, p.198.

Dale Miller|| Amy Felty. "An Integration of Resolution and Natural Deduction Theorem Proving". Proceedings of the AAAI Conference on Artificial Intelligence, 5, (1986): 198.

Dale Miller|| Amy Felty. An Integration of Resolution and Natural Deduction Theorem Proving. AAAI[Internet]. 1986[cited 2023]; 198.


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