Abstract
In order to provide a propositional tableau-based theorem prover with learning capabilities, we describe generalization mechanisms that characterize the concepts of valid and non-valid formulae. Our generalization language is founded on the notion of formula schemata enriched with a system of constraints. We show how the most “attractive” generalizations of a given instance can be found. Successes or failures of proofs are handled within a same formalism.
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References
Belleannée (C.) and Nicolas (J.). — Static learning for an adaptative theorem prover. In: Proccedings of EWSL 91 (European Working Session on Learning). pp. 298–311. — Springer-Verlag.
Gallier (J.H.). — Logic for Computer Science: Foundations of Automatic Theorem Proving. — Harper and Row, New-York, 1986.
Harmelen (van F.) and Bundy (A.). — Explanation based-generalisation = partial evaluation. Artificial Intelligence, vol. 36, 1988, pp. 401–412.
Korf. — Macro-operators: a weak method for learning. Artificial Intelligence, vol. 26, 1985, pp. 35–77.
Mackworth (A.K.). — Consistency in networks of relations. Artificial Intelligence, vol. 8, 1977, pp. 99–118.
Minton (S.N.), Carbonel (J.G.), Knoblock (C.A.), Kuokka (D.R.), Etzioni (O.) and Gil (Y.). — Explanation based learning: A problem solving perspective. Artificial Intelligence, vol. 40, 1989, pp. 63–118.
Mitchell (T.M.), Keller (R.M.) and Kedar-Cabelli (S.T.). — Explanation based learning: A unifying view. Machine Learning, vol. 1, 86, pp. 47–80.
Mitchell (T.M.). — Generalization as search. Artificial Intelligence, vol. 18, 1982, pp. 203–226.
O'Rorke (P.). — Lt revisited: Explanation-based learning and the logic of principia mathematica. Machine Learning, vol. 2, 1989, pp. 117–159.
Plotkin (G.D.). — A note on inductive generalization. Machine Intelligence, vol. 5, 1970, pp. 47–80.
Reynolds (J.C.). — Transformational systems and the algebraic structure of atomic formulas. Machine Intelligence, vol. 5, 1970, pp. 135–152.
Smullyan (R.M.). — First Order Logic. — Springer-Verlag, 1968.
Whitehead (A.N.) and Russel (A.N.). — Principia Mathematica. — Cambridge University Press, London, 1962.
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© 1991 Springer-Verlag Berlin Heidelberg
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Vorc'h, R. (1991). Generalization for a propositional calculus: a constraints-based approach. In: Barahona, P., Moniz Pereira, L., Porto, A. (eds) EPIA 91. EPIA 1991. Lecture Notes in Computer Science, vol 541. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54535-2_39
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DOI: https://doi.org/10.1007/3-540-54535-2_39
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