L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. Contradiction removal semantics with explicit negation. In M. Masuch and L. Polos, editors, Knowledge Representation and Reasoning Under Uncertainty, number 808 in LNAI, pages 91--106. Springer-Verlag, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of plans and intentions through abductive inferences over discourse sentences. The possible actions, world knowledge, events and states are represented by extended logic programs (LP with explicit negation) and the abductive inference process is modeled by the framework proposed by Pereira ([10]) which is based on the Well Founded Semantics augmented with explicit negation (WFSX) and contradiction removal semantics (CRSX) It will be shown how this framework supports abductive planning with Event Calculus ( 4] and some classical examples will be shown ( 7, 11] in the domain of ....

.... inference process we have used the event calculus to represent events, time and actions and a logic programming framework with a given and de ned semantics, Well Founded Semantics of eXtended Logic Programs (WFSX) augmented with Contradiction Removal Semantics (CRSX) from the work of Pereira ([10]) This framework extends logic programming and alllows the modeling of several kinds of non monotonic reasoning, namely dafault, abductive and hypothetical reasoning. Furthermore, it allows the removal of contradictions allowing the desambiguation of dialogues. In section 2 a description of the ....

Lus Moniz Pereira, Jose Julio Alferes, and Joaquim Nunes Aparcio. Contradiction removal semantics with explicit negation. In M. Masuch and L. Polos, editors, Knowledge Representation and Reasoning Under Uncertainty, Volume 808 of LNAI, pages 91-106. Springer-Verlag, 1994.

....of plans and intentions through abductive inferences over discourse sentences. The possible actions, world knowledge, events and states are represented by extended logic programs (LP with explicit negation) and the abductive inference process is modeled by the framework proposed by Pereira ([9]) which is based on the Well Founded Semantics augmented with explicit negation (WFSX) and contradiction removal semantics (CRSX) It will be shown how this framework supports abductive planning with Event Calculus ( 3] and some classical examples will be shown ( 6, 10] in the domain of ....

.... support this kind of reasoning we have used the event calculus to represent events, time and actions and a logic programming framework with a de ned semantics, Well Founded Semantics of eXtended Logic Programs (WFSX) augmented with Contradiction Removal Semantics (CRSX) from the work of Pereira ([9]) This framework extends logic programming and alllows the modelling of several kinds of non monotonic reasoning, namely default, abductive and hypothetical reasoning. Furthermore, it allows the removal of contradictions allowing the desambiguation of dialogues. In section 2 a description of the ....

Lus Moniz Pereira, Jose Julio Alferes, and Joaquim Nunes Aparcio. Contradiction removal semantics with explicit negation. In M. Masuch and L. Polos, editors, Knowledge Representation and Reasoning Under Uncertainty, Volume 808 of LNAI, pages 91-106. Springer-Verlag, 1994.

.... states and world knowledge are represented by extended logic programs (LP with explicit negation) and the abductive inference process is modeled by a framework wich is based on the Well Founded Semantics augmented with explicit negation (WFSX) and contradiction removal semantics (CRSX) [13]) It will be shown how this framework supports abductive reasoning with Event Calculus ( 4] and some classical examples in the domain of information seeking dialogues will be shown ( 9, 14] Finally, some open problems will be pointed out. 1 Introduction A natural language understanding ....

.... event calculus to represent events, time and actions and a logic programming framework Well Founded Semantics of eXtended Logic Programs (WFSX) augmented with Contradiction Removal Owns a scholarship from JNICT, reference n o BD 1766 IA Semantics (CRSX) from the work of Pereira et al. [13]) This framework, has a well de ned semantics and extends logic programming allowing to model several kinds of non monotonic reasoning, namely default, abductive and hypothetical reasoning. In section 2 a description of the extended logic programming framework showing how non monotonic reasoning ....

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Lus Moniz Pereira, Jose Julio Alferes, and Joaquim Nunes Aparcio. Contradiction removal semantics with explicit negation. In M. Masuch and L. Polos, editors, Knowledge Representation and Reasoning Under Uncertainty, Volume 808 of LNAI, pages 91-106. Springer-Verlag, 1994.

.... refinement (dealing with contradiction) of the argumentation approach has been defined in [38] Besides relating our work with these semantics, we will also relate our approach with other semantics considering explicit negation rather than pseudo negation and based on contradiction removal [57, 60, 58, 4, 9] or contradiction avoidance [7, 8] 4.4.1 Argumentation Semantics Dung shows in [39] that the most of the approaches to non monotonic reasoning in artificial intelligence and logic programming can be expressed as different forms of argumentation. This idea is applied in [35] to develop a simple, ....

