J.W. Lloyd and R.W. Topor. Making Prolog more Expressive. Journal of Logic Programming, 3:225-240, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....minimality relative to set inclusion. In other words, we say that X is an answer set for if X satis es but no proper subset of X satis es . for each atom a. When the head of every rule of is a single atom, Comp( is equivalent to the propositional case of completion de ned in [ Lloyd and Topor, 1984 ] For instance, let 1 be the program: p ; q: The answer sets for 1 are fpg and fqg. Comp( 1 ) is p :q q :p and its models are fpg and fqg also. 2 is the following program that adds two rules to 1 : p ; q p q q p p q p :q q q :p p; and its only model ....

John Lloyd and Rodney Topor. Making Prolog more expressive. Journal of Logic Programming, 3:225-240, 1984.

....generalized in [ Babovich et al. 2000 ] In this paper we show how to extend Fages theorem to programs with nested expressions in the bodies of rules. A generalization of the completion The term used by Fages is positive order consistent. semantics to such programs was proposed in [ Lloyd and Topor, 1984 ] and a similar generalization of the answer set semantics is given in [ Lifschitz et al. 1999 ] Here is an example. Program p not not p; 1) contains nested occurrences of negation as failure in the body of the rst rule. It belongs to the syntactic class for which our theorem ....

....to the left or to the right) is p; r. The positive part of (p; not q) not r is p; not q. The positive part of p; not q; r is p; not q; r. The positive part of not p is . 2 X that L is a parent of L relative to and X if there is a rule (4) This is essentially the de nition from [Lloyd and Topor, 1984] restricted to the propositional case. It is restricted to nite programs to avoid the need to use an in nite disjunction in (7) X j= Body , L 2 lit (Body ) and L = Head . For instance, the parents of p relative to the program p not q; q not p; p p; r (9) and the set fp; ....

John Lloyd and Rodney Topor. Making Prolog more expressive. Journal of Logic Programming, 3:225-240, 1984.

....(atoms with or without classic negation) connectives such as negation as failure not, disjunction ; and conjunction , This is a proper subset of the class of programs considered in [Lifschitz et al. 1999] where the head of a rule can also be an arbitrary formula. Lloyd and Topor [Lloyd and Topor, 1984] defined nested logic programs without negation as failure, and argued for the higher expressive power of the extended language, while Lifschitz et al. further showed the role of negation as failure in nested logic programs. Our goal in this paper is to provide a characterization of answer sets ....

J Lloyd and R. Topor. Making Prolog more expressive. J. Logic Programming, 1(3):225-- 240, 1984.

....its logical meaning is given by the formula 8( l 1 : l n ) A normal theory consists of normal de nitions (one de nition per de ned predicate) and normal axioms. Every theory can be transformed into an equivalent normal one using a simple transformation, the Lloyd Topor transformation [30]. By the denotational convention of representing a de nition as a set of rules without explicit completion, normal theories syntactically and semantically correspond to Abductive Logic Programs or Open Logic Programs [8] under the 2 valued completion semantics of [6] As a consequence of ....

J.W. Lloyd and R.W. Topor. Making prolog more expressive. Journal of Logic Programming, 1(3):225-240, 1984.

.... property quadruples (similar to RDF triples, but including an explicit ID for each tuple) Furthermore, the ConceptBase database implements a query and reasoning mechanism based on (negated) Datalog, first order formulas can be used in rules and constraints based on the Lloyd Topor transformation [13]. This reasoning functionality is an important service needed in the Edutella network e.g. for enabling automatic data consistency based on the data content, for fast and highly flexible data retrieval, and for general reasoning purposes. The O Telos Peer implements two basic services in order to ....

J. W. Lloyd and R. W. Topor. Making prolog more expressive. Journal of Logic Programming, 3:225--240, 1984.

....The first task of a query compiler starting from a query description Q is to generate code for an efficient evaluation. We already presented the transformation of query class descriptions into rules. This intermediate representation can be compiled to sets of rules utilizing the algorithm in [31] for translating general logic programs. Our example query class WrongDrugPatient results in the rules W rongDrugP atient(p; w) Gamma In(p; #P atient) In(w; #Drug) A(p; takes; w) WDPH(p;w) WDPH(p;w) Gamma In(d; #Disease) A(p; suffers; d) A(w; against; d) 16 The second ....

