Abstract
A logical entropy-based Informational Logic is presented which provides new tools for probabilistic automated reasoning and knowledge representation. Applications in automated theorem proving are examined, and a decision theory for probabilistic theorems is proposed.
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References
Avenhaus, J. and Madlener, K.: Term rewriting and equational reasoning, in Formal Techniques in Artificial Intelligence, North-Holland, Amsterdam, 1990, pp. 1–43.
Boyer, R. S. and Moore, J. S.: Proving theorems about LISP functions, JACM (1975), 129–144.
Holldobler, S. and Thielsher, M.: Computing change and specificity with equational logic programs, Annals Math. Artificial Intelligence (1995), pp. 99–133.
Gentilini, P., Forcheri, P., and Molfino, M. T.: Conjectural provability logic based on logical information measures, Bulletin of Symbolic Logic (1997), 29–30.
Gardenfors, P.: Three levels of inductive inference, in D. Prawtz, B. Skyrms and D. Westerthal (eds), Logic, Methodology and Philosophy of Science IX, North-Holland, 1994, pp. 427–449.
Dubois, D., Lang, J. and Prade, H.: Possibilistic logic, in Dov M. Gabbey, C. J. Hogger and J. A. Robinson (eds), Handbook of Logic in AI and Logic Programming, Clarendon Press, Oxford, 1994.
Forcheri, P., Gentilini, P. and Molfino, M. T.: Research in automated deduction as a basis for a probabilistic proof-theory, in P. Agliano' and A. Ursini (eds), Logic and Algebra, Dekker, New York, 1996, pp. 491–527.
Gallager, R.: Information Theory and Reliable Communication, John Wiley and Sons, New York, 1968.
Montagna, F., Simi, G. and Sorbi, A.: Logic and probabilistic systems, Archive of Mathematical Logic 35 (1996), 225–261.
Montagna, F.: An algebraic treatment of quantifier-free systems of arithmetic, Archive of Math-ematical Logic 35 (1996), 209–224.
Halpern, J. Y.: An analysis of first-order logics of probability, Artificial Intelligence 46 (1990), 311–350.
Gentilini, P.: Provability logic in the Gentzen formulation of arithmetic, Z. Math. Log. Grund-lagen. Math. 38 (1992), 536–550.
Girard, J. Y.: Linear logic, TCS 50 (1987), 1–102.
Smorynski, C.: The incompleteness theorems, in J. Barwise (ed.), Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, pp.000–000.
Gentilini, P.: Informational proof-theory, in Centro F. Enriquez (ed), Proc. Int. Conf. on Logic Methodology and Philosophy of Science, Florence, 1995, p. 47.
Krajicek, J. and Pudlak, P.: The number of proof lines and the size of proofs in first-order logic, Arch. Math. Logic (1988), 69–84.
Khinchin, A. I.: Mathematical Foundations of Information Theory, Dover Publications, New York, 1957.
Kyburg, H. E.: Uncertainty logics, in Dov M. Gabbay, C. J. Hogger and J. A. Robinson (eds), Handbook of Logic in AI and Logic Programming Vol. 3, Clarendon Press, Oxford, 1994.
Parikh, R. J.: Some results on the length of proofs, Trans. Amer. Math. Soc. 177 (1973) 29–36.
Perlis, D. and Subrahmanian, V. S.: Meta-languages, reflection principles and self-reference, in Dov M. Gabbay, C. J. Hogger, and J. A. Robinson (eds), Handbook of Logic in AI and Logic Programming Vol. 2, Clarendon Press, Oxford, 1994.
Scott, D. and Krauss, P.: Assigning probabilities to logical formula, in J. Hintikka and P. Suppes (eds), Aspects of Inductive Logic, North-Holland, Amsterdam, 1966.
Takeuti, G. Proof Theory, North-Holland, Amsterdam, 1987.
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Forcheri, P., Gentilini, P. & Molfino, M.T. Informational Logic as a Tool for Automated Reasoning. Journal of Automated Reasoning 20, 167–190 (1998). https://doi.org/10.1023/A:1005905025531
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DOI: https://doi.org/10.1023/A:1005905025531