Fair Derivations in Logic Programming: Operational and Greatest Fixpoint Semantics

1987 ◽  
Vol 10 (3) ◽  
pp. 247-307
Author(s):  
Mohand-Areski Nait Abdallah
Keyword(s):  
Logic Programming ◽  
Topological Methods ◽  
Soundness And Completeness ◽  
Fix Point ◽  
Fixpoint Semantics ◽  
Uniform Treatment

Using topological methods, we study the operational and greatest fixpoint semantics of infinite computations in logic programming. We show the equivalence of the operational and greatest fix point semantics in the case of fair derivations. We give some canonical partition, and soundness and completeness results which generalize already known results about the finitary case. Since fair derivations are a generalization of successful derivations, we thus give a uniform treatment of all meaningful computations in logic programming.

A Modal Semantics of Negation in Logic Programming

1992 ◽  
Vol 16 (3-4) ◽  
pp. 231-262
Author(s):  
Philippe Balbiani
Keyword(s):  
Modal Logic ◽  
Logic Programming ◽  
Modal Logics ◽  
Kripke Models ◽  
Logic Programs ◽  
Modal Semantics ◽  
Soundness And Completeness ◽  
Modal Completion ◽  
Well Foundedness

The beauty of modal logics and their interest lie in their ability to represent such different intensional concepts as knowledge, time, obligation, provability in arithmetic, … according to the properties satisfied by the accessibility relations of their Kripke models (transitivity, reflexivity, symmetry, well-foundedness, …). The purpose of this paper is to study the ability of modal logics to represent the concepts of provability and unprovability in logic programming. The use of modal logic to study the semantics of logic programming with negation is defended with the help of a modal completion formula. This formula is a modal translation of Clack’s formula. It gives soundness and completeness proofs for the negation as failure rule. It offers a formal characterization of unprovability in logic programs. It characterizes as well its stratified semantics.

NESTED GUARDED HORN CLAUSES

1990 ◽  
Vol 01 (03) ◽  
pp. 249-263 ◽  
Author(s):  
MORENO FALASCHI ◽  
MAURIZIO GABBRIELLI ◽  
GIORGIO LEVI ◽  
MASAKI MURAKAMI
Keyword(s):  
Logic Programming ◽  
Operational Semantics ◽  
Horn Clauses ◽  
Fixpoint Semantics ◽  
New Feature ◽  
Definition Of

This paper defines a new concurrent logic language, Nested Guarded Horn Clauses (NGHC). The main new feature of the language is its concept of guard. In fact, an NGHC clause has several layers of (standard) guards. This syntactic innovation allows the definition of a complete (i.e. always applicable) set of unfolding rules and therefore of an unfolding semantics which is equivalent, with respect to the success set, to the operational semantics. A fixpoint semantics is also defined in the classic logic programming style and is proved equivalent to the unfolding one. Since it is possible to embed Flat GHC into NGHC, our method can be used to give a fixpoint semantics to FGHC as well.

scholarly journals A Denotational Semantics for Logic Programming

1985 ◽  
Vol 14 (201) ◽  
Author(s):  
Gudmund Skovbjerg Frandsen
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Denotational Semantics ◽  
Power Domain ◽  
Fixpoint Semantics ◽  
Standard Domain

A fully abstract denotational semantics for logic programming has not been constructed yet. In this paper we present a denotational semantics that is almost fully abstract. We take the meaning of a logic program to be an element in a Plotkin power domain of substitutions. In this way our result shows that standard domain constructions suffice, when giving a semantics for logic programming. Using the well-known fixpoint semantics of logic programming we have to consider two different fixpoints in order to obtain information about both successful and failed computations. In contrast, our semantics is uniform in that the (single) meaning of a logic program contains information about both successful, failed and infinite computations. Finally, based on the full abstractness result, we argue that the detail level of substitutions is needed in any denotational semantics for logic programming.

scholarly journals Description, Implementation, and Evaluation of a Generic Design for Tabled CLP

2019 ◽  
Vol 19 (3) ◽  
pp. 412-448 ◽  
Author(s):  
JOAQUÍN ARIAS ◽  
MANUEL CARRO
Keyword(s):  
Logic Programming ◽  
Experimental Evaluation ◽  
Additional Constraint ◽  
Next Generation ◽  
Constraint Solver ◽  
Difference Constraints ◽  
Finite Lattices ◽  
Soundness And Completeness ◽  
Generic Design