J. W. Lloyd and R. W. Topor, "Making PROLOG more expressive", in Journal of Logic Programming, pp. 225--240, 1984.

....equations. We continue our employee example by demonstrating the different stages with the recursive bossrule and the query class IndEmp. The semantically optimized rules described in section 2. 3 are compiled to plain Datalog utilizing the algorithm proposed for general logic programs in [LT84]. A:#boss(e; t) Gamma A:#dept(e; d) A:#head(d; t) A:#boss(e; t) Gamma A:#boss(e; m) A:#boss(m; t) IndEmp(e; c) Gamma A:#salary(e; s) A:#salary(c; t) s t; IE 1 (e) IE 1 (e) Gamma A:#boss(e; m) The last Datalog rule is an auxiliary rule concluding a new literal IE 1 . It ....

Lloyd J.W., Topor R.W., "Making PROLOG more expressive", In Journal of Logic Programming, pp. 225-240, March 1984. 37

.... which is a deductive object oriented database, very useful as a repository for modeling and storing metadata (e.g. Jeusfeld et al. 1998] ConceptBase implements a powerful query and reasoning mechanism (rules and constraints) based on (stratified) Datalog and uses the Lloyd Topor transformation [Lloyd and Topor, 1984] to allow arbitrary first order logic formulas in the body of rules. Our O Telos Peer provides advanced query capabilities (up to RDF QEL5) for RDF data stored in or imported into the ConceptBase subsystem of the O Telos Peer. In order to store the RDF metadata in ConceptBase the peer has to ....

Lloyd, J. W. and Topor, R. W. (1984). Making prolog more expressive. Journal of Logic Programming, 3:225 240.

.... The Java binding (available from the Edutella Project Page 4 ) is composed of the following packages: Note, that as input format we can even allow arbitrary first order logic formulas in the body of rules, which then can be transformed into a set of rules using the Lloyd Topor transformation [24]. http: edutella.jxta.org net.jxta.edutella.util.datamodel: Contains all classes for the Edutella common data model as described in Figure 4. This common model is used for transmitting queries within the Edutella network. net.jxta.edutella.util: Contains classes RDF QEL 1, RDF QEL 2, etc. ....

.... reflexive, as advocated in [2] typeof(X,Y) typeof(X,Y) not(typeof(X,Z) subclassof(Z,Y) subclassof(X,Y) subclassof(X,Y) not(subclassof(X,Z) subclass(Z,Y) Anonymous nodes, i.e. existential variables in the RDF graph itself, can be handled by the usual Lloyd Topor transformation [24]. or the other way around, if we assume that the local peer stores only the typeof and subclassof facts subclassof(X,Y) subclassof(X,Y) subclassof(X,Y) subclassof(X,Z) subclassof(Z,Y) typeof(X,Y) typeof(X,Y) typeof(X,Y) subclassof(Z,Y) typeof(X,Z) and alternatively ....

J. W. Lloyd and R. W. Topor. Making prolog more expressive. Journal of Logic Programming, 3:225--240, 1984.

.... of queries) Any peer can plug in additional classes here to support further query languages (see [11] Note, that as input format we can even allow arbitrary first order logic formulas in the body of rules, which then can be transformed into a set of rules using the Lloyd Topor transformation [8]. hasHead:EduStatementLiteral hasBody:EduLiteral EduRule hasResult hasResults:EduResult EduResultSet hasBindings:EduVariableBinding EduTupleResult RDFModel EduResult negated:boolean EduLiteral hasBody hasPredicate:Resource hasArguments:RDFNode EduStatementLiteral ....

J. W. Lloyd and R. W. Topor. Making prolog more expressive. Journal of Logic Programming, 3:225--240, 1984.

....de ning the predicates in the head. rules that encode constraints on the solutions. A constraint represented by a rst order axiom F is encoded by adding the rule f not F; not f and by simplifying it to normal form using a standard transformation such as the method of Lloyd and Topor [21]. Here f is a new predicate symbol representing false. rules that encode open predicates. These are predicates on which the expert has incomplete knowledge and which do not appear in the head of the rules. For each open predicate p, a new predicate p is introduced and the rules: p not p ....

J.W. Lloyd and R.W. Topor. Making prolog more expressive. Journal of Logic Programming, 1(3):225-240, 1984.

....the completion sentences are first order also. Applying literal completion is all that needs to be done to eliminate the second order quantifiers from the sentence representing CBW . Literal completion is similar to the process of completion familiar from logic programming ( Clark, 1978 ] Lloyd and Topor, 1984 ] Its main new feature is that the completed definition of an explainable predicate constant P consists of two equivalences, one positive and one negative. Positive completion sentences are obtained from the rules whose heads are positive literals in exactly the same way as in [ Lloyd and ....

