The application of automated reasoning to proof translation and to finding proofs with specified properties: A case study in many-valued sentential calculus
In both mathematics and logic, many theorems exist such that each can be proved in entirely different ways. For a striking example, there exist theorems from group theory that can be proved by relying solely on equality and (from the viewpoint of automated reasoning) the use of paramodulation, but can also be proved in a notation in which equality is totally absent and the inference rule is condensed detachment (captured with a single clause and the rule hyperresolution). A study of such examples immediately shows how far from obvious is the problem of producing a proof in one system even in the presence of a proof in another; such problems can be viewed as ones of translation, where the rules of translation and the translation itself are frequently difficult to obtain. In this report, we discuss in detail various techniques that can be applied by the automated reasoning program OTTER to address the translation problem to obtain a proof in one notation and inference system given a proof in a completely different notation and inference system. To illustrate the techniques, we present a full treatment culminating in a successful translation'' of a proof of a theorem from many-valued sentential calculus. To our delight and amazement, instead of the expected translation consisting of approximately 175 applications of condensed detachment, OTTER obtained a far shorter proof. We also touch on techniques for finding shorter proofs and techniques for finding proofs satisfying some given property. 19 refs.
- Research Organization:
- Argonne National Lab., IL (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 5263373
- Report Number(s):
- ANL-91/19; ON: DE91018971
- Country of Publication:
- United States
- Language:
- English
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