T. Przymusinski, Non-monotonic Formalisms and Logic Programming, Proceedings of the 6th International Conference on Logic Programming 655-674, June, 1989.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Kripke like semantics neatly captures this trichotomy; either A 2 I(P ) or A 62 I(P ) but A is true in some world above P or A is false in all worlds. Thus it seems natural to extend the definition of an interpretation as follows (similar to the notion of 3 valued interpretation of Przymusinki [15]) Definition 3 Let P be a program. An interpretation is any function I : P H Theta H satisfying the following conditions, where I(P ) hS; F i: 1. S F = 2. for all worlds w 1 ; w 2 such that w 1 w 2 ; I(w 1 ) hS 1 ; F 1 i; I(w 2 ) hS 2 ; F 2 i, we have S 1 S 2 and F 1 F 2 Let ....

T. Przymusinski, Non-monotonic Formalisms and Logic Programming, Proceedings of the 6th International Conference on Logic Programming 655-674, June, 1989.

....as alternative enlarged consistent belief models an agent may have of the world, all of each containing the WFM . The agent s world view may be completed (or refined) by hypothesizing (e.g. abducing, using default rules, the closed world assumption, etc. about unknown information. Przymusinski [11, 12, 13] shows that Well Founded semantics is equivalent to suitable forms of four major nonmonotonic reasoning formalisms (Circumscription, Closed World Assumption, Autoepistemic Logic and Default Logic) In the case the WFM is a 2 valued model then no degree of freedom is left to the agent to ....

T. C. Przymusinski. Non-monotonic formalisms and logic programming. In ICLP-89-Lisbon, Portugal, pages 655--674. mit press, 1989.

....with constraints. We mention here work by Elkan [55] Reinfrank [143] Giordano and Martelli [73] Witteveen [174] and Jonker [78] The area is related to classical negation and to abduction. Relations with Other Non monotonic Formalisms are abundant (see e.g. Nerode et al. 116] and Przymusinski [131, 134]) As negation as failure is a non monotonic inference rule, there has been a cross fertilization between semantics for non monotonic logics and logic programming. In one direction, stable expansions of auto epistemic logic (Moore [111] inspired Gelfond [67, 68] to define the stable semantics. A ....

T.C. Przymusinski. Non-monotonic formalisms and logic programming. In Levi and Martelli [89], pages 655--674.

.... 0 then OE j 0 Right weakening If OE OE 0 j and OE j OE 0 then OE j Cut If OE j OE 0 and OE j then OE OE 0 j Cautious monotony Figure 4: Properties of nonmonotonic inference relations. and for default logic. A first overview of these connections is given in [93]. More recent work in this direction can be found in the proceedings of the conferences Non Monotonic Extensions of Logic Programming [33] and Logic Programming and Nonmonotonic Reasoning [76] ....

T. Przymusinski. Non-monotonic formalisms and logic programming. In Proceedings of the 6th International Conference on Logic Programming, pages 655--674, Cambridge, MA, 1989. MIT Press.

.... and Walker [3] and by Van Gelder [23] as the declarative semantics for the class of stratified logic programs [3, 23] and the class of locally stratified logic programs [13] This semantics is known to be equivalent to natural forms of all four major formalisms of non monotonic reasoning in AI [8, 9, 14, 15]: McCarthy s circumscription; Reiter s default theory; Moore s autoepistemic logic; Reiter s closed world assumption (CWA) Przymusinski also gave an ideal procedural semantics, called SLS resolution, for above classes of logic programs. Although the procedure is complete with respect to the ....

T. C. Przymusinski. Non-monotonic formalisms and logic programming. In G. Levi and M. Martelli, editors, Proc. of the Sixth International Conference on Logic Programming, pp. 655--674. the MIT Press, 1989.

....closed world reasoning and abduction, whose relations with logic programming are clear and well studied. Other reasoning problems, like reasoning on inheritance networks or belief revision are only briefly mentioned. We refer the reader to works like [39, 89] for extensive surveys on NMR and to [123] for a survey on the relations between NMR and logic programming. Works on NMR that survey complexity results have been done by Minker [103] and Schlipf [139] Many results that have appeared in the literature are concerned with decidable fragments of non monotonic logics. In the spirit of a ....

T. Przymusinski. Non-monotonic formalisms and logic programming. In Proceedings of the Sixth International Conference on Logic Programming, pages 655--674. The MIT Press, 1989.

