V. Lifschitz. Foundations of logic programming. In Principles of Knowledge Representation, pages 69--127. CSLI Publications, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....class of programs formalizes inheritance reasoning with incomplete information which was not previously considered. 2. Logic programs In this section we give a brief introduction to the answer set semantics for logic programs with two kinds of negation [23] For a more detailed discussion see [5,31]. For programs without classical negation the answer set semantics coincides with the stable model semantics of [21] The language of a logic program, like a typed first order language, is determined by its signature #, consisting of types (types(#) object constants for each type # (obj(# , ....

V. Lifschitz, Foundations of logic programming, in: Principles of Knowledge Representation, ed. G. Brewka (CSLI Publications, 1996) pp. 69--128.

....if it is v free (i.e. 8R 2 P : jH(R)j 1) A normal program is also called a Datalog program. As usual, a term (atom, rule etc) is ground, if no variables appear in it. A ground program is also called propositional. 16 Answer sets of DLPs are defined as consistent answer sets for EDLPs as in [12,25]. That is, for any program P , let U P be its Herbrand universe and B P be the Herbrand base of P over U P (if no constant appears in P , an arbitrary constant is added to U P ) Let ground(P ) R2P ground(R) denote the grounding of P , where ground(R) is the set of all ground instances of R. ....

.... the actions in A i 1 (i.e. those actions which are executed at step i 1) Moreover, trajectories encoded in the answer sets of lp(P) are guaranteed to establish the goal of the planning problem, and the underlying sequence of action sets is We only consider consistent answer sets, while in [12,25] also the (inconsistent) set B P may be an answer set. Technically, we assume that negative classical literals :a are viewed as new atoms a, and constraints : a; a are implicitly added. This is the standard way how true negation is implemented in systems like DLV or Smodels. therefore an ....

Lifschitz, V., 1996. Foundations of Logic Programming. In: Brewka, G. (Ed.), Principles of Knowledge Representation. CSLI Publications, Stanford, pp. 69--127.

....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 knowledge representation and commonsense reasoning [7, 73, 100, 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, ....

V. Lifschitz. Foundations of Logic Programming. In G. Brewka, editor, Principles of Knowledge Representation, pages 69--127. CSLI Publications, Stanford, 1996.

....colon in [w : stems from the DLV language, which allows to specify a priority layer after the colon. We do not need priority layers in our translation, but stick to the DLV syntax. See [13] for further details. Semantics The answer sets of a program without weak constraints are defined as in [16, 26]. There is one difference, though: We do not consider inconsistent answer sets. The answer sets of a program with weak constraints are defined by selection from the answer sets S of the weak constraint free part of as optimal answer sets. A weak constraint c of form (3) is violated, if ....

V. Lifschitz. Foundations of Logic Programming. In G. Brewka, editor, Principles of Knowledge Representation, pages 69--127. CSLI Publications, Stanford, 1996.

....the program the additional clauses p( x; f ) not p( x; t d ) that would include in the models all the negative information we usually keep implicit via the closed world assumption. Moreover, we would be left with a normal disjunctive program, for which a stable model semantics could be used [12]. Example 8. example 7 cont. The coherent plausible minimal models of the program presented in example 7 are: To distinguish them from the minimal model of the annotated theory. 9 Eurbook(kafka; methamorph; 1919 ; f a ) Eurbook(kafka; methamorph; 1919 ; f Notice, that in ....

Lifschitz, V. \Foundations of Logic Programming". In Principles of Knowledge Representation, G. Brewka (ed.), CSLI Publications, 1996, pp. 69-127.

....issues and on the implementation, we conclude with a short discussion. This paper regroups and strongly extends the work found in [Delgrande et al. 2000c; Delgrande et al. 2000b; Delgrande et al. 2000d; Delgrande et al. 2000a] 2 Definitions and Notation We deal with extended logic programs [Lifschitz, 1996] that contain the symbol : for classical negation in addition to not used for negation as failure. This allows for distinguishing between goals that fail in the sense that they do not succeed and goals that fail in the stronger sense that their negation succeeds. Classical negation is thus also ....

