Abstract
It is claimed that the notion of preference is a fundamental modality in computing and is a generalization of the notion of minimality. A logic of feasible preference is presented. The non-monotonic behavior of negation in logic programming is modeled as a symbolic optimization problem. As a case study, for the class of logic programs with one or more stable models, we give a preferential transformation of logic programs that identifies their stable models as the optimal worlds in the intended model of the corresponding preferential theory. Minimization and minimization orderings are given explicit syntactic representations and their due status in the model theory. Preference logics gives a very elegant model theory for defaults, without any mention of fixpoints. Further, nonmonotonic reasoning is carried out in a monotonic logic, since members of the optimal worlds are not identified with theorems of a preferential theory. Preference logics have great potential to bring the areas of Symbolic Computation, Knowledge Representation and Classical Optimization closer.
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References
K.R. Apt, H. Blair, A. Walker. Towards a Theory of Declarative Knowledge In Foundations of Deductive Databases and Logic Programming, ed. Jack Minker, Morgan Kaufmann Publishers, 1988.
A. L. Brown Jr., S. Mantha, T. Wakayama. Preferences as Normative Knowledge: Towards Declarative Obligations To be presented at the First International Workshop on Deontic Logic in Computer Science.
A. L. Brown Jr., S. Mantha, T. Wakayama. Preference Logics: Towards a Unified Approach to Nonmonotonicity in Deductive Reasoning To be presented at the Second International Symposium on Artificial Intelligence and Mathematics.
A. L. Brown Jr., S. Mantha, T. Wakayama. A Logical Reconstruction of Constraint Relaxation Hierarchies in Logic Programming Submitted to Conference on Automated Deduction.
A. L. Brown Jr., S. Mantha, T. Wakayama. Assigning Meaning to Markup: A Study in the Logical Foundations of Document Representation In preparation.
Allen L. Brown Jr., Surya Mantha, Toshiro Wakayama. An Axiomatic Account of Preferential Structures, Submitted for Publication.
B. F. Chellas. Modal Logic, an introduction Cambridge University Press, 1980.
D. Gabbay, F. Guenthner. Handbook of Philosophical Logic, Vol. II. D. Reidel Publishing Company, 1984.
M. Gelfond, V. Lifschitz. The Stable Model Semantics for Logic Programming Proc. of the 5th Conference on Logic Programming, MIT Press, 1988.
I. L. Humberstone. Inaccessible Worlds Notre Dame Journal of Formal Logic, Volume 24, Number 3, July 1983.
K. Kunen. Negation in Logic Programming Journal of Logic Programming.
V. Lifschitz. On the Declarative Semantics of Logic Programs with Negation In Foundations of Deductive Databases and Logic Programming, ed. Jack Minker, Morgan Kaufmann Publishers, 1988.
Vladimir Lifschitz. Pointwise Circumscription: Preliminary Report, Proceedings of AAAI-86.
J Lloyd. Foundations of Logic Programming Springer-Verlag Publishers, 1984.
W. Marek, A. Nerode, J. Remmell Nonmonotonic Rule Systems Proceedings of the LICS, 1990.
R. C. Moore. Semantical Considerations on Non-monotonic Logic Artificial Intelligence, 28 (1985), pp. 75–94.
S. Mantha. First-Order Preference Theories and their Applications PhD thesis, Dept. of Computer Science, University of Utah, 1991.
W. Marek, M. Truszczynski. Autoepistemic Logic Technical Report 115-88, Dept. of Computer Science, Univ. of Kentucky.
T.C. Przymusinski. On the Declarative Semantics of Deductive Databases and Logic Programs In Foundations of Deductive Databases and Logic Programming, ed. Jack Minker, Morgan Kaufmann Publishers, 1988.
R. Reiter. A Logic for Default Reasoning In Readings in Nonmonotonic Reasoning, ed. Matthew Ginsburg, Morgan Kaufmann Publishers, 1987
J. Shepherdson Negation in Logic Programming In Foundations of Deductive Databases and Logic Programming, ed. Jack Minker, Morgan Kaufmann Publishers, 1988.
J. Shoenfield. Mathematical Logic Addison-Wesley Publishing Company, 1967.
Y. Shoham. Reasoning About Change, Time and Causation from the Standpoint of Artificial Intelligence MIT Press, 1987.
R. Stalnaker A theory of conditionals in N. Rescher (ed.) Studies in Logical Theory, American Philosophical Quarterly Monograph Series, No. 2, Blackwell, Oxford.
R. Stalnaker. A Note on Non-Monotonic Modal Logic Cornell University, Unpublished Manuscript.
R. Turner. Logics for Artificial Intelligence Horwood Series in AI, 1984.
M. H. van Emden, R. Kowalski. The Semantics of Predicate Logic as a Programming Language JACM 23(4):733–742.
G.H. von Wright. The Logic of Preference Edinburgh, 1963.
L. Y. Yuan, J. You. Discriminant Circumscription Proceedings of the Tenth FSTTCS, Bangalore, India, Dec.1990.
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© 1992 Springer-Verlag Berlin Heidelberg
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Brown, A.L., Mantha, S., Wakayama, T. (1992). Preference logics and nonmonotonicity in logic programming. In: Nerode, A., Taitslin, M. (eds) Logical Foundations of Computer Science — Tver '92. LFCS 1992. Lecture Notes in Computer Science, vol 620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023862
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DOI: https://doi.org/10.1007/BFb0023862
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