....1984 ] Its main new feature is that the completed definition of an explainable predicate constant P consists of two equivalences, one positive and one negative. Positive completion sentences are obtained from the rules whose heads are positive literals in exactly the same way as in [ Lloyd and Topor, 1984 ] Negative completion sentences are generated in a similar way from the rules whose heads are negative literals. In addition, for every rule F G whose head F does not contain explainable symbols, there is a corresponding completion sentence, which is simply the universal closure of G oe F . ....

John Lloyd and Rodney Topor. Making Prolog more expressive. Journal of Logic Programming, 3:225--240, 1984.

....to different semantic formalisms used in the Edutella peers. It should be as easily be connected 3 Note, that as input format we can even allow arbitrary first order logic formulas in the body of rules, which then can be transformed into a set of rules using the Lloyd Topor transformation [24]. 8 to simple RDFS repositories, relational databases or object relation ones, and inference systems, which all have different base semantics and capabilities. Transformability of the query language. The basic query exchange language model must be easy to translate to many different query ....

.... as advocated in [2] typeof(X,Y) typeof(X,Y) not(typeof(X,Z) subclassof(Z,Y) subclassof(X,Y) subclassof(X,Y) not(subclassof(X,Z) subclass(Z,Y) 6 Anonymous nodes, i.e. existential variables in the RDF graph itself, can be handled by the usual Lloyd Topor transformation [24]. 14 or the other way around, if we assume that the local peer stores only the typeof and subclassof facts subclassof(X,Y) subclassof(X,Y) subclassof(X,Y) subclassof(X,Z) subclassof(Z,Y) typeof(X,Y) typeof(X,Y) typeof(X,Y) subclassof(Z,Y) typeof(X,Z) and ....

J. W. Lloyd and R. W. Topor. Making prolog more expressive. Journal of Logic Programming, 3:225--240, 1984.

....to be implemented on top of XSB (i.e. Prolog with tabled resolution) analogously to the F Logic Flora [12] Figure 5 shows the rewrite rules for mapping RDFspeci c features like resources and statements. All other mappings are well known (Lloyd Topor transformations for handling of quanti er [11]) or straightforward (see the SiLRI system [5] Example: p:jdow[p:lastname doe] m1: true(statement(resource(p, jdow) resource(p, lastname) doe) m1) In a future document, a model theoretic semantics based on minimal Herbrand models and x point operators will be provided. 5 ....

J.W. Lloyd and R.W. Topor. Making Prolog more Expressive. Journal of Logic Programming, 3:225{ 240, 1984.

....as smodels [13] and dlv [6] This possibility is important from the perspective of answer set programming. The idea of this programming method is to reduce a given computational problem to computing an answer set for a logic program. Examples and references can be found in [11] Lloyd and Topor [12] generalized the completion semantics to programs containing nested expressions (formulas) in the bodies of rules. A similar generalization of the answer set semantics was proposed in [10] In this note we show how Fages theorem on the relationship between completion and answer sets can be ....

.... turned into a program of this kind using the equivalent transformations discussed in [10, Section 4] For instance, the rule p q; not r does not have the form (11) but it can be equivalently replaced by the pair of rules p q; p ; not r: 12) 7 This is essentially the de nition from [12] restricted to the propositional case. In fact, some disjunctive programs can be converted to this special form as well; for instance, p; not q r can be equivalently replaced by p r; not not q ( 10] Proposition 6(iii) An occurrence of a formula F in a formula is singular if the symbol ....

John Lloyd and Rodney Topor. Making Prolog more expressive. Journal of Logic Programming, 3:225-240, 1984.

....is simple to transform T to an abductive logic program of the type that can be dealt with by SLDNFA. Construct the general abductive logic program by adding general clauses, violated :F , for each F 2 T . Here, violated is a new propositional predicate. Then apply the Lloyd Topor transformation [39] on this general abductive program. The result is a normal abductive logic program P 0A such that (P 0A ; f:violatedg) is logically equivalent to T . More precisely, for any formula F based on the original alphabet, we have T j= Sigma F iff (P 0A ; f:violatedg) j= Sigma F iff P 0A j= ....

J.W. Lloyd and R.W. Topor. Making prolog more expressive. Journal of Logic Programming, 1(3):225--240, 1984.