....and Explicit Negation In this section, we briefly review some works dealing with contradiction removal and contradiction avoidance semantics for explicit negation. All these works are inspired on the well founded semantics [72] and on the coherence principle [56] Pereira, Alferes and Aparicio [57, 60, 58] define a semantics that extends the WFSX semantics for explicit negation [56] Roughly speaking, the key idea is to remove some contradictions and to identify the models of the program obtained by revising the Closed World Assumptions (CWA) 38 supporting such contradictions. More precisely, the ....

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L.M. Pereira, J.J. Alferes, and J.N. Aparicio. Contradiction Removal Semantics with Explicit Negation. In M. Masuch, J.N. Aparicio, and J.J. Alferes, editors, Knowledge Representation and Reasoning under Uncertainty, LNAI, Vol. 808, pages 91--106. Springer-Verlag, 1994.

....avoidance. This method [137] is not able to restore consistency in all cases, as illustrated by the following example. Example 6.2 given the extended logic program p q q p r p :r p the method of [137] is unable to restore consistency by withdrawing the hypothesis p . In [134] and [140] Pereira and Alferes present two different modifications of the method of [137] to deal with this problem. For the program in example 6.2, the method in [134] restores consistency by letting p undefined, while the method in [140] restores consistency by assigning p to truth. This second ....

....p q q p r p :r p the method of [137] is unable to restore consistency by withdrawing the hypothesis p . In [134] and [140] Pereira and Alferes present two different modifications of the method of [137] to deal with this problem. For the program in example 6. 2, the method in [134] restores consistency by letting p undefined, while the method in [140] restores consistency by assigning p to truth. This second method is more suitable for diagnosis applications. Both methods, 46] and [137, 134, 140] can deal only with inconsistencies that can be attributed to NAF hypotheses, ....

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Pereira, L.M., Alferes, J.J., Aparicio, J.N., Contradiction removal semantics with explicit negation Proc. Applied Logic Conference, Amsterdam (1992)

....[7, 8] that allows models to contain the atom . 1 a; a and b; b are implicitly assumed. 4 2.4 Contradiction Removal Sets To revise contradiction, the first issue to consider is which default literals true by CWA are allowed to change their truth values. We simplify the approach of [18] along the lines of [17] taking as candidates for change default literals true by CWA in the WFSXp model. By making this simplification we can give a syntactic condition for electing the revisable literals, in contradistinction to the semantic one of [18] Definition 2.1 (Revisables) The ....

....truth values. We simplify the approach of [18] along the lines of [17] taking as candidates for change default literals true by CWA in the WFSXp model. By making this simplification we can give a syntactic condition for electing the revisable literals, in contradistinction to the semantic one of [18]. Definition 2.1 (Revisables) The revisables of a program P are all the default literals not L having no rules for L in P , and so true by CWA. The set of all revisables is called Rev(P ) Thus, all the objective literals that do not appear in rule heads but only in rule bodies, either in a ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. Contradiction removal semantics with explicit negation. In M. Masuch and L. Polos, editors, Knowledge Representation and Reasoning Under Uncertainty, number 808 in LNAI, pages 91--106. Springer-Verlag, 1994.

....[ADP94a] describes a more general method, by going back on the values of open literals, by changing them from false to either undefined or true. In this paper, for simplicity, we adopt the two valued revision approach. For a mixed two and three valued approach see Pereira, Alferes, and Apar icio [PAA94], and the above cited paper. Diagnosis Preferences and Strategies Representation with Logic Meta programming 21 can switch their truth value from false to true, i.e. we can assume the and gate to be abnormal, stuck at 0 or 1, or in an unknown fault mode. It turns out that SD and [OBS[H is not ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. Contradiction removal semantics with explicit negation. In M. Masuch and L. P'olos, editors, Knowledge Representation and Reasoning Under Uncertainty, volume 808 of LNAI, pages 91--106. Springer-Verlag, 1994.