V. Lifschitz. Foundations of logic programming. In G. Brewka, editor, Principles of Knowledge Representation, pages 69--127. CSLI Publications, 1996.

....A. Gabaldon Building a knowledge base: an example information which was not previously considered. 2. Logic Programs In this section we give a brief introduction to the answer set semantics for logic programs with two kinds of negation [21] 3 . For a more detailed discussion see [5] and [30]. The language of a logic program, like a typed first order language, is determined by its signature oe, consisting of types (types(oe) object constants for each type (obj( oe) and typed function and predicate constants (func(oe) and pred(oe) respectively) Signature oe 1 is a sub signature ....

V. Lifschitz. Foundations of logic programming. In Gerhard Brewka, editor, Principles of Knowledge Representation, pages 69--128. CSLI Publications, 1996.

....by viewing r as an integrity constraint. WC(P ) denotes the set of weak constraints in P . As usual, a term (atom, rule, is ground, if no variables appear in it. Semantics. Answer sets for LPs with weak constraints are defined by extending consistent answer sets for LPs as introduced in [17, 20]. We proceed in three steps: we first define answer sets (1) of ground positive programs, then (2) of arbitrary ground programs, and (3) finally (optimal) answer sets of ground programs with weak constraints. As usual, the (optimal) answer sets of a non ground program P are those of its ground ....

....set for P if it is a minimal set (wrt. set inclusion) closed under P . 2) Let P I be the Gelfond Lifschitz reduct of a program P w.r.t. I B P , i.e. the program obtained from P by deleting all rules r 2 P such that B (r) I 6= and 1 We only consider consistent answer sets, while in [20] also the (inconsistent) set BP may be an answer set. INFSYS RR 1843 02 01 5 all negative body literals from the remaining rules. Then, I B P is an answer set of P iff I is an answer set of P I . By AS(P ) we denote the set of all answer sets of P . Example 2 The program a v b. b v c. ....

Vladimir Lifschitz. Foundations of Logic Programming. In G. Brewka, editor, Principles of Knowledge Representation, pages 69--127. CSLI Publications, Stanford, 1996.

....as particular logic programs without negation. There are two major di erences: i) patterns play the role of terms and (ii) uni cation has to be realized modulo the equational theory E = f(x; y; z) x; y) z)g; where is interpreted as concatenation of patterns. As for logic programs (cf. [13], e.g. the semantics of an ordinary EFS S, denoted by Sem o (S) can be de ned via the operator TS (see below) In the corresponding de nition, we use the following notations. For any EFS S = we let B(S) denote the set of all well formed ground atoms over and . Moreover, we let ....

....is as follows. If, for instance, A = p(x 1 ; xn ) and B 1 = q(x 1 ; xn ) then the predicate p succeeds i the predicate q fails. However, taking the conceptual diculties into consideration that occur when de ning the semantics of logic programs with negation as failure (cf. [13], e.g. AEFSs are constrained to meet several additional syntactic requirements (cf. De nition 4) The requirements posed guarantee that, similarly to strati ed logic programs (cf. 13] e.g. the semantics of AEFSs can easily be described. Moreover, as a side e ect, it is guaranteed that AEFSs ....

[Article contains additional citation context not shown here]

V. Lifschitz, Foundations of logic programming, in: Principles of knowledge representation, G. Brewka (ed.), CSLI Publications, 1996, pp. 69-127.

....if it is v free (i.e. 8R 2 P : jH(R)j 1) A normal program is also called a Datalog program. As usual, a term (atom, rule etc) is ground, if no variables appear in it. A ground program is also called propositional. Answer sets of DLPs are defined as consistent answer sets for EDLPs as in [12, 28]. That is, for any program P , let U P be its Herbrand universe and B P be the Herbrand base of P over U P (if no constant appears in P , an arbitrary constant is added to U P ) Let ground(P ) S R2P ground(R) denote the grounding of P , where ground(R) is the set of all ground instances of ....

