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362
A SteptoStep Example of Negation Elimination in Hereditary Harrop Formulae
"... exp) ! exp: app : exp ! (exp ! exp): linear : exp ! o: linx : (exp ! exp) ! o: The representation function is given by: pxq = x : exp px : eq = lam (x : exp: peq) pe 1 e 2 q = app pe 1 q pe 2 q pe linearq = linear peq px : e linear in xq = linx(x : exp: peq) 1 We use objectlogic capital to av ..."
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exp) ! exp: app : exp ! (exp ! exp): linear : exp ! o: linx : (exp ! exp) ! o: The representation function is given by: pxq = x : exp px : eq = lam (x : exp: peq) pe 1 e 2 q = app pe 1 q pe 2 q pe linearq = linear peq px : e linear in xq = linx(x : exp: peq) 1 We use objectlogic capital
Cut Formulae and Logic Programming
"... . In this paper we present a mechanism to define names for proofwitnesses of formulae and thus to use Gentzen's cutrule in logic programming. We consider a program to be a set of logical formulae together with a list of such definitions. Occurrences of the defined names guide the proofsearch ..."
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Cited by 3 (1 self)
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search by indicating when an instance of the cutrule should be attempted. By using the cutrule there are proofs that can be made dramatically shorter. We explain how this idea of using the cutrule can be applied to the logic of hereditary Harrop formulae. 1 Introduction The computation mechanisms both for logic
Implementing a Fixpoint Semantics for a Constraint Deductive Database based on Hereditary Harrop Formulas
"... This work is aimed to show a concrete implementation of a deductive database system based on the scheme HH¬(C) (Hereditary Harrop Formulas with Negation and Constraints) following a fixpoint semantics proposed in a previous work. We have developed a Prolog implementation for this scheme that is co ..."
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This work is aimed to show a concrete implementation of a deductive database system based on the scheme HH¬(C) (Hereditary Harrop Formulas with Negation and Constraints) following a fixpoint semantics proposed in a previous work. We have developed a Prolog implementation for this scheme
Logic programming
"... Indexing is generally viewed as an implementation artifact, indispensable to speed up the execution of logic programs and theorem provers, but with little intrinsically logical about it. We show that indexing can be given a justification in proof theory on the basis of focusing and linearity. We dem ..."
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demonstrate this approach on predicate indexing for Horn clauses and several formulations of hereditary Harrop formulas. We also show how to refine this approach to discriminate on function symbols as well.
Inductive Constraint Logic
, 1995
"... . A novel approach to learning first order logic formulae from positive and negative examples is presented. Whereas present inductive logic programming systems employ examples as true and false ground facts (or clauses), we view examples as interpretations which are true or false for the target theo ..."
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Cited by 95 (19 self)
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. A novel approach to learning first order logic formulae from positive and negative examples is presented. Whereas present inductive logic programming systems employ examples as true and false ground facts (or clauses), we view examples as interpretations which are true or false for the target
Providing Declarative Semantics for HH Extended Constraint Logic Programs
 In Proceedings of the 6th ACM SIGPLAN Int. Conf. on PPDP, pages 55 – 66
, 2004
"... This paper is focused on a double extension of traditional Logic Programming which enhances it following two different approaches. On one hand, extending Horn logic to hereditary Harrop formulas (HH), in order to improve the expressive power; on the other, incorporating constraints, in order to inc ..."
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Cited by 4 (2 self)
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This paper is focused on a double extension of traditional Logic Programming which enhances it following two different approaches. On one hand, extending Horn logic to hereditary Harrop formulas (HH), in order to improve the expressive power; on the other, incorporating constraints, in order
On the Computational Cost of Disjunctive Logic Programming: Propositional Case
, 1995
"... This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whethe ..."
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Cited by 141 (26 self)
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whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy
Structural Properties of Logic Programs
 Proceedings of the Fourteenth Australian Computer Science Conference
"... Miller has shown that disjunctions are not necessary in a large fragment of hereditary Harrop formulae, a class of formulae which properly includes Horn clauses. In this paper we extend this result to include existential quantifications, so that for each program D, there is a program D 0 which ..."
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Cited by 1 (1 self)
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Miller has shown that disjunctions are not necessary in a large fragment of hereditary Harrop formulae, a class of formulae which properly includes Horn clauses. In this paper we extend this result to include existential quantifications, so that for each program D, there is a program D 0 which
A Clausal Form for the Completion of Logic Programs
 In Logic Programming. Proceedings of the Eighth International Conference
, 1991
"... The Clark completion of a program is a way of making explicit the inferences which may be made from the program using the Negation as Failure (NAF) rule. This may be thought of as adding negative information to the program in such a way that an atom fails iff its negation is derivable from the compl ..."
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. In this way the richer framework of hereditary Harrop formulae allows the completion to be given in a more explicit form than that of Clark. This also allows the completion to be seen as a set of clauses, i.e. a program, rather than just as a formula of firstorder logic. With the restriction that programs
Loop Formulas for Logic Programs with Arbitrary Constraint Atoms
"... We formulate loop formulas for logic programs with arbitrary constraint atoms, for the semantics based on conditional satisfaction. This provides a method for answer set computation by computing models of completion. One particular attractive candidate for the latter task is pseudoboolean constrain ..."
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Cited by 7 (3 self)
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We formulate loop formulas for logic programs with arbitrary constraint atoms, for the semantics based on conditional satisfaction. This provides a method for answer set computation by computing models of completion. One particular attractive candidate for the latter task is pseudo
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