....for it. 15 SLDNFA is not developed for dealing with FOL axioms, but there is a general technique to transform an open logic program P and a theory of FOL axioms T into an equivalent open logic program P 0 . This transformation technique is a trivial extension of the transformation proposed in [23]. In a first step, P is extended with: false : F for each FOL axiom F 2 T . The result is an open logic program with general clauses. In the second step, it is transformed to a normal open logic program P 0 using the technique in [23] The transformation is correct in the sense that P T is ....

....is a trivial extension of the transformation proposed in [23] In a first step, P is extended with: false : F for each FOL axiom F 2 T . The result is an open logic program with general clauses. In the second step, it is transformed to a normal open logic program P 0 using the technique in [23]. The transformation is correct in the sense that P T is equivalent with P 0 f:falseg according to completion semantics. The remaining FOL axiom :false can be added as an extra literal to the query to be solved by the abductive solver. This result shows that FOL (with FEQ) and open logic ....

[Article contains additional citation context not shown here]

J.W. Lloyd and R.W. Topor. Making prolog more expressive. Journal of Logic Programming, 1(3):225--240, 1984.

....for dealing with FOL integrity constraints, but there is a general technique to transform an incomplete program P and a theory of FOL integrity constraints IC into an equivalent incomplete program P 0 . This transformation technique is a trivial extension of the transformation proposed in [16]. In a first step, P is extended with: false : F for each integrity constraint F 2 IC. The result is a general incomplete program. In the second step, it is transformed to a normal incomplete program P 0 using the technique in [16] The transformation is correct in the sense that P IC is ....

....is a trivial extension of the transformation proposed in [16] In a first step, P is extended with: false : F for each integrity constraint F 2 IC. The result is a general incomplete program. In the second step, it is transformed to a normal incomplete program P 0 using the technique in [16]. The transformation is correct in the sense that P IC is equivalent with P 0 f:falseg according to completion semantics. The remaining integrity constraint :false can be added as an extra literal to the query to be solved by the abductive solver. This result shows that FOL (with FEQ) and ....

[Article contains additional citation context not shown here]

J.W. Lloyd and R.W. Topor. Making prolog more expressive. Journal of Logic Programming, 1(3):225--240, 1984.

....abducibles goals and efficient treatment of abduced equality atoms by the methods presented earlier. Integrity constraints can be represented by adding for any integrity constraint IC, the rule: f alse not(IC) transforming these rules to a normal program using the transformation of Lloyd Topor [17], and adding the literal not false to the query. A prototype of this method has been implemented. An interesting experiment was its extension to an abductive planner based on the event calculus. Our prototype planner was able to solve some hard problems with context dependent events, problems ....

J.W. Lloyd and R.W. Topor. Making prolog more expressive. Journal of Logic Programming, 1(3):225--240, 1984. 29

....is a clause with an empty body, while an integrity constraint is a clause of the form false Body. A rule is a clause which is neither a fact nor an integrity constraint. As is well known, more general rules and constraints can be reduced to this format through the transformations proposed in [62]. Constraints in this format are referred to as inconsistency indicators in [84] For the purposes of this paper, it is convenient to consider a database to be inconsistent, or violating the integrity constraints, iff false is derivable in the database via SLDNF resolution. Other views of ....

J. W. Lloyd and R. W. Topor. Making PROLOG more expressive. Journal of Logic Programming, 1(3):225--240, 1984.

....interpretation is motivated by the semantics of universal quantification: 8x:G(x) is true of P if for all terms t, G(t) is true of P. Often an additional predicate is supplied to restrict the domain of t) This interpretation of universal quantification is used often in database applications. See [6] for a formal treatment of this interpretation of universal quantification. In this paper, we shall, however, use an intensional interpretation of universal quantification that is motivated by proof theory: 8x:G(x) follows from P if G(c) follows from P for some constant c that does not occurs in ....

J. Lloyd and R. Topor, Making Prolog More Expressive, Journal of Logic Programming 1(3), October 1984, 225 -- 240.

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J. W. Lloyd and R. W. Topor. Making Prolog more expressive. Journal of Logic Programming, 1:225-240, 1984.

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J.W. Lloyd and R.W. Topor. Making Prolog more Expressive. Journal of Logic Programming, 3:225-240, 1984.

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J. W. Lloyd and R. W. Topor. Making PROLOG more expressive. Journal of Logic Programming, 1(3):225-240, 1984.

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J. W. Lloyd and R. W. Topor. 1984. Making Prolog more Expressive. Journal of Logic Programming 1(3): 225--240.

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