G. Wagner. Vivid Logic -- Knowledge-BasedReasoning with Two Kinds of Negation, volume 764 of Lecture Notes in Computer Science. Springer-Verlag, Heidelberg, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....be defined in a number of ways depending on which attacks we allow the proponent and opponent to use. Normal logic programs do not have negative conclusions, which means that we cannot use rebuts. Thus both opponents can only launch undercuts on each other s assumptions. Extended logic programs [10, 2, 20], on the other hand, introduce explicit negation, which states that a literal is explicitly false. As a result, both undercuts and rebuts are possible forms of attack; there are further variations depending on whether any kind of counter attack is admitted. A variety of argumentation semantics ....

G. Wagner, Vivid Logic -- Knowledge-Based Reasoning with Two Kinds of Negation, volume LNAI 764, Springer--Verlag, 1994.

....i = P then the children of move i are all the defeaters of an argument A i . To implement an argumentation algorithm we need agents with an expressive knowledge system and reaction rules such as vivid agents [16, 14] 5 Vivid Agents A vivid agent is a software controlled system, defined in [15], whose state is represented by a knowledge base, and whose behavior is represented by means of action and reaction rules. In this section we recap some basic issues of vivid agents needed for the underestanding of the algorithm and examples in the next section. For detail see [13] The basic ....

....is a tuple of reagents S = hR 1 ; Rn i. 5.1 Operational Semantics of Reaction Rules Reaction rules encode the behavior of vivid agents in response to perception events created by the agent s perception subsystems, and to communication events created by communication acts of other agents. [15] distinguishes between epistemic, physical and communicative reaction rules, and uses L PEvt and L CEvt to denote the perception and communication event languages, and L Evt = L PEvt [ L CEvt . The following table describes the different formats of epistemic, physical and communicative reaction ....

Gerd Wagner. Vivid Logic -- Knowledge-Based Reasoning with Two Kinds of Negation, volume LNAI 764. Springer--Verlag, 1994.

....of non classical negation, beside the usual default one, has been stressed for use in deductive databases, knowledge representation, and non monotonic reasoning. This has been recognized lately by several authors [39, 22, 28, 57, 41] which have proposed an enhanced language and its semantics [22, 47, 41, 60]. Extended logic programming came thus to be born. A recent study of this explicit form of negation (and its strong form) compared with classical negation can be found in [ However, the introduction of explicit negation enables and requires being able to reason with, or at least detect, ....

....form) compared with classical negation can be found in [ However, the introduction of explicit negation enables and requires being able to reason with, or at least detect, contradictory information. Indeed, information is not only normally incomplete but contradictory as well. As remarked in [43, 60] there are three main ways of dealing with inconsistent information in logic programs (see also the introduction of Chapter 3 in this volume) Explosive approach: If the program is contradictory then every formula is derived from it. This corresponds to the usual approach in mathematical logic, ....

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G. Wagner. Vivid logic: Knowledge-based reasoning with two kinds of negation. Lecture Notes on Artificial Intelligence, 764, 1994.

....we have shown that intuitionistic negation is less desirable than the strong negation of constructive logics. In logic programming and deductive databases, the application of strong negation for explicit representation of negative information is originally proposed in [79] See also [108] 109] [110]. Gelfond and Lifschitz in [48] 49] 5 We are assuming that the evidence supporting the negation correct and reliable. 4. Deductive Databases 73 also proposed to extend logic programs with classical negation from the knowledge representation viewpoint. But, as it is pointed out in [109] what ....

....kind of negation: non monotonic negation. In this chapter, we study the semantics of logic programs with two different kinds of negation: non monotonic negation and strong negation. Our discussion shall be mainly based on the work in Gelfond and Lifschitz [48] 49] Pearce and Wagner [80] Wagner [110], and our own work in the last chapter. In the following, we shall first of all review the main motivations behind the two kinds of negation, and then give the definition of an extended logic program, followed by a review of the answer set semantics and its modification under the quasi stable ....

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G. Wagner. Vivid Logic: Knowledge-Based Reasoning with Two Kinds of Negation. Springer-Verlag, Berlin, 1994.

....form of non classical negation, alongside the usual default or implicit one, has been stressed for use in deductive databases, knowledge representation, and non monotonic reasoning. This has been pointed out by several authors [23, 17, 18, 36, 25] and an enhanced language and semantics [17, 32, 25, 38] have been proposed. Extended logic programming was thus born. A recent study of this explicit form of negation (and its strong form) compared with classical negation can be found in [3] However, the introduction of explicit negation permits and requires being able to reason with, or at least ....

