Predicate Introduction for Logics with Fixpoint Semantics. Part II: Autoepistemic Logic

• Autorzy: Vennekens J. , Wittocx J. , Mariën M. , Denecker M.
• Języki publikacji: EN

Abstrakty

EN

We study the transformation of "predicate introduction" in non-monotonic logics. By this, we mean the act of replacing a complex formula by a newly defined predicate. From a knowledge representation perspective, such transformations can be used to eliminate redundancy or to simplify a theory. From a more practical point of view, they can also be used to transform a theory into a normal form imposed by certain inference programs or theorems. In a companion paper, we developed an algebraic theory that considers predicate introduction within the framework of "approximation theory," a fixpoint theory for non-monotone operators that generalizes all main semantics of various non-monotonic logics, including logic programming, default logic and autoepistemic logic. We then used these results to show that certain logic programming transformations are equivalence preserving under, among others, both the stable and well-founded semantics. In this paper, we now apply the same algebraic results to autoepistemic logic and prove that a transformation to reduce the nesting depth of modal operators is equivalence preserving under a family of semantics for this logic. This not only provides useful theorems for autoepistemic logic, but also demonstrates that our algebraic theory does indeed capture the essence of predicate introduction in a generally applicable way.

Słowa kluczowe

EN

fixpoint extension; autoepistemic logic; approximation

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2007
• Tom: Vol. 79, nr 1-2
• Strony: 209--227
• Opis fizyczny: bibliogr. 10 poz., tab.

Twórcy

autor

Vennekens J.

autor

Wittocx J.

autor

Mariën M.

autor

Denecker M.

• Department of Computer Science, K.U. Leuven, Celestijnlaan 200A, B-3001 Leuven, Belgium

Bibliografia

• [1] Bonatti, P.: Autoepistemic logics as a unifying framework for the semantics of logic programs, Journal of Logic Programming, 22, 1995, 91-149.
• [2] Denecker, M., Marek, V., Truszczynski, M.: Fixpoint 3-valued semantics for autoepistemic logic, Proceedings of the Fifteenth National Conference on Artificial Intelligence,MIT Press / AAAI-Press, 1998.
• [3] Denecker, M., Marek, V., Truszczyński, M.: Approximating operators, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning, in: Logic-based Artificial Intelligence (J. Minker, Ed.), chapter 6, Kluwer Academic Publishers, 2000, 127-144.
• [4] Denecker,M.,Marek, V., Truszczynski,M.: Uniform semantic treatment of default and autoepistemic logics, Artificial Intelligence, 143(1), January 2003, 79-122.
• [5] Konolige, K.: On the Relation between Default and Autoepistemic Logic, in: Readings in Nonmonotonic Reasoning (M. L. Ginsberg, Ed.), Kaufmann, Los Altos, CA, 1987, 195-226.
• [6] Konolige, K.: On the relation between default and autoepistemic logic, Artificial Intelligence, 35, 1988, 343-382.
• [7] Marek, V. W., Truszczyński, M.: Autoepistemic Logic., J. ACM, 38(3), 1991, 588-619.
• [8] Meyer, J.-J., van der Hoek,W.: Epistemic Logic for Computer Science and Artificial Intelligence, Cambridge University Press, 1995.
• [9] Moore, R.: Possible-World Semantics for Autoepistemic Logic, Proc. of the Non-Monotonic Reasoning Workshop, AAAI Press, Mohonk, N.Y, 1984.
• [10] Vennekens, J., Wittocx, J., Mari¨en, M., Denecker, M., Bruynooghe, M.: Predicate Introduction for Logics with Fixpoint Semantics. Part I: Logic Programming, Fundamenta Informaticae.