G. Wagner. A Database Needs Two Kinds of Negation. In 3rd Symposium on Mathematical Fundamentals of Database and Knowledge Base Systems (MFDBS'91), pages 357--371. Springer-Verlag, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....semantics alike. Because of their arbitrary monotonic and antitonic operators over a complete lattice, these programs pave the way to combine and integrate into a single framework several forms of reasoning, such as fuzzy, probabilistic, uncertain, and paraconsistent ones. Many works (e.g. [11, 14, 25, 20]) have argued about the convenience of introducing into logic programming a way to distinguish what can be shown to be false from what is false by default because it cannot be proven true. So called Extended Logic Programs add explicit negation to normal programs. In [20] it is claimed that ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357-371. LNCS 495, Springer-Verlag, 1991.

....semantics alike. Because of their arbitrary monotonic and antitonic operators over a complete lattice, these programs pave the way to combine and integrate into a single framework several forms of reasoning, e.g. fuzzy, probabilistic, uncertain, and paraconsistent ones. Many works (e.g. [10, 13, 24, 19]) have argued about the convenience of introducing into logic programming a way to distinguish what can be shown to be false from what is false by default because it cannot be proven true. So called Extended Logic Programs add explicit negation to normal programs. In [19] it is claimed that ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357-371. LNCS 495, Springer-Verlag, 1991.

....programs using Belnap s four valued logic [4] The result was generalized by Subrahmanian [32] to programs possibly containing disjunctive information. Recently, the paraconsistent logic programming framework is further extended to treat default negation along with explicit negation in a program [28, 35, 21, 17]. However, in the context of extended disjunctive programs, a suitable paraconsistent extension of the answer set semantics has not been studied in the literature. In this paper, we present declarative semantics of possibly inconsistent ex2 tended disjunctive programs. We introduce the ....

....a general framework for logic programming in terms of bilattices, but he does not discuss programs containing two kinds of negation. Kifer and Lozinskii [21] extend Blair and Subrahmanian s annotated logic programming framework to 23 a theory possibly containing default negation, and Wagner [35] also develops a theory of inconsistent logic programs with two kinds of negation. Compared with our approach, they do not treat disjunctions in a program and the underlying logics presented in these literature are different from our stable model semantics. Subrahmanian [32] has extended the ....

G. Wagner. A database needs two kinds of negation. In Proceedings of the Third Symposium on Mathematical Fundamentals of Database and Knowledge Base Systems, Lecture Notes in Computer Science, 495, Springer-Verlag, pp. 357-371, 1991.

....:shave(b; b) implies not shave(b; b) which derives shave(b; b) by the clause. As a result, the program becomes inconsistent. This observation suggests that the coherency principle is not always appropriate (although it is possible to include this property to our formalism, if desired) Wagner [Wa91] has also introduced a logic for possibly inconsistent logic programs with two kinds of negation. His logic is paraconsistent and not destructive in the presence of an inconsistent information, but it is still restricted and different from our lattice valued logic. Several studies have also been ....

Wagner, G., A Database Needs Two kinds of Negation, Proc. 3rd Symp. on Mathematical Fundamentals of Database and Knowledge Base Systems (LNCS 495), 357-371, 1991. 15

....programs. The importance of extending logic programming with an explicit form 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 ....

....By translating GHPs into logic programs a derivation procedure based on SLD is readily implementable. 3. 4 Wagner s logic programs with strong negation Wagner has been a supporter of the introduction of explicit negation and constructive based paraconsistent logics in logic programming [39, 40, 57, 58, 59, 60]. His main motivating works are Nelson s constructive logic N with strong negation [35] Belnap s system B [7] and Levesque s vivid reasoning research programme [30, 31] In his book [60] several proposals for extending logic programming with strong negation in Nelson s sense are explored, ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H.-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357--371. LNCS 495, Springer--Verlag, 1991.

.... [3] while well founded semantics [31] is the sole representative of scepticism [3] Recently, several authors have stressed and shown the importance of 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 ....

.... 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, ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, MFDBS'91, pages 357--371. Springer-Verlag, 1991.

....and DCS, U. Nova de Lisboa 2825 Monte da Caparica, Portugal fjja lmpg fct.unl.pt Abstract Recently several authors have stressed and 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 ....