....the way for using efficient computation methods, developed for logic programs and deductive databases, as inference engines for non monotonic reasoning. For more information about the relationship between non monotonic reasoning, logic programming and deductive databases, the reader is referred to [Prz88b, Prz89b]. 8 Conclusion In the paper we have described various proposed semantics for deductive databases and logic programs and discussed their mutual relations. We have particularly emphasized recent research work in this area which appears to be very significant and lead to a change of perspective. As ....

T. C. Przymusinski. Non-monotonic formalisms and logic programming. In G. Levi and M. Martelli, editors, Proceedings of the Sixth International Logic Programming Conference, Lisbon, Portugal, pages 655--674, Cambridge, Mass., 1989. Association for Logic Programming, MIT Press.

....also be viewed as being based on autoepistemic logic. 1 Introduction Autoepistemic logic AEL, introduced by Moore [Moo85] proved to be a very successful approach to formalizing commonsense, non monotonic reasoning [Kon87, Gel88, Lif89, MT88] It also plays an important role in logic programming [Prz88b, Prz89], where it is used to define the so called stable model semantics [GL88] However, Moore s autoepistemic logic AEL also has some important drawbacks: ffl Quite reasonable theories are often inconsistent in AEL [Mor88, Prz91b] ffl Even for consistent theories AEL does not always lead to the ....

T. C. Przymusinski. Non-monotonic formalisms and logic programming. In G. Levi and M. Martelli, editors, Proceedings of the Sixth International Logic Programming Programming Conference, Lisbon, Portugal, pages 655--674, Cambridge, Mass., 1989. Association for Logic Programming, MIT Press.

....semantics. They also differ from the Generalized Disjunctive Well founded Semantics, proposed in [BLM89] because the latter neither extends the stable nor the well founded semantics. We also show that both disjunctive stable semantics naturally correspond to non monotonic formalisms in AI (see [Prz89b]) Namely, we prove that, after a suitable translation of a disjunctive program P into an autoepistemic theory P , the disjunctive (respectively, partial disjunctive) stable semantics of P coincides with the autoepistemic (respectively, 3 valued autoepistemic) semantics of P ( Prz91c] see also ....

T. C. Przymusinski. Non-monotonic formalisms and logic programming. In G. Levi and M. Martelli, editors, Proceedings of the Sixth International Logic Programming Programming Conference, Lisbon, Portugal, pages 655--674, Cambridge, Mass., 1989. Association for Logic Programming, MIT Press.

....acknowledges support from the National Science Foundation under grant #IRI 8910729 and from the Army Research Office under grant #27079 MA SAH. logic programming and deductive databases. It also reveals a close relationship existing between logic programming and non monotonic reasoning (see [Prz88b, Prz89b, PP90]) On the one hand, due to the non monotonic character of negation operators used in logic programs and deductive databases, any such intended semantics of a program P must be non monotonic and therefore the problem of finding a proper semantics for logic programs and deductive databases can be ....

T. C. Przymusinski. Non-monotonic formalisms and logic programming. In G. Levi and M. Martelli, editors, Proceedings of the Sixth International Logic Programming Programming Conference, Lisbon, Portugal, pages 655--674, Cambridge, Mass., 1989. Association for Logic Programming, MIT Press.

.... of the other proposed approaches (see [PP90] for an overview) The wellfounded semantics has been proven to share many of the natural properties of the perfect model semantics [Prz89a] and it has been shown to be equivalent to suitable (3 valued) forms of all four major non monotonic formalisms [Prz91, Prz89b]. Recently, D. S. Warren introduced the Extended Warren Abstract Machine (XWAM) for this semantics [War89] and developed an elegant interpreter in Prolog. The stable model semantics has been introduced in [GL88] see also [BF88] It is a 2 valued semantics, which also extends the perfect model ....

....importance of stable models, at the same time indicating that the proper definition of stable models should be 3 valued. The 3 valued stable model semantics not only provides a natural extension of the well founded semantics, but it also naturally corresponds to nonmonotonic formalisms in AI (cf. [Prz89b, Prz88b]) Namely, every program P can be translated into an autoepistemic (resp. default) theory P , so that the 3 valued stable semantics of P coincides with the (3 valued) autoepistemic (resp. default) semantics of P [Prz91] Similar results hold for circumscription and CWA. In [Prz90a, Prz90b] we ....

T. C. Przymusinski. Non-monotonic formalisms and logic programming. In G. Levi and M. Martelli, editors, Proceedings of the Sixth International Logic Programming Programming Conference, Lisbon, Portugal, pages 655--674, Cambridge, Mass., 1989. Association for Logic Programming, MIT Press.

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