Minker, J.: On indefinite databases and the closed world assumption. In: Lecture Notes in Computer Science 138, Springer, Berlin (1982) 292--308  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Management and Information Integration (see also Section 8) has renewed the interest in advanced logic based formalisms for Knowledge Representation and Reasoning (KR R) which started in the early 1980s. Among them, Disjunctive Logic Programming (DLP) which has first been considered by Minker [76] in the deductive database context, is one of the most expressive KR R formalisms. Disjunctive logic programs are logic programs where disjunction is allowed in the heads of the rules and negation may occur in the bodies of the rules. Such programs are now widely recognized as a valuable tool for ....

.... 32, 55, 70, 77, 6] One of the attractions of disjunctive logic programming (DLP) is its capability of allowing the natural modeling of incomplete knowledge [7, 73] Much research has been spent on the semantics of disjunctive logic programs, and several alternative semantics have been proposed [10, 47, 55, 76, 85, 88, 86, 92, 93] (see [2, 24, 73, 77, 78] for comprehensive surveys) The most widely accepted semantics is the answer sets semantics proposed by Gelfond and Lifschitz [55] as an extension of the stable model semantics of normal logic programs [54] According to this semantics, a disjunctive logic program may ....

J. Minker. On Indefinite Data Bases and the Closed World Assumption. In D. Loveland, editor, Proceedings 6 Conference on Automated Deduction (CADE '82), number 138 in Lecture Notes in Computer Science, pages 292--308, New York, 1982. Springer.

.... languages, which extend Horn clause programming for dealing with various aspects such as incomplete or indefinite information, have been proposed to date, cf. 1, 33] In particular, the use of disjunction in rule heads for expressing indefinite information was proposed in Minker s seminal paper [32], which started interest in disjunctive logic programming [30, 10] For example, the rule lives in(x; US) lives in(x; canada) lives in(x; mexico) lives in(x; n america) 1) informally states that a person living in north America lives in one of the three countries there. The semantical and ....

....from the inference rules. For example, the complexity of evaluating DB is exponentially lower when is fixed. In section 3, we shall define data and query complexity to give a formal meaning to this intuition. Semantics. The semantics of DDDBs has been defined in terms of their minimal models [32, 30]. For a DDDB DB = E) we denote by HU DB its Herbrand universe, i.e. the set of all constants occurring in DB. The Herbrand base HB DB (resp. disjunctive Herbrand base DHB DB ) is the set of all ground atoms (resp. disjunctive ground facts) of predicates in DB over HU DB . The ground ....

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J. Minker. On indefinite data bases and the closed world assumption. In D. Loveland, editor, Proc. 6 Conference on Automated Deduction (CADE '82), LNCS 138, pp. 292--308, New York, 1982. Springer.

....rule r is satisfied by an interpretation I if the head is true or if the body is false. A constraint is treated as a rule with empty head (it is satisfied iff its body is false) An interpretation M is a model of a Datalog P , if all rules in ground(P) are satisfied by M . Minker proposed in [29] a model theoretic semantics for (positive) Datalog programs P , which assigns P the set MM(P) of its minimal models, where a model M for P is minimal, if no proper subset of M is a model for P . Accordingly, the program P = fa b g has the two minimal models fag and fbg, i.e. MM(P) f fag; ....

J. Minker. On Indefinite Data Bases and the Closed World Assumption. In D. Loveland, editor, Proceedings 6 Conference on Automated Deduction (CADE '82), number 138 in Lecture Notes in Computer Science, pages 292--308, New York, 1982. Springer.

....logic programs. Many approaches been proposed to tackle this problem, some of which well known and implemented in deductive databases and nonmonotonic reason2 ing systems. These include the disjunctive stable models [31] the static semantics [33] the generalized closed world assumption (GCWA)[28] and the extended GCWA (EGCWA) 46] Despite some work has been done in relating consistency based abduction with disjunctive logic programs [3, 11, 26, 29, 39] the problem of how to perform argumentation based abduction in disjunctive logic programming is rarely explored seriously [6, 29] ....

