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Fixpoint semantics for logic programming  a survey
, 2000
"... The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and manyvalued logic, lattice theory, game theory, and topology. One source of this richness is the inherent nonmonotonicity of its negation, something that does not have close para ..."
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Cited by 131 (0 self)
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The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and manyvalued logic, lattice theory, game theory, and topology. One source of this richness is the inherent nonmonotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies.
MODULARITY IN LOGIC PROGRAMMING
 J. LOGIC PROGRAMMING 1993:12:1199
, 1993
"... The research on modular logic programming has evolved along two different directions during the past decade. Various papers have focused primarily on the problems of programminginthelarge. They have proposed module systems equipped with compositional operators for building programs as combination ..."
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Cited by 89 (4 self)
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The research on modular logic programming has evolved along two different directions during the past decade. Various papers have focused primarily on the problems of programminginthelarge. They have proposed module systems equipped with compositional operators for building programs as combinations of separate and independent components. Other proposals have instead concentrated on the problem of programminginthesmall in an attempt to enrich logic programming with abstraction and scoping mechanisms available in other programming paradigms. The issues that arise in the two approaches are substantially different. The compositional operators of the former allow one to structure programs without any need to extend the theory of Horn clauses. The scoping and abstraction mechanisms of the latter are modeled in terms of the logical connectives of extended logic languages.
Hypothetical Datalog: Complexity and Expressibility
 Theoretical Computer Science
, 1988
"... We present an extension of Hornclause logic which can hypothetically add and delete tuples from a database. Such logics have been discussed in the literature, but their complexities and expressibilities have remained an open question. This paper examines two such logics in the functionfree, predic ..."
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Cited by 40 (15 self)
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We present an extension of Hornclause logic which can hypothetically add and delete tuples from a database. Such logics have been discussed in the literature, but their complexities and expressibilities have remained an open question. This paper examines two such logics in the functionfree, predicate case. It is shown, in particular, that augmenting Hornclause logic with hypothetical addition increases its datacomplexity from PTIME to PSPACE. When deletions are added as well, complexity increases again, to EXPTIME. We then augment the logic with negationasfailure and develop the notion of stratified hypothetical rulebases. It is shown that negation does not increase complexity. To establish expressibility, we view the logic as a query language for relational databases. It is shown that any typed generic query that is computable in PSPACE can be expressed as a stratified rulebase of hypothetical additions. Similarly, any typed generic query that is computable in EXPTIME can be exp...
A Proof Procedure for the Logic of Hereditary Harrop Formulas
 JOURNAL OF AUTOMATED REASONING
, 1993
"... A proof procedure is presented for a class of formulas in intuitionistic logic. These formulas are the socalled goal formulas in the theory of hereditary Harrop formulas. Proof search inintuitionistic logic is complicated by the nonexistence of a Herbrandlike theorem for this logic: formulas cann ..."
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Cited by 34 (12 self)
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A proof procedure is presented for a class of formulas in intuitionistic logic. These formulas are the socalled goal formulas in the theory of hereditary Harrop formulas. Proof search inintuitionistic logic is complicated by the nonexistence of a Herbrandlike theorem for this logic: formulas cannot in general be preprocessed into a form such as the clausal form and the construction of a proof is often sensitive to the order in which the connectives and quantifiers are analyzed. An interesting aspect of the formulas we consider here is that this analysis can be carried out in a relatively controlled manner in their context. In particular, the task of finding a proof can be reduced to one of demonstrating that a formula follows from a set of assumptions with the next step in this process being determined by the structure of the conclusion formula. An acceptable implementation of this observation must utilize unification. However, since our formulas may contain universal and existential quantifiers in mixed order, care must be exercised to ensure the correctness of unification. One way of realizing this requirement involves labelling constants and variables and then using these labels to constrain unification. This form of unification is presented and used in a proof procedure for goal formulas in a firstorder version of hereditary Harrop formulas. Modifications to this procedure for the relevant formulas in a higherorder logic are also described. The proof procedure that we present has a practical value in that it provides the basis for an implementation of the logic programming language lambdaProlog.
Extending definite clause grammars with scoping constructs
 International Conference in Logic Programming
, 1990
"... Definite Clause Grammars (DCGs) have proved valuable to computational linguists since they can be used to specify phrase structured grammars. It is well known how to encode DCGs in Horn clauses. Some linguistic phenomena, such as fillergap dependencies, are difficult to account for in a completely ..."