....form) compared with classical negation can be found in [3] However, the introduction of explicit negation permits and requires being able to reason with, or at least detect, contradictory information. Indeed, information is not only normally incomplete but contradictory as well. As remarked in [30, 38] there are three main ways of dealing with inconsistent information in logic programs: Explosive approach: If the program is contradictory then every formula is derived from it. This corresponds to the usual approach in mathematical logic, and of several of the semantics for extended logic ....

[Article contains additional citation context not shown here]

G. Wagner. Vivid logic: Knowledge-based reasoning with two kinds of negation. Lecture Notes on Artificial Intelligence, 764, 1994.

....form of non classical negation, alongside the usual default or implicit one, has been stressed for use in deductive databases, knowledge representation, and non monotonic reasoning. This has been pointed out by several authors [25, 16, 19, 37, 27] and an enhanced language and semantics [16, 31, 27, 39] have been proposed. Extended logic programming was thus born. A recent study of this explicit form of negation (and its strong form) compared with classical negation can be found in [ However, the introduction of explicit negation permits and requires being able to reason with, or at least ....

....compared with classical negation can be found in [ However, the introduction of explicit negation permits and requires being able to reason with, or at least detect, contradictory information. Indeed, information is not only normally incomplete but contradictory as well. As remarked in [29, 39] there are three main ways of dealing with inconsistent information in logic programs: Explosive approach: If the program is contradictory then every formula is derived from it. This corresponds to the usual approach in mathematical logic, and of several of the semantics for extended logic ....

[Article contains additional citation context not shown here]

G. Wagner. Vivid logic: Knowledge-based reasoning with two kinds of negation. Lecture Notes on Artificial Intelligence, 764, 1994.

....literals which was not available before. The importance of extending LP with a second kind of negation, has been stressed because of its use in deductive databases, knowledge representation, and non monotonic reasoning. Different semantics for extended LPs with : negation have appeared (e.g. [13, 21, 20, 24]) The coherence principle of [20] relates the two forms of negation, default and explicit: it stipulates that the latter entails the former, i.e if L ( L) is entailed then so is not :L (not L) and it is adopted as a fundamental principle of the WFSX semantics [20] The introduction of ....

G. Wagner. Vivid logic: Knowledge-based reasoning with two kinds of negation. Lecture Notes on Artificial Intelligence, 764, 1994. This article was processed using the L a T E X macro package with LLNCS style

....classically negated atoms are usually treated as new atoms. However, in the process of selecting intended models, the inconsistent ones (that is, the ones containing an atom A and its classical negation :A) are discarded. Overviews of this area can be found in Alferes and Pereira [1] Wagner [171] and and Minker and Ruiz [110] Abductive Logic Programming views, roughly speaking, the query as an observation, which must be explained by means of additional hypotheses. Explanations can be found by following the rules of the program backwards , as in SLD resolution and its generalizations. A ....

G. Wagner. Vivid Logic -- Knowledge-Based Reasoning with Two Kinds of Negation. PhD thesis, Freie Universitat Berlin, 1993.

.... from, add to or specialise more abstract accounts of defeasible argumentation of e.g. POL 87, VRE 93a, BTK 93, Dung 95] Another interesting topic is the relation with model theoretic approaches to the semantics of extended logic programming, in particular with partial semantics; see e.g. WAG 94] Briefly, the general idea of this semantics is that an interpretation I is not just one set of atoms (supposed to be true) but two sets, I and I Gamma , where I contains the atoms that are definitely true and I Gamma contains the atoms that are definitely false. Let Gamma be an ....

G. Wagner. Vivid logic - Knowledge-based reasoning with two kinds of negation. Springer Lecture Notes on AI 764, Springer Verlag, Berlin.

....to be the recovered knowledge base. The common property shared by every recovered knowledge base is that it considers some contradictory information as useless, and regards all the remaining information not depending on it as unaffected. This kind of approach is called conservative (skeptical) [Wa94] or coherent [BCDLP, BDP95] It should be emphasized at this point that our method, like many other well known approaches in the literature of AI, does not act as a complete reasoner. That is, it does not always propose a unique solution which is the best interpretation of the conflicts in the ....