....information is not explicitly represented in databases and thus a meta rule is often employed to derive negative information from deductive databases. Reiter s [35] closed world assumption (CWA) provides such an excellent mechanism for non disjunctive databases. As first observed by Minker [28], CWA becomes inconsistency for disjunctive programs and, thus, the generalized closed world assumption (GCWA) for positive disjunctive programs is proposed for inferring negative information in disjunctive deductive databases. However, an important deficiency of GCWA is that it is unable to infer ....

Minker,J., On Indefinite Databases and the Closed World Assumption, in: LNCS 138, Springer, pp.292-308, 1982.

....is available and the latter is related with disjunctiv information represented by a finite disjunction of formulas. Disjunctive information is indefinite if at least one of the formulas should be true. Researches such as [Prad83] Imie84] Reit84] Kel185] Kong95] featured the incompleteness, and [Mink82][Reit84] Chiu95] tackled th indefiniteness especially in deductive databases. Refer to [Pars96] for the full survey of this issue. The material dealt with in this chapter is to introduce a uniform framework for seamlessly supporting unknown values, which encompass incompleteness, indefiniteness, ....

....the latter regards database as a set of first order formulas not as an interpretation. Queries are formulas to be proven, given the database as premises. It is denoted by DB I Q. He also discussed incomplete information including disjunctive information and null values in this framework. [Mink82] [Reit84] Yang91 ] Kong95] refined his work in indefinite (disjunctive) databases that contain disjunctive formulas in the first order logic. To be specific, Ymg91] encoded the subtle semantics of unknown values in terms of a predicate called IP(Implicit Predicate) and formalized a query ....

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J. Minker, "On Indefinite Databases and the Closed World Assumption," 6 th Conference on Automated Deduction, New York, in Lecture Notes in Computer Science, No. 138, Springer-Verlag, 1982.

....variables appearing on the left hand side of also appear on the right hand side of . The declarative semantics of disjunctive deductive databases is based on Herbrand models. Such databases do not possess a unique smallest Herbrand model, but instead have a collection of minimal Herbrand models [10]. The following theorem illustrates the declarative semantics: Theorem 4 (Minker 1982) For a disjunctive deductive database P and for every positive clause E, P j= E if and only if E is true in every minimal model of P. The fixpoint semantics of disjunctive deductive databases is based on the ....

Jack Minker. On indefinite databases and the closed world assumption. In Lecture Notes in Computer Science, N138, pages 292--308. Springer-Verlag, 1982.

....false iff A is not in the unique minimal model of the database. CWA is not applicable to DDDBs since it may produce inconsistent results. For DDDBs the rule used to define negated atoms is the Generalized Closed World Assumption (GCWA) which is an extension of the CWA rule to the disjunctive case [26]. GCWA is able to consistently define those atoms whose negation can be assumed to be true in the database. To assume negative clauses the Extended Generalized Closed World Assumption (EGCWA) is used[43] The default rules for negation in the disjunctive case are formally defined as follows: ....

....those atoms whose negation can be assumed to be true in the database. To assume negative clauses the Extended Generalized Closed World Assumption (EGCWA) is used[43] The default rules for negation in the disjunctive case are formally defined as follows: Definition 2. 5 (Closed World Assumption)[26, 43] Let DB be a DDDB. Then CWA(DB) f:A 1 Delta Delta Delta :An jA i 2 HBDB and n 0 and 6 9 a minimal model of DB; M s.t. fA 1 ; Delta Delta Delta ; An g Mg. The definition reduces to the CWA of [33] for definite databases. n always equal to 1 gives the GCWA [26] Allowing arbitrary values ....

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J. Minker. On Indefinite Databases and the Closed World Assumption. Lecture Notes in Computer Science 138, pages 292--308. Springer, 1982.