....the translated program lp(P) corresponds to a successful trajectory T = hhs 0 ; A 1 ; s 1 i; hs n 1 ; A n ; s n ii of P in the following sense: The fluent literals in AS having timestamp 0 represent a (legal) initial state s 0 of T . 2 We only consider consistent answer sets, while in [12, 28] also the (inconsistent) set BP may be an answer set. Technically, we assume that negative classical literals :a are viewed as new atoms a, and constraints : a; a are implicitly added. This is the standard way how true negation is implemented in systems like DLV or Smodels. INFSYS RR ....

V. Lifschitz, Foundations of Logic Programming, in: G. Brewka (Ed.), Principles of Knowledge Representation, CSLI Publications, Stanford, 1996, pp. 69--127.

....] the other based on stable models, or answer sets [ Gelfond and Lifschitz, 1988 ] Fran cois Fages [1994] showed that if a logic program satis es a certain syntactic condition, which is now called tightness, then its stable models can be characterized as the models of its completion. Lifschitz [1996] observed that Fages theorem can be extended to programs with in nitely many rules and to programs with classical negation [ Gelfond and Lifschitz, 1991 ] if the concept of completion in the statement of the theorem is replaced by its semantic counterpart the concept of a supported model [ Apt ....

Vladimir Lifschitz. Foundations of logic programming. In Gerhard Brewka, editor, Principles of Knowledge Representation, pages 69-128. CSLI Publications, 1996.

No context found.

V. Lifschitz. Foundations of logic programming. In Principles of Knowledge Representation, pages 69--127. CSLI Publications, 1996.

No context found.

Vladimir Lifschitz. Foundations of logic programming. In Principles of Knowledge Representation, pages 69--127. CSLI Publications, 1996.

No context found.

Lifschitz, V.: Foundations of logic programming. In: Principles of Knowledge Representation. CSLI Publications (1996) 69--127

No context found.

V. Lifschitz. Foundations of Logic Programming. In G. Brewka, editor, Principles of Knowledge Representation, pages 69--127. CSLI Publications, Stanford, 1996.

No context found.

Vladimir Lifschitz. Foundations of Logic Programming. In G. Brewka, editor, Principles of Knowledge Representation, pages 69--127. CSLI Publications, Stanford, 1996.

No context found.

V. Lifschitz. Foundations of Logic Programming. In G. Brewka, editor, Principles of Knowledge Representation, pages 69--127. CSLI Publications, Stanford, 1996.

No context found.

V. Lifschitz. Foundations of Logic Programming. In G. Brewka, editor, Principles of Knowledge Representation, pages 69--127. CSLI Publications, Stanford, 1996.

No context found.

V. Lifschitz. Foundations of logic programming. In Gerhard Brewka, editor, Principle of knowledge representation, pages 69--127. The University of Chicago Press, 1996.

No context found.

Vladimir Lifschitz. Foundations of Logic Programming. In G. Brewka, editor, Principles of Knowledge Representation, pages 69--127. CSLI Publications, Stanford, 1996.

No context found.

V. Lifschitz. Foundations of logic programming. In Gerhard Brewka, editor, Principles of Knowledge Representation, pages 69--127. The University of Chicago Press, 1996.

No context found.

V. Lifschitz, `Foundations of logic programming', in Principles of Knowledge Representation, ed., G. Brewka, 69--127, CSLI, (1996).

No context found.

V. Lifschitz, Foundations of logic programming, in: Principles of knowledge representation, G. Brewka (ed.), CSLI Publications, 1996, pp. 69--127.

No context found.

V. Lifschitz. Foundations of Logic Programming. In G. Brewka, editor, Principles of Knowledge Representation, pages 69--127. CSLI Publications, Stanford, 1996.

No context found.

V. Lifschitz. Foundations of logic programming. In Gerhard Brewka, editor, Principles of Knowledge Representation, pages 69-128. CSLI Publications, 1996. 42

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC