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Uniform proofs as a foundation for logic programming
 ANNALS OF PURE AND APPLIED LOGIC
, 1991
"... A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its ..."
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Cited by 375 (109 self)
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A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its operational meaning, provided by interpreting logical connectives as simple and fixed search instructions. The operational semantics is formalized by the identification of a class of cutfree sequent proofs called uniform proofs. A uniform proof is one that can be found by a goaldirected search that respects the interpretation of the logical connectives as search instructions. The concept of a uniform proof is used to define the notion of an abstract logic programming language, and it is shown that firstorder and higherorder Horn clauses with classical provability are examples of such a language. Horn clauses are then generalized to hereditary Harrop formulas and it is shown that firstorder and higherorder versions of this new class of formulas are also abstract logic programming languages if the inference rules are those of either intuitionistic or minimal logic. The programming language significance of the various generalizations to firstorder Horn clauses is briefly discussed.
Elimination of Negation in a Logical Framework
, 2000
"... Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [15] cannot express directly negative information, although negation is a useful specification tool. Since negationasfailure does not fit well in a logical framework, especially one endowed with ..."
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Cited by 10 (3 self)
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Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [15] cannot express directly negative information, although negation is a useful specification tool. Since negationasfailure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgements, we adapt the idea of elimination of negation introduced in [21] for Horn logic to a fragment of higherorder HHF. This entails finding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and dynamic clauses do not overlap.
Proof Procedures for Logic Programming
, 1994
"... Proof procedures are an essential part of logic applied to artificial intelligence tasks, and form the basis for logic programming languages. As such, many of the chapters throughout this handbook utilize, or study, proof procedures. The study of proof procedures that are useful in artificial intell ..."
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Cited by 4 (0 self)
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Proof procedures are an essential part of logic applied to artificial intelligence tasks, and form the basis for logic programming languages. As such, many of the chapters throughout this handbook utilize, or study, proof procedures. The study of proof procedures that are useful in artificial intelligence would require a large book so we focus on proof procedures that relate to logic programming. We begin with the resolution procedures that influenced the definition of SLDresolution, the procedure upon which Prolog is built. Starting with the general resolution procedure we move through linear resolution to a very restricted linear resolution, SLresolution, which actually is not a resolution restriction, but a variant using an augmented logical form. (SLresolution actually is a derivative of the Model Elimination procedure, which was developed independently of resolution.) We then consider logic programming itself, reviewing SLDresolution and then describing a general criterion for ...
The Satisfiability problem for the SchÃ¶enfinkelBernays fragment: Partial Instantiation and Hypergraph Algorithms
 Proceedings of 8th subcommission "Magnetic
, 1994
"... A partial instantiation approach to the solution of the satisfiability problem in the SchoenfinkelBernays fragment of 1 st order logic is presented. It is based on a reduction of the problem to a finite sequence of satisfiability problems in the propositional logic and it improves upon the ori ..."
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Cited by 4 (2 self)
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A partial instantiation approach to the solution of the satisfiability problem in the SchoenfinkelBernays fragment of 1 st order logic is presented. It is based on a reduction of the problem to a finite sequence of satisfiability problems in the propositional logic and it improves upon the original idea of partial instantiation, as proposed by Jeroslow. In the second part of the paper a new interpretation of the partial instantiation approach in terms of Directed Hypergraphs is proposed and a particular implementation for the Datalog case is described in detail. 1 Introduction. The problem of Logical Inference plays a fundamental role in Decision Sciences and has several applications in fields such as decision support systems, logic circuit design, data bases, and programming languages. Although classical approaches to formalize and solve inference problems have been of symbolic nature, in the last few years many scientists in the Operations Research community have studied ...
Transforming specifications of observable behaviour into programs
 In Logic Program Synthesis and Transformation. Proceedings of LOPSTR'94
, 1994
"... A methodology for deriving programs from specifications of observable behaviour is described. The class of processes to which this methodology is applicable includes those whose state changes are fully definable by labelled transition systems, for example communicating processes without internal sta ..."
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Cited by 1 (0 self)
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A methodology for deriving programs from specifications of observable behaviour is described. The class of processes to which this methodology is applicable includes those whose state changes are fully definable by labelled transition systems, for example communicating processes without internal state changes. A logic program representation of such labelled transition systems is proposed, interpreters based on path searching techniques are defined, and the use of partial evaluation techniques to derive the executable programs is described. 1