.... 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 ....

[Article contains additional citation context not shown here]

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, MFDBS'91, pages 357--371. Springer-Verlag, 1991.

....in chapter 3 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 ....

....way. This 7. Quasi stable Semantics with Strong Negation 138 consideration led us to the use of strong negation. The idea of using strong negation in logic programming and deductive databases is not novel. It was proposed by Pearce and Wagner in [79] and [80] and further developed by Wagner in [108], 109] and [110] Although [48] and [49] call the second negation classical negation , it is argued in [109] that this is in fact strong negation. See section 7.4 for the argument and related example in [109] We shall give further arguments to show term classical negation is indeed a ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, Demetrovics J., and H.-D. Gerhardt, editors, The 3rd Symposium on Mathematical Fundamentals of Database and Knowledge Bases Systems MFDBS-91, pages 357--371. Springer, 1991. 171

.... authors have underscored the importance of extending logic programming (LP) with a second kind of negation : for use in knowledge representation, deductive databases and nonmonotonic reasoning (NMR) GL90, GL92, 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 ....

....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 properties, WFS is more suitable ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357--371. LNCS 495, Springer--Verlag, 1991.

....The importance of extending logic programming with an explicit 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 ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H.-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357--371. LNCS 495, Springer--Verlag, 1991.

....The importance of extending logic programming with an explicit 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 ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H.-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357--371. LNCS 495, Springer--Verlag, 1991.

....within CRSX 36 10 Related work 37 A CRSX Review 44 1. Introduction Recently, several authors have stressed and showed the importance of having an explicit second kind of negation within logic programs, for use in deductive databases, knowledge representation, and non monotonic reasoning [3, 6, 11, 18, 16, 32, 33, 34, 43, 39]. In non monotonic reasoning with logic programming there are two main ways of giving meaning to sets of rules when a given semantics is assigned to a program defined by the set of rules. We either accept as consequences the intersection of all models identified by some semantics, which is called ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, MFDBS'91, pages 357--371. Springer-Verlag, 1991.

....the contradiction removal semantics coincides with WFSX. 1 Introduction Recently, several authors have stressed and showed the importance of having an explicit second kind of negation within logic programs, for use in deductive databases, knowledge representation, and nonmonotonic reasoning [2, 4, 5, 7, 6, 14, 15, 16, 23, 21]. Some proposals for extending logic programming semantics with a second kind of negation has been advanced. One such extension is the Answer Set semantics (AS) 4] which is shown to be an extension of Stable Model (SM) semantics [3] from the class of logic programs [8] to those with a second ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, MFDBS'91, pages 357--371. Springer-Verlag, 1991. This article was processed using the L a T E X macro package with LLNCS style

....programs, one more credulous than WFS in the sense that it accepts more negative assumptions. A number of authors have underscored the advantages of extending logic programming with a second kind of negation : for use in deductive databases, knowledge representation, and nonmonotonic reasoning [GL90, KS90, PAA91, Wag91]. Different semantics for extended logic programs with : negation (ELP) have appeared [DR91, GL90, KS90, PA92, Prz90, Prz91, Wag91] AP92] contrasts some of these, where distinct meanings of : negation are identified: classical, strong and explicit. It is argued there that explicit negation is ....

.... have underscored the advantages of extending logic programming with a second kind of negation : for use in deductive databases, knowledge representation, and nonmonotonic reasoning [GL90, KS90, PAA91, Wag91] Different semantics for extended logic programs with : negation (ELP) have appeared [DR91, GL90, KS90, PA92, Prz90, Prz91, Wag91]. AP92] contrasts some of these, where distinct meanings of : negation are identified: classical, strong and explicit. It is argued there that explicit negation is preferable. The well founded semantics with explicit negation (WFSX) PA92] incorporates this prefered : negation, and also ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357--371. LNCS 495, Springer--Verlag, 1991.

....WFS is defined for every normal logic program and assigns it a unique meaning. Not so with SM . The main differences between these two semantics result from their treatment of infinite recursion through negation by default. More recently, a second form of negation was proposed by several authors [19, 13, 23, 20, 4]) to provide a mechanism for explicitly declaring the falsity of 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. ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H.-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357--371. LNCS 495, Springer--Verlag, 1991.