.... including a second kind of negation in logic programs, for use in deductive databases, knowledge representation, and non monotonic reasoning [8, 9, 10, 11, 13, 21, 22, 23, 24, 32] Different semantics for logic programs extended with an explicit negation (extended logic programs) have appeared [6, 8, 11, 15, 17, 19, 26, 27, 28, 32]. Many of these semantics are either a generalization of stable models semantics [7] or of well founded semantics (WFS) 31] cf. 1] for a comparison) Others are based on constructive logic [12, 13, 14] While generalizations of stable models semantics are clearly credulous in their approach, ....

....Others are based on constructive logic [12, 13, 14] While generalizations of stable models semantics are clearly credulous in their approach, no semantics whatsoever has attempted to seriously explore the sceptical approach. A closer look at the works generalizing well founded semantics [6, 15, 17, 19, 26, 27, 28] shows these generalizations to be rather technical in nature, where the different techniques introduced to characterize the well founded semantics of normal logic programs are slightly modified in some way to become applicable to the more general case. Our first contribution is the presentation ....

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L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. Contradiction removal semantics with explicit negation. In Applied Logic Conf. ILLC, Amsterdam, 1992.

.... showed the importance of having a second kind of negation in logic programs for use in deductive databases, knowledge representation, and nonmonotonic reasoning [6, 7, 8, 9, 13, 14, 15, 24] Different semantics for logic programs extended with : negation (extended logic programs) have appeared [1, 4, 6, 9, 11, 12, 17, 19, 24] but, contrary to what happens with semantics for normal logic programs, there is no general comparison among them, specially in what concerns the use and meaning of the newly introduced : negation. The goal of this paper is to contrast a variety of these semantics in what concerns their use and ....

....one the axioms AX: defining : negation; another the minimality conditions not cond defining not negation. By adjusting these parameters in the schema we can then specify several semantics involving two kinds of negation [6, 11, 17, 19, 24] Other semantics, dealing with contradiction removal [1, 4, 12, 22], are not addressed yet by the schema. The issue will be briefly touched upon in section 5, as well as that of incorporating disjunction. The structure of the paper is as follows: we begin with preliminary definitions; in section 2 we present the parametrizeable schema; next we present properties ....

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J. N. Apar'icio, L. M. Pereira, and J. J. Alferes. Contradiction removal semantics with explicit negation. Technical report, AI Centre, Uninova, March 1992.

....exists a paraconsistent version of WFSX, called WFSXp [7, 8] that allows models to contain the atom . 2.4 Contradiction Removal Sets To revise contradiction, the first issue to consider is which default literals true by CWA are allowed to change their truth values. We simplify the approach of [17] along the lines of [16] taking as candidates for change default literals true by CWA in the WFSXp model. By making this simplification we can give a syntactic condition for electing the revisable literals, in contradistinction to the semantic one of [17] Definition 2.1 (Revisables) The ....

....truth values. We simplify the approach of [17] along the lines of [16] taking as candidates for change default literals true by CWA in the WFSXp model. By making this simplification we can give a syntactic condition for electing the revisable literals, in contradistinction to the semantic one of [17]. Definition 2.1 (Revisables) The revisables of a program P are all the default literals not L having no rules for L in P , and so true by CWA. The set of all revisables is called Rev(P ) Thus, all the objective literals that do not appear in rule heads but only in rule bodies, either in a ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. Contradiction removal semantics with explicit negation. In M. Masuch and L. Polos, editors, Knowledge Representation and Reasoning Under Uncertainty, number 808 in LNAI, pages 91--106. Springer-Verlag, 1994.

....not b; not c; d; not d; not :d; e; not e; not :eg 1 a; a and b; b are implicitly assumed 3 2.4 Contradiction Removal Sets To abolish contradiction, the rst issue to consider is which default literals true by CWA are allowed to change their truth values. We simplify the approach of [17] along the lines of [16] taking as candidates for change default literals true by CWA in the WFSXp model. By making this simpli cation we can give a syntactic condition for electing the revisable literals, in contradistinction to the semantic one of [17] De nition 2.1 (Revisables) The revisables ....

....truth values. We simplify the approach of [17] along the lines of [16] taking as candidates for change default literals true by CWA in the WFSXp model. By making this simpli cation we can give a syntactic condition for electing the revisable literals, in contradistinction to the semantic one of [17]. De nition 2.1 (Revisables) The revisables of a program P are the elements of a chosen subset Rev(P ) of the set of all objective literals L having no rules for them in P . The revisables thus are objective literals that do not appear in rule heads but only in rule bodies, either in a positive ....

