Abstract
The main goal of this paper is to establish a nonmonotonic epistemic logic εB with two modalities — provability and belief — capable of expressing and comparing a variety of known semantics for extended logic programs, and clarify their meaning. In particular we present here, for the first time, embeddings into epistemic logic of logic programs extended with a second kind of negation under the well-founded semantics, and contrast them to the recent embeddings into autoepistemic logics of such programs under stable models based semantics.
Furthermore, the language of the epistemic logic presented here being more general than that of extended programs, it offers a basic tool for further generalizations of the latter, for instance regarding disjunction and modal operators.
We thank Esprit BRA Compulog 2 (no. 6810), and JNICT — Portugal for their support. Thanks to Carlos Damásio and Teodor Przymusinski for helpful discussions.
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J. J. Alferes, C. V. Damásio, and L. M. Pereira. Top-down query evaluation for well-founded semantics with explicit negation. In A. Cohn, editor, European Conf. on AI, pages 140–144. Morgan Kaufmann, 1994. To appear.
J. J. Alferes, P. M. Dung, and L. M. Pereira. Scenario semantics of extended logic programs. In L. M. Pereira and A. Nerode, editors, 2nd Int. Ws. on LP & NMR, pages 334–348. MIT Press, 1993.
J. J. Alferes and L. M. Pereira. On logic program semantics with two kinds of negation. In K. Apt, editor, Int. Joint Conf. and Symp. on LP, pages 574–588. MIT Press, 1992.
J. J. Alferes and L. M. Pereira. Contradiction: when avoidance equal removal. In R. Dyckhoff, editor, 4th Int. Ws. on Extensions of LP, volume 798 of LNAI. Springer-Verlag, 1994. To appear.
José Júlio Alferes. Semantics of Logic Programs with Explicit Negation. PhD thesis, Universidade Nova de Lisboa, October 1993.
N. Bidoit and C. Froidevaux. Minimalism subsumes default logic and circumscription in stratified logic programming. In Symp. on Principles of Database Systems. ACM SIGACT-SIGMOD, 1987.
P. Bonatti. Autoepistemic logics as a unifying framework for the semantics of logic programs. In K. Apt, editor, Int. Joint Conf. and Symp. on LP, pages 417–430. MIT Press, 1992.
B. Chellas. Modal Logic: An introduction. Cambridge Univ. Press, 1980.
J. Chen. Minimal knowledge + negation as failure-only knowing (sometimes). In L. M. Pereira and A. Nerode, editors, 2nd Int. Ws. on LP & NMR, pages 132–150. MIT Press, 1993.
J. Dix. Classifying semantics of logic programs. In A. Nerode, W. Marek, and V. S. Subrahmanian, editors, LP & NMR, pages 166–180. MIT Press, 1991.
J. Dix. A framework for representing and characterizing semantics of logic programs. In B. Nebel, C. Rich, and W. Swartout, editors, 3rd Int. Conf. on Principles of Knowledge Representation and Reasoning. Morgan Kaufmann, 1992.
P. M. Dung. Negation as hypotheses: An abductive framework for logic programming. In K. Furukawa, editor, 8th Int. Conf. on LP, pages 3–17. MIT Press, 1991.
P. M. Dung and P. Ruamviboonsuk. Well founded reasoning with classical negation. In A. Nerode, W. Marek, and V. S. Subrahmanian, editors, LP & NMR, pages 120–132. MIT Press, 1991.
K. Eshghi and R. Kowalski. Abduction compared with negation by failure. In 6th Int. Conf. on LP. MIT Press, 1989.
A. Van Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620–650, 1991.
M. Gelfond. On stratified autoepistemic theories. In AAAI'87, pages 207–211. Morgan Kaufmann, 1987.
M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In R. Kowalski and K. A. Bowen, editors, 5th Int. Conf. on LP, pages 1070–1080. MIT Press, 1988.
M. Gelfond and V. Lifschitz. Logic programs with classical negation. In Warren and Szeredi, editors, 7th Int. Conf. on LP, pages 579–597. MIT Press, 1990.
G. Hughes and M. Cresswell. A companion to modal logic. Methuen, 1984.
K. Jonker. On the semantics of conflit resolution in truth maintenance systems. Technical report, Univ. of Utrecht, 1991.
R. Kowalski and F. Sadri. Logic programs with exceptions. In Warren and Szeredi, editors, 7th Int. Conf. on LP. MIT Press, 1990.
P. Lamarre and Y. Shoham. On knowledge, certainty, and belief (draft). Personal communication of the second author, Stanford Univ., 1993.
V. Lifschitz. Minimal belief and negation as failure. Technical report, Dep. of Computer Science and Dep. of Philisophy, Univ. of Texas at Austin, 1992.