....L the translation B L; with the reading L is believed to be false . Several authors have stressed the importance of extending logic programming with a second kind of negation : in addition to default negation, for use in deductive databases, knowledge representation, and nonmonotonic reasoning [GL90, KS90, PAA91b, Wag91]. Different semantics for extended logic programs with : negation have appeared [DR91, GL90, KS90, PA92, Prz90, Prz91b, Wag91] AP92] contrasts some of these, where distinct meanings of : negation are identified: classical, strong and explicit. It is also argued that explicit negation is ....

.... of extending logic programming with a second kind of negation : in addition to default negation, for use in deductive databases, knowledge representation, and nonmonotonic reasoning [GL90, KS90, PAA91b, Wag91] Different semantics for extended logic programs with : negation have appeared [DR91, GL90, KS90, PA92, Prz90, Prz91b, Wag91]. AP92] contrasts some of these, where distinct meanings of : negation are identified: classical, strong and explicit. It is also argued that explicit negation is preferable. Some work exists comparing extended logic programs semantics and nonmonotonic reasoning formalisms. In [GL90] the ....

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.

....results. Introduction The scenario semantics paradigm of logic programs [4] has been recently expanded in [1] to encompass important logic programming semantics (including those extended with two kinds of negation explicit negation and the traditionally named negation as failure (NAF) [6, 8, 15, 18]. The scenario semantics paradigm, recapitulated below, is built upon simple primitive notions, such as those of scenario a program plus a set of NAF hypotheses , acceptability of a hypothesis wrt to a scenario , evidence contrary to a hypothesis , admissible scenario , completeness of a ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, MFDBS'91, pages 357--371. Springer-Verlag, 1991.

....avoidance and removal approaches. 1 Introduction Recently several authors have stressed and illustrated the importance of including a second kind of negation in logic programs besides negation as failure , and its use in deductive databases, knowledge representation, and nonmonotonic reasoning [9, 12, 13, 14, 10, 18, 19, 20, 27]. Proposals for extending logic programming semantics with a second negation have been advanced. One is the Answer Sets semantics [9] shown to be an extension of the Stable Model semantics [8] of normal logic programs. In [13] a similar extension proposal was introduced, based also on stable ....

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, MFDBS, pages 357--371. SpringerVerlag, 1991.

No context found.

G. Wagner. A Database Needs Two Kinds of Negation. In 3rd Symposium on Mathematical Fundamentals of Database and Knowledge Base Systems (MFDBS'91), pages 357--371. Springer-Verlag, 1991.

No context found.

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H.-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357--371. LNCS 495, Springer--Verlag, 1991.

No context found.

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H.-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357--371. LNCS 495, Springer--Verlag, 1991.

No context found.

G. Wagner. A database needs two kinds of negation. In B. Thalheim and H.- D. Gerhardt, editors, Proc. of the 3rd. Symp. on Mathematical Fundamentals of Database and Knowledge Base Systems, Lecture Notes in Computer Science, pages 357--371. Springer-Verlag, 1991.

No context found.

G. Wagner. A Database Needs Two Kinds of Negation. In B. Thalheim and H.-D. Gerhardt (eds.), Proc. of the 3rd Symp. on Mathematical Fundamentals of Database and Knowledge Base Systems (MFDBS'91), LNCS 495, pages 357-371, Springer-Verlag, 1991.

....two kinds of falsity in knowledge representation are captured by the two negations, called weak and strong, of partial logic. 2 In the monotonic base system of partial logic, weak negation corresponds to classical negation by 1 In the sense of Korner [Koe66] 2 This was already noticed in [Wag91]. 1. Introduction 2 virtue of a straightforward translation of partial logic into classical logic which is discussed in section 3. In the nonmonotonic refinements of partial logic, discussed in sections 4 and 5, weak negation corresponds to negation as failure, and hence can be used to express ....

....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. A database needs two kinds of negation. In B. Thalheim and H.- D. Gerhardt, editors, Proc. of the 3rd. Symp. on Mathematical Fundamentals of Database and Knowledge Base Systems, Lecture Notes in Computer Science, pages 357--371. Springer-Verlag, 1991.

No context found.

G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357-371. LNCS 495, Springer-Verlag, 1991.

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