L. M. Pereira, J. J. Alferes, and J. N. Aparcio. Contradiction removal semantics with explicit negation. In M. Masuch and L. Polos, editors, Knowledge Representation and Reasoning Under Uncertainty, number 808 in LNAI, pages 91-106. Springer-Verlag, 1994.

....Ino91, Kow90, KS90, PW90, PAA91b, PAA91d, PAA92b, PDA93b, PDA93c, PDA93a, PAA93, Wag91] BG93] makes an overview of the use of such programs in knowledge representation and NMR. Different semantics for extended logic programs with : negation (ELP) have appeared [DR91, GL90, KS90, PA92, PAA91a, PAA92a, Prz90, Prz91a, Sak92, Wag91] Each of these semantics is a generalization for ELP of either the stable models semantics (SM) GL88] or the well founded semantics (WFS) GRS91] of normal programs. In [Prz90, Dix91, Dix92] SM and WFS are contrasted, and it is argued that, by its structural ....

....to disjunctive programs, in the spirit of [BLM90, Prz91c, Prz91b, Prz93] where several semantics for disjunctive normal programs are defined. By generalizing LP with either explicit negation or integrity constrains, a new issue arises: how to deal with contradiction. DR91, Jon91, PA93b, PAA91a, PAA92a] present several proposal for that issue. AP93c, PA93a] distinguish between two generic approaches to deal with contradiction: one consists in avoiding it; the other in removing it. The definition on procedures for removing contradiction has been generalized to deal with two valued revisions ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. Contradiction removal semantics with explicit negation. In Applied Logic Conf. Preproceedings by ILLC, Amsterdam, 1992. To appear in Springer--Verlag LNAI.

....namely, in cooperative informationseeking dialogues. In our framework, the possible actions, events, states, and world knowledge are represented by extended logic programs (LP with explicit negation) and the abductive inference process is modeled by the framework proposed by Pereira et al. [13], which is based on the Well Founded Semantics augmented with explicit negation (WFSX) and contradiction removal semantics (CRSX) It will be shown how this framework supports abductive planning with Event Calculus [5] and some examples will be shown [10, 14] in the domain of information seeking ....

.... inference process, nonmonotonic reasoning, we have used the event calculus to represent events, time, and actions and a logic programming framework Well Founded Semantics of eXtended Logic Programs (WFSX) augmented with Contradiction Removal Semantics (CRSX) from the work by Pereira et al. [13]. This framework has a given and de ned semantics and extends logic programming. It enables one to model several kinds of nonmonotonic reasoning, namely, default, abductive, and hypothetical reasoning. In Section 2, a description of the extended logic programming framework showing how ....

[Article contains additional citation context not shown here]

Lus Moniz Pereira, Jose Julio Alferes, and Joaquim Nunes Aparcio. Contradiction removal semantics with explicit negation. In M. Masuch and L. Polos, editors, Knowledge Representation and Reasoning Under Uncertainty, Volume 808 of LNAI, pages 91-106. Springer-Verlag, 1994.

....However, l :l is not mandatory, so the ability is kept for the truth value of some literals to remain undefined (cf. 1] for other approaches) When a second form of negation is introduced contradiction may be present (i.e. l and :l hold for some l) and no semantics is given by WFSX 1 . In [29] the authors define CRSX extending WFSX by introducing the notion of removing some contradictions and identifying the models obtained by revising closed world assumptions supporting those contradictions. One unique model, if any such revised model exists, is singled out as the contradiction free ....

....reasoning problems with our CRSX semantics of logic programs. We argue that Logic Programming extended with the concept of undefinedness and a suitable form of explicit negation, is very rich to represent such problems. This paper is organized as follows. In section 2 we review CRSX semantics [29] which is an extension of the (WFSX) 26] for programs which have no WFSX semantics. Then we identify simple forms of commonsense reasoning (e.g. defeasible reasoning with exceptions, hypothetical reasoning) and show how they are represented by logic programs when CRSX is used. Using the notion of ....

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L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. Contradiction removal semantics with explicit negation. In Proceedings of Applied Logic at Work, LNCS. Springer-- Verlag, December 1992.

....and to declarative debugging. The expressive power of XLP to do so is attained by allowing would be contradictory programs to be adequately revised by a contradiction removal semantics which withdraws assumptions that support contradiction and revises them to false. We elaborate on the work of [15, 16] on contradiction removal of extended logic programs (CRSX) and also show how Reiter s algorithm DIAGNOSE [25, 10] is used to implement a sound contradiction removal algorithm based on the Well Founded Semantics meta interpreters of [19, 18] so as to obtain three valued revisions (to the ....