....hypothesis of P . Although these semantics stem from very different intuitions, all of them share a number of attractive properties. In particular, each of these semantics extends both the well founded semantics [12] for normal logic programs and the generalized closed world assumption (GCWA) [9] for positive disjunctive programs (i.e. without default negation) It has been proven that D WFS is equivalent to a restricted version of STATIC [3] But the relation of these semantics to the argumentation basedsemantics and unfounded sets are as yet unclear. In this paper, we modify some ....

....Intuitively, not b (i.e. John is not visiting Berlin) should be inferred from P . It can be verified that neither b nor its negation not b can be derived from P under D WFS and STATIC while not b can be derived under WFDS. The intuition behind Minker s Generalized Closed World Assumption (GCWA) [9] can be read off its proof theoretic characterization: If, for every positive disjunction A, P a A implies P A, then not a is derivable from P , where is the inference relation in the classical logic and P is considered as a classical logic theory. The above principle for positive DLP ....

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J. Minker. On indefinite databases and the closed world assumption. LNCS 138, pages 292308, 1982.

.... the set of atoms occurring in I , and by I Gamma the set of atoms whose negation belongs to I . I is a total interpretation if I [ I Gamma = B P . A set M of atoms is a model for P if the total interpretation M [ B P Gamma M) satisfies each rule in P . Model M is a minimal model [19] for P if there is no model N for P such that N ae M . Given a disjunctive logic program P , we use MM(P ) and MOD(P ) to denote the set of all minimal models of P and the set of all models of P , respectively. M is a stable model (or answer set) 7] of P if M is a minimal model of P M where P ....

....to elegantly and declaratively encode a variety of problems. Given a (possibly disjunctive) logic program P , there has been an immense amount of work on characterizing the declarative semantics of P . Many of these semantics (such as the stable model semantics [6] the minimal model semantics [19, 2], and the all models semantics) identify a class of models of the program as being epistemically acceptable. In this paper, we take the point of view that a user of a logic program (which is presumably written by a logic programming professional) may wish to add criteria that she cares about, ....

Jack Minker. On Indefinite Data Bases and the Closed World Assumption. In D.W. Loveland, editor, Proceedings 6 th Conference on Automated Deduction (CADE '82), number 138 in Lecture Notes in Computer Science, pages 292--308, New York, 1982. Springer.

.... of paraconsistent logic programs [5] and also reduces to van Emden and Kowalski s fixpoint semantics in definite logic programs [34] For positive disjunctive programs, our fixpoint construction characterizes Sakama s possible model semantics [29] 3 and Minker s minimal model semantics [24]. Let PM P (resp. MM P ) be the set of all possible models (resp. minimal models) of a positive disjunctive program P . Theorem 2.9 Let P be a positive disjunctive program. Then, i) PM P = T P ) ii) MM P = min( T P ) The above (i) also presents that for a positive extended ....

J. Minker. On indefinite data bases and the closed world assumption. In Proceedings of the Sixth International Conference on Automated Deduction, Lecture Notes in Computer Science, 138, Springer-Verlag, 292-308, 1982.

.... representation, database querying, and for representing incomplete information, is generally acknowledged (see Gelfond and Lifschitz [1991] and Baral and Gelfond [1994] Various semantics of DLPs have been proposed; they are commonly based on the paradigm of minimal models, which underlies Minker s [1982] Generalized Closed World Assumption. For an overview of various semantics for DLPs, the reader may consult Lobo et al. 1992] and Minker s more recent article [Minker 1994] In this article, we limit our attention to three important semantics for disjunctive logic programming (and thus for ....

...., disjunctive Datalog, is the language of all query programs. 3. 2 Semantics There are several proposals to capture the meaning of disjunctive logic programs, based on different concepts of the intended models of a program (cf. Lobo et al. 1992] and Minker [1994] We consider minimal models [Minker 1982] (arising in the AI community in circumscription [McCarthy 1986] and in advanced forms of the Closed World Assumption, e.g. the Extended Generalized CWA [Yahya and Henschen 1985] the perfect models [Przymusinski 1988] and the (disjunctive) stable models [Gelfond and Lifschitz 1988; ....