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Cited by 27 (5 self)
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Definite Clause Grammars (DCGs) have proved valuable to computational linguists since they can be used to specify phrase structured grammars. It is well known how to encode DCGs in Horn clauses. Some linguistic phenomena, such as fillergap dependencies, are difficult to account for in a completely satisfactory way using simple phrase structured grammar. In the literature of logic grammars there have been several attempts to tackle this problem by making use of special arguments added to the DCG predicates corresponding to the grammatical symbols. In this paper we take a different line, in that we account for fillergap dependencies by encoding DCGs within hereditary Harrop formulas, an extension of Horn clauses (proposed elsewhere as a foundation for logic programming) where implicational goals and universally quantified goals are permitted. Under this approach, fillergap dependencies can be accounted for in terms of the operational semantics underlying hereditary Harrop formulas, in a way reminiscent of the treatment of such phenomena in Generalized Phrase Structure Grammar (GPSG). The main features involved in this new formulation of DCGs are mechanisms for providing scope to constants and program clauses along with a mild use of λterms
Representing Objects in a Logic Programming Language with Scoping Constructs
 International Conference in Logic Programming
, 1990
"... We present a logic programming language that uses implications and universal quantifiers in goals and the bodies of clauses to provide a simple scoping mechanism for program clauses and constants. Within this language it is possible to define a simple notion of parametric module and local constant. ..."
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Cited by 27 (8 self)
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We present a logic programming language that uses implications and universal quantifiers in goals and the bodies of clauses to provide a simple scoping mechanism for program clauses and constants. Within this language it is possible to define a simple notion of parametric module and local constant. Given this ability to structure programs, we explore how objectoriented programming, where objects are viewed as abstractions with behaviors, state, and inheritance, might be accommodated. To capture the notion of mutable state, we depart from the pure logic setting by adding a declaration that certain local predicates are deterministic (they succeed at most once). This declaration, along with a goalcontinuation passing style of programming is adequate to model the state of objects. We also examine a few aspects of how having objects embedded in logic programming can be used to enrich the notion of object: for examples, objects may be partial (that is, may contain free variables) and nond...
A logic for hypothetical reasoning
 In Proc. of AAAI88
, 1988
"... This paper shows that classical logic is inappropriate for hypothetical reasoning and develops an alternative logic for this purpose. The paper focuses on a form of hypothetical reasoning which appears computationally tractable. Specifically, Hornclause logic is augmented with rules, called embed ..."
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Cited by 16 (9 self)
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This paper shows that classical logic is inappropriate for hypothetical reasoning and develops an alternative logic for this purpose. The paper focuses on a form of hypothetical reasoning which appears computationally tractable. Specifically, Hornclause logic is augmented with rules, called embedded implications, which can hypothetically add atomic formulas to a rulebase. By introducing the notion of ruZebuse independence, it is shown that these rules can express hypothetical queries which classical logic cannot. By adopting methods from modal logic, these rules are then shown to be intuitionistic. In particular, they form a subset of intuitionistic logic having semantic properties similar to those of Hornclause logic. 1
A Modal Extension of Logic Programming: Modularity, Beliefs and Hypothetical Reasoning
, 1995
"... In this paper we present a modal extension of logic programming, which allows both multiple modalities and embedded implications. We show that this extension is well suited for structuring knowledge and, specifically, for defining module constructs within programs, for representing agents beliefs, a ..."
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Cited by 15 (2 self)
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In this paper we present a modal extension of logic programming, which allows both multiple modalities and embedded implications. We show that this extension is well suited for structuring knowledge and, specifically, for defining module constructs within programs, for representing agents beliefs, and also for hypothetical reasoning. The language contains modalities [a i ] to represent agent beliefs, and a modality 2 which is a kind of common knowledge operator. It allows sequences of modalities to occur in front of clauses, goals and clause heads, and hypothetical implications to occur in goals and in clause bodies. A goal directed proof procedure of the language is presented, and several examples of its use for defining modules are given. In particular, the language is shown to capture different proposal for module definition and composition presented in the literature. The modal logic, of which our programming language is a clausal fragment, is introduced through its Kripke semantic...
Expressing Database Queries with Intuitionistic Logic
 Proceedings of the North American Conference on Logic Programming
, 1989
"... This paper develops a declarative language with intuitionistic semantics which expresses exactly the generic database queries. Syntactically, the language is an extension of Datalog (functionfree Horn logic) which allows rules themselves to appear in the bodies of other rules. Such rules are called ..."
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Cited by 12 (3 self)
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This paper develops a declarative language with intuitionistic semantics which expresses exactly the generic database queries. Syntactically, the language is an extension of Datalog (functionfree Horn logic) which allows rules themselves to appear in the bodies of other rules. Such rules are called embedded implications. Several researchers have studied restricted versions of these rules, but in their full incarnation, universal quantifiers may appear in the premises, as in the rule A / 8 x [B(x) / C(x)]. This paper focuses on these embedded universal quantifiers. It is shown, for instance, that such quantifiers give the logic the ability to create new constant symbols hypothetically during inference. This, in turn, allows the logic to simulate unbounded counters and arbitrary Turing machines. In addition, when the logic is augmented with negationasfailure, it becomes expressively complete, that is, it can express any database query which is typed and generic. Similar results exist...
Hypothetical Datalog: Negation and Linear Recursion
 In Proceedings