Abstract
We report on an experiment in interactive reasoning with FOL. The subject of the reasoning is elementary algebra. The main point of the paper is to show how the use of meta-theoretic knowledge results in improving the quality of the resulting proofs in that, in this environment, they are both easier to find and easier to understand.
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Aiello, L. Evaluating Functions Defined in First Order Logic or In Defense of Semantic Attachment in FOL, Stanford Artificial Intelligence Laboratory Memo, in preparation (1980).
Boyer, R.S. and Moore, J.S. Metafunctions: Proving them correct and using them efflciently as new proof procedures, Computer Science Laboratory, SRI International (1979).
Birkoff, G. and McLane, S. Brief Survey of Modern Algebra, The McMillan Company (1965).
Filman, R.E. The Interaction of Observation and Inference, Ph.D. Thesis, Stanford University, Stanford (1978).
Filman, R.E. Observation and Inference applied in a Formal Representation System, Proc. of the 4-th Workskop on Automated Deduction, Austin, Texas (1979)
Prawitz, D. Natural Deduction — a Proof-Theoretical Study, Almqvist & Wiksell, Stockholm (1965).
Talcott, C. FOLISP: a System for Reasoning about LISP Programs, Stanford Artificial Intelligence Laboratory Memo, in preparation (1980).
Weyhrauch, Richard W. FOL: A Proof Checker for First-order Logic, Stanford Artificial Intelligence Laboratory Memo AIM-235.1 (1977).
Weyhrauch, Richard W. The Uses of Logic in Artiflcial Intelligence, Lecture Notes prepared for the Summer School on the Foundations of Artificial Intelligence and Computer Science (FAICS '78), Pisa (1978).
Weyhrauch, Richard W. Prolegomena to a Mechanized Theory of Formal Reasoning, Stanford Artificial Intelligence Laboratory Memo AIM-315 (1979); to appear in Artificial Intelligence Journal (1980)
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© 1980 Springer-Verlag Berlin Heidelberg
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Aiello, L., Weyhrauch, R.W. (1980). Using meta-theoretic reasoning to do algebra. In: Bibel, W., Kowalski, R. (eds) 5th Conference on Automated Deduction Les Arcs, France, July 8–11, 1980. CADE 1980. Lecture Notes in Computer Science, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10009-1_1
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DOI: https://doi.org/10.1007/3-540-10009-1_1
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Online ISBN: 978-3-540-38140-2
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