V. Lifschitz and G. Schwarz. Extended logic programs as autoepistemic theories. In L. M. Pereira and A. Nerode, editors, 2nd Int. Ws. on LP & NMR, pages 101–114. MIT Press, 1993.
V. Marek and M. Truszczynski. Reflexive autoepistemic logic and logic programming. In L. M. Pereira and A. Nerode, editors, 2nd Int. Ws. on LP & NMR, pages 115–131. MIT Press, 1993.
J. Minker. On indefinite databases and the closed world assumption. In M. Ginsberg, editor, Readings in Nonmonotonic Reasoning, pages 326–333. Morgan Kaufmann, 1987.
R. Moore. Semantics considerations on nonmonotonic logic. Artificial Intelligence, 25:75–94, 1985.
D. Nelson. Constructible falsity. JSL, 14:16–26, 1949.
D. Pearce. Answer sets and constructive logic, II: Extended logic programs and related nonmonotonic formalisms. In L. M. Pereira and A. Nerode, editors, 2nd Int. Ws. on LP & NMR, pages 457–475. MIT Press, 1993.
L. M. Pereira and J. J. Alferes. Well founded semantics for logic programs with explicit negation. In B. Neumann, editor, European Conf. on AI, pages 102–106. John Wiley & Sons, 1992.
L. M. Pereira and J. J. Alferes. Optative reasoning with scenario semantics. In D. S. Warren, editor, 10th Int. Conf. on LP, pages 601–615. MIT Press, 1993.
L. M. Pereira, J. J. Alferes, and J. N. Aparício. Contradiction Removal within Well Founded Semantics. In A. Nerode, W. Marek, and V. S. Subrahmanian, editors, LP & NMR, pages 105–119. MIT Press, 1991.
L. M. Pereira, J. J. Alferes, and J. N. Aparício. Default theory for well founded semantics with explicit negation. In D. Pearce and G. Wagner, editors, Logics in AI. Proceedings of the European Ws. JELIA'92, volume 633 of LNAI, pages 339–356. Springer-Verlag, 1992.
L. M. Pereira, J. N. Aparício, and J. J. Alferes. Nonmonotonic reasoning with well founded semantics. In Koichi Furukawa, editor, 8th Int. Conf. on LP, pages 475–489. MIT Press, 1991.
L. M. Pereira, J. N. Aparício, and J. J. Alferes. Non-monotonic reasoning with logic programming. Journal of Logic Programming. Special issue on Nonmonotonic reasoning, 17(2, 3 & 4):227–263, November 1993.
L. M. Pereira, C. Damásio, and J. J. Alferes. Diagnosis and debugging as contradiction removal. In L. M. Pereira and A. Nerode, editors, 2nd Int. Ws. on LP & NMR, pages 316–330. MIT Press, 1993.
H. Przymusinska and T. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in AI, a Sourcebook, pages 321–367. North Holland, 1990.
T. Przymusinski. Extended stable semantics for normal and disjunctive programs. In Warren and Szeredi, editors, 7th Int. Conf. on LP, pages 459–477. MIT Press, 1990.
T. Przymusinski. Autoepistemic logic of closed beliefs and logic programming. In A. Nerode, W. Marek, and V. S. Subrahmanian, editors, LP & NMR, pages 3–20. MIT Press, 1991.
T. Przymusinski. A semantics for disjunctive logic programs. In Loveland, Lobo, and Rajasekar, editors, ILPS'91 Ws. in Disjunctive Logic Programs, 1991.
T. Przymusinski. Static semantics for normal and disjunctive programs. Technical report, Dep. of Computer Science, Univ. of California at Riverside, 1993.
R. Reiter. On closed-world data bases. In H. Gallaire and J. Minker, editors, Logic and DataBases, pages 55–76. Plenum Press, 1978.
R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:68–93, 1980.
G. Schwarz. Autoepistemic logic of knowledge. In A. Nerode, W. Marek, and V. S. Subrahmanian, editors, LP & NMR, pages 260–274. MIT Press, 1991.
G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, Mathematical Foundations of Database Systems, volume 495 of LNCS, pages 357–371. Springer-Verlag, 1991.
G. Wagner. Reasoning with inconsistency in extended deductive databases. In L. M. Pereira and A. Nerode, editors, 2nd Int. Ws. on LP & NMR, pages 300–315. MIT Press, 1993.
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Alferes, J.J., Pereira, L.M. (1994). Belief, provability, and logic programs. In: MacNish, C., Pearce, D., Pereira, L.M. (eds) Logics in Artificial Intelligence. JELIA 1994. Lecture Notes in Computer Science, vol 838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021967
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DOI: https://doi.org/10.1007/BFb0021967
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