MINKER, J. 1982. On indefinite data bases and the closed world assumption. In Proceedings of the Sixth Conference on Automated Deduction (CADE-82) (New York, NY, July 11--14), LNCS 138, 292--308.

.... databases comprise explicit data and logical rules for computing queries on the data, which amount to a logic program without function symbols, i.e. datalog programs (extended with negation) 39, 6] The need for representing disjunctive information led to disjunctive deductive databases [26], which fertilized also work on disjunctive logic programming [25, 27] In this paper, we address disjunctive deductive databases, which are identified with disjunctive function free logic programs [20] and refer to them simply as programs. To date, the total stable (or 2 valued stable) model ....

....called justifiability in [42, 43] basically prescribes that every positive literal in an interpretation must be be derived from the rules possibly using negative literals as additional axioms. Let for any positive (i.e. free) program P denote MM(P ) the set of the minimal total models of P [26], where a total model M is minimal iff there does not exist a total model N of P such that N ae M . Moreover, let for any program LP and interpretation I be LP(I) the program obtained from ground(LP) as follows: i) remove all rules r having a negative literal :p 2 B(r) such that :p 62 I ....

[Article contains additional citation context not shown here]

J. Minker, On indefinite data bases and the closed world assumption, in Proc. 6th Conference on Automated Deduction (CADE '82), New York, D.W. Loveland ed., LNCS 138, Springer, 1982, pp. 292--308.

....logic programs is based on minimal Herbrand models, as the least (unique minimal) model does not exist in general. Example 5 P = fp q g has the two minimal models M 1 = fpg and M 2 = fqg. Denote by MM(P ) the set of minimal Herbrand models of P . The Generalized Closed World Assumption [104] (GCWA) for negation free P amounts to the meaning MGCWA (P ) fL j MM(P ) j= Lg. Example 6 Consider the following program P 0 , describing the behavior of a reviewer while reviewing a paper: good bad paper happy good angry bad smoke happy smoke angry paper The following ....

J. Minker. On Indefinite Data Bases and the Closed World Assumption. In D. Loveland, editor, Proc. 6th CADE, LNCS 138, pp. 292--308, New York, 1982. Springer.

....indicates, non monotonic knowledge bases must be equipped with a nonmonotonic semantics. Intuitively this means that we need to provide a meaning to the default negation atoms Not F . We want the intended meaning of default atoms Not F to be based on the principle of predicate minimization (see [Min82, GPP89] and [McC80] Not F holds if F is minimally entailed or, equivalently: Not F holds if F is false in all minimal models. In order to make this intended meaning precise we first have to define what we mean by a minimal model of a knowledge base. Definition 2.4 (Minimal Models [Prz97] A model ....

Jack Minker. On indefinite databases and the closed world assumption. In Proceedings of the 6th Conference on Automated Deduction, New York, pages 292--308, Berlin, 1982. Springer.

....problem can be avoided if bird is fixed (i.e. not allowed to vary) in circumscribing f lies. The circumscription actually deduces :bird oe :f lies; so we conclude that it does not fly unless it is a bird. In classical logic programming, every predicate is usually minimized in a PDP by GCWA [48], in which the answer sets of the program are exactly the minimal Herbrand models. An exception can be seen in ECWA proposed by Gelfond et al. 24] which is equivalent to circumscription in the existence of the unique name and domain closure assumptions. We now formalize ECWA for PDPs without ....

Minker, J., On Indefinite Data Bases and the Closed World Assumption, in: Proceedings of the Sixth International Conference on Automated Deduction, Lecture Notes in Computer Science 138, Springer, 1982, pp. 292--308.

....processing is a harder problem in the disjunctive case, than it is in a definite case. Since negative information is not explicitly represented in the database, a meta rule for negation is used to derive it. For DDDB negated atoms are defined by the Generalized Closed World Assumption (GCWA) [12] which consistently defines those atoms whose negation can be assumed to be true in the database. The Extended Generalized Closed World Assumption (EGCWA) 18] a generalization of GCWA, is used to determine the truth or falsity of conjunctions of atoms. Although negative facts are not ....