....say S is contradictory iff there is objective literal L such that fL; Lg S. S is contradictory wrt to L. 3 Revising Contradictory Extended Logic Programs Once we introduce explicit negation programs are liable to be contradictory. Next we review the Contradiciton Removal Semantics (CRSX) of [16]. Example 3.1 Consider P = fa; a not bg. Since we have no rules for b, by CWA it is natural to accept not b as true. By the second rule in P wehave :a, leading to an inconsistency with the fact a. It is arguable that the CWA may not be held of atom b since it leads to contradiction. ....

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L. M. Pereira, J. J. Alferes, and J.N. Apar'icio. Contradiction removal semantics with explicit negation. In Proc. Applied Logic Conf., Amsterdam, 1992. ILLC.

....be made, i.e. the assumption of their truthfulness can be removed, is called the set of revisable literals, and can be any subset of not H: In [6] a revision semantics was defined where only base closed world assumptions are revisable, i.e. those default literals whose complement has no rules. In [8] the notion of base closed world assumption was improved, in order to deal with the case of direct loops, i.e. without interposing nots 2 . The notion of revisables there presented is similar to the notion of prime optatives in [1] We show in section 5 that the issue of which are the revisables ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. Contradiction removal semantics with explicit negation. In Applied Logic Conf. ILLC, Amsterdam, 1992.

.... notion of optative acceptance of hypotheses, and proceed to illustrate its application to both the problems of fault diagnosis [16] and declarative debugging of logic programs [7] using the formulations initially devised for them in [1] Whereas the contradiction removal semantics approach of [10] has been shown applicable to a wide range of non monotonic reasoning problems [11] including the applications in this paper [12, 13] it is based on minimally or sceptically taking back the most primitive (closed world) assumptions contributing to contradiction. In contrast, we show how to ....

....scenaria. The close relationship to contradiction removal allows us to rely on our latter s present implementation for expeditiously computing results. In recent work [3, 9] we show the equivalence between contradiction avoidance as defined here and the contradiction removal approach of [10]. 1 Scenaria for Extended Logic Programs Next we review the scenario semantics paradigm of [1] By extended logic program we mean a set of (ground) rules of the form: L A 1 ; A n ; not B 1 ; not Bm n; m 0 where each of L; A 1 ; A n ; B 1 ; Bm is an objective ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. Contradiction removal semantics with explicit negation. In Applied Logic Conf. ILLC, Amsterdam, 1992.

....called explicit negation, preserving the well founded property (cf. 1] for a comparison of the above approaches) and procedural reading. When a second form of negation is introduced contradiction may be present (i.e. l and :l hold for some l) and no semantics is given by WFSX 1 . In [14] (also submitted to this conference) the authors define CRSX extending WFSX by introducing the notion of removing some contradictions and identifying the models obtained by revising closed world assumptions supporting those contradictions. One unique model, if any such revised model exists, is ....

....obtained by revising closed world assumptions supporting those contradictions. One unique model, if any such revised model exists, is singled out as the contradiction free semantics. When no contradiction is present CRSX semantics reduces to WFSX semantics. Here, using CRSX (which is assumed [14]) we show how to cast in the language of logic programs extended with explicit negation different forms of non monotonic reasoning such as defeasible reasoning and hypothetical reasoning, and apply it to diverse domains of knowledge representation such as hierarchies and reasoning about actions. ....

L. M. Pereira, J. J. Alferes, and J. N. Apar'icio. Contradiction removal semantics with explicit negation. Technical report, AI Centre, Uninova, July 1992. Submitted.

....techniques achieve it. Keywords: Diagnosis, Debugging, Non monotonic Reasoning, Logic Programming 1 Introduction There is evidence that non monotonic reasoning problems can be solved with recourse to contradiction removal techniques in logic programs extended with a second (explicit) negation [10, 11, 12]. Here we adapt to normal logic programs with integrity rules the contradiction removal approach, and use it to uniformly treat diagnosis and debugging, in fact envisaging programs as artifacts, and fault finding as debugging. Our originality resides in applying to normal logic programs the ....

L. M. Pereira, J. J. Alferes, and J.N. Apar'icio. Contradiction removal semantics with explicit negation. In Proc. Applied Logic Conf., Amsterdam, 1992. ILLC.

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