....set to choose. Before turning to the technical details, a few words on implementation issues: A major challenge encountered by every reasoning method is to turn the proposed formalism into a computationally feasible process. There are many ways of dealing with this problem: The method proposed in [Le86, Wa94], e.g. is to restrict the representation language, taking 1 The idea of using two partial orders may be traced back to Belnap and his well known four valued logic [Be77a, Be77b] which is exactly the simplest bilattice FOUR (see below) Belnap was also the one who first proposed FOUR as being ....

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G.Wagner. Vivid logic: knowledge-based reasoning with two kinds of negation. Lecture Notes in AI No.764, Springer-Verlag, 1994.

....These support sets are the candidates to be the recovered knowledge base. The common feature shared by each support set is that it considers some contradictory information as useless, and regards all the remaining information not depending on it as unaffected. This kind of approach is called in [Wa94] conservative (skeptical ) and it apparently has not yet been studied in the literature (refer also to [Wa94, p.107] 2 Preliminary definitions and notations In this section we briefly review the notions that will be significant in what follows. For a more detailed presentation of the following ....

G.Wagner. Vivid logic: knowledge-based reasoning with two kinds of negation. Lecture Notes in AI No.764, Springer-Verlag, Germany; 1994.

.... A preliminary method for efficiently constructing (four valued) mcms is presented in [AA97b] This approach is applied to knowledge bases which are of a specific structure (called stratified knowledge bases) Another possible approach for dealing with computational limitations is considered in [Le86, Wa94]. The method proposed there is to restrict the representation language, taking again into account the trade off between expressiveness and efficiency. In both cases there is still much work to be done in order to obtain reasoning processes that are general enough on the one hand and that are ....

G.Wagner. Vivid logic: Knowledge-based reasoning with two kinds of negations. Lecture Notes in AI No.764, Springer-Verlag, 1994.

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G. Wagner. Vivid Logic -- Knowledge-BasedReasoning with Two Kinds of Negation, volume 764 of Lecture Notes in Computer Science. Springer-Verlag, Heidelberg, 1994.

.... , and an input language L Input ; an inference relation such that F holds if F Query can be inferred from X LKB ; and an update operation Upd, such that the result of updating X LKB with F Input is the knowledge base Upd(X, F ) An abstract knowledge system is called vivid in [27], if it is a conservative extension of the knowledge system of relational databases. Positive vivid knowledge systems use a general closed world (or completeness) assumption, whereas general vivid knowledge systems employ predicate specific completeness assumptions and possibly two kinds of ....

Gerd Wagner. Vivid Logic -- Knowledge-Based Reasoning with Two Kinds of Negation, volume LNAI 764. Springer--Verlag, 1994.

....and to allow for arbitrary formulas in the body of a rule. The interpretation of negation as failure as weak negation in partial logic according to our stable semantics seems to be the first general logical treatment of nonmonotonic logic programs. 18 It was already proposed by Wagner in [Wag91, Wag94b], but without the full generality of the stable semantics proposed in the present paper. 18 There have been many meta logical (notably modal logic) proposals, though. 6. Conclusion 33 Proposition 30 An answer set of an extended logic program Pi is the diagram of a minimally stable coherent ....

G. Wagner. Vivid Logic -- Knowledge-Based Reasoning with Two Kinds of Negation, volume 764 of Lecture Notes in Computer Science. Springer-Verlag, Heidelberg, 1994.

....They are associated with an operational and a logical semantics. In particular, relational databases incorporate the Closed World Assumption as the basis of evaluating negation which is indispensable in practice. Knowledge systems extending relational databases conservatively are called vivid in [46]. To our knowledge, the vivid agent model is the only model incorporating the fundamental concepts of the Closed World Assumption and of negation asfailure. It is therefore the only model which allows knowledge representation with two kinds of negation, such as in extended logic programs, and ....

....Query , i.e. closed query formulas, are also called if queries. Knowledge systems of various complexity can be distinguished (see Figure 1) The knowledge system of relational databases allows only atomic sentences and requires complete information. Conservative extensions of it are called vivid [46]. Formally we can define a vivid knowledge system as follows: Definition 2.1 Vivid Knowledge System An abstract knowledge system [47] consists of three languages and two operations: a knowledge representation language LKB , a query language L Query ,an input language L Input , an inference ....

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Gerd Wagner. Vivid Logic -- Knowledge-Based Reasoning with Two Kinds of Negation, volume LNAI 764. Springer--Verlag, 1994.

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