AbstractLogic programming with tabling and constraints (TCLP, tabled constraint logic programming) has been shown to be more expressive and in some cases more efficient than LP, CLP, or LP + tabling. Previous designs of TCLP systems did not fully use entailment to determine call/answer subsumption and did not provide a simple and well-documented interface to facilitate the integration of constraint solvers in existing tabling systems. We study the role of projection and entailment in the termination, soundness, and completeness of TCLP systems and present the design and an experimental evaluation of Mod TCLP, a framework that eases the integration of additional constraint solvers. Mod TCLP views constraint solvers as clients of the tabling system, which is generic w.r.t. the solver and only requires a clear interface from the latter. We validate our design by integrating four constraint solvers: a previously existing constraint solver for difference constraints, written in C; the standard versions of Holzbaur’s and , written in Prolog; and a new constraint solver for equations over finite lattices. We evaluate the performance of our framework in several benchmarks using the aforementioned solvers. Mod TCLP is developed in Ciao Prolog, a robust, mature, next-generation Prolog system.

scholarly journals Selective Unification in (Constraint) Logic Programming*

2020 ◽  
Vol 177 (3-4) ◽  
pp. 359-383
Author(s):  
Fred Mesnard ◽  
Étienne Payet ◽  
Germán Vidal
Keyword(s):  
Logic Programming ◽  
Object Oriented ◽  
Constraint Logic Programming ◽  
Specific Procedure ◽  
Restricted Version ◽  
Concolic Testing ◽  
Non Linear ◽  
Soundness And Completeness ◽  
Validation Technique ◽  
Run Time

Concolic testing is a well-known validation technique for imperative and object oriented programs. In a previous paper, we have introduced an adaptation of this technique to logic programming. At the heart of our framework lies a specific procedure that we call “selective unification”. It is used to generate appropriate run-time goals by considering all possible ways an atom can unify with the heads of some program clauses. In this paper, we show that the existing algorithm for selective unification is not complete in the presence of non-linear atoms. We then prove soundness and completeness for a restricted version of the problem where some atoms are required to be linear. We also consider concolic testing in the context of constraint logic programming and extend the notion of selective unification accordingly.

scholarly journals Constraint Logic Programming with Hereditary Harrop formulas

2001 ◽  
Vol 1 (4) ◽  
pp. 409-445 ◽  
Author(s):  
JAVIER LEACH ◽  
SUSANA NIEVA ◽  
MARIO RODRÍGUEZ-ARTALEJO
Keyword(s):  
Logic Programming ◽  
Programming Language ◽  
Proof Theory ◽  
Completeness Theorem ◽  
Constraint Logic Programming ◽  
Strong Completeness ◽  
Logic Programming Language ◽  
Constraint System ◽  
Soundness And Completeness ◽  
Abstract Formulation

Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are two well known ways to enhance the expressivity of Horn clauses. In this paper, we present a novel combination of these two approaches. We show how to enrich the syntax and proof theory of HH with the help of a given constraint system, in such a way that the key property of HH as a logic programming language (namely, the existence of uniform proofs) is preserved. We also present a procedure for goal solving, showing its soundness and completeness for computing answer constraints. As a consequence of this result, we obtain a new strong completeness theorem for CLP that avoids the need to build disjunctions of computed answers, as well as a more abstract formulation of a known completeness theorem for HH.

scholarly journals An effective fixpoint semantics for linear logic programs

2001 ◽  
Vol 2 (1) ◽  
pp. 85-122 ◽  
Author(s):  
MARCO BOZZANO ◽  
GIORGIO DELZANNO ◽  
MAURIZIO MARTELLI
Keyword(s):  
Logic Programming ◽  
Petri Nets ◽  
Abstract Interpretation ◽  
Theoretical Foundation ◽  
Linear Logic ◽  
Sufficient Conditions ◽  
Logic Programs ◽  
Bottom Up ◽  
Interesting Class ◽  
Fixpoint Semantics

In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog (Andreoli, 1992) that consists of the language LO (Andreoli & Pareschi, 1991) enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint semantics based on a new operator in the style of TP working over constraints. An application of the fixpoint operator can be computed algorithmically. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional LO. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. As an application of our framework, we also present a formal investigation of the relations between LO and Disjunctive Logic Programming (Minker et al., 1991). Using an approach based on abstract interpretation, we show that DLP fixpoint semantics can be viewed as an abstraction of our semantics for LO. We prove that the resulting abstraction is correct and complete (Cousot & Cousot, 1977; Giacobazzi & Ranzato, 1997) for an interesting class of LO programs encoding Petri Nets.

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