J. Minker. On indefinite databases and the closed world assumption. In Lecture Notes in Computer Science 138, pages 292--308. Springer-Verlag, 1982.

....the most basic and indispensable criteria that each semantics for commonsense reasoning should obey [Sch92] This is also the case in the context of disjunctive logic programs, logic programs containing indefinite information. Namely, the minimal model semantics for positive disjunctive programs [Min82] and the disjunctive stable model semantics for normal disjunctive programs [Prz91a] are both minimal. However, such a minimalism is not always appropriate in a theory containing indefinite information. Ross and Topor [RT88] have firstly noticed this problem in the context of inferring negation ....

....assumption (CWA) Rei78] as a default rule for inferring negation from a program. However, Reiter has also pointed out that the CWA works well only for Horn logic programs and causes an inconsistency in the presence of indefinite information in a program. In positive disjunctive programs, Minker [Min82] has extended Reiter s CWA to the generalized closed world assumption (GCWA) On the other hand, Ross and Topor [RT88] have proposed an alternative rule called the disjunctive database rule (DDR) which turns out to be equivalent to the weak generalized closed world assumption (WGCWA) that is ....

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Minker, J., On Indefinite Data Bases and the Closed World Assumption, Proc. 6th Int. Conf. on Automated Deduction, Lecture Notes in Computer Science 138, Springer-Verlag, 292-308, 1982.

....Object Oriented Databases (DOOD 89) North Holland, pp. 369 383, 1989. 1 such databases, two alternative rules are known. The first approach considers the collection of minimal models and the facts which are not true in any minimal model are assumed to be false by the generalized CWA (GCWA) [Min82, YH85]. On the other hand, the other approach which is not based on the minimal model semantics is the disjunctive database rule (DDR) RT88] or equivalently the weak GCWA (WGCWA) RLM89] Both the GCWA and the DDR provide simple and powerful mechanisms for inferring negation, however, each rule also ....

....of a program is a subset of the Herbrand base of the program. An interpretation I is called a minimal model of a database D if there is no smaller interpretation J satisfying the database. A database is consistent if it has a minimal model, otherwise it is inconsistent. The minimal model semantics [Min82] of a disjunctive database D is defined as the set of all minimal models of D. Note that a database possibly becomes inconsistent in the presence of negative clauses. In this paper, we assume a database to be consistent unless stated otherwise. Next we introduce the notion of split databases. 2 ....

[Article contains additional citation context not shown here]

Minker, J., On Indefinite Data Bases and The Closed World Assumption, Proc. 6th Int. Conf. on Automated Deduction, Lecture Notes in Computer Science 138, Springer-Verlag, 292--308, 1982.

No context found.

Minker, J.: On indefinite databases and the closed world assumption. In: Lecture Notes in Computer Science 138, Springer, Berlin (1982) 292--308

No context found.

J. Minker, "On Indefinite Data Bases and the Closed World Assumption," Proc. Sixth Conf. Automated Deduction, D.W. Loveland, ed., pp. 292-308, 1982.

No context found.

J. Minker. On indefinite databases and the closed world assumption. In Proceedings of the 6th Conference on Automated Deduction, pages 292--308, New York, 1982. Springer, Berlin, Heidelberg, New York.

No context found.

J. Minker. On indefinite databases and the closed world assumption. LNCS 138, pages 292308, 1982.

No context found.

J. Minker. On indefinite databases and the closed world assumption. In Proceedings of the Sixth International Conference on Automated Deduction (CADE'82), pages 292--308, 1982.

No context found.

Minker, J.: On indefinite databases and the closed world assumption. In Lecture Notes in Computer Science 138, Springer-Verlag (1982) pp. 292--308

No context found.

J. Minker. On Indefinite Data Bases and the Closed World Assumption. In Proc. CADE '82, LNCS 138, pp. 292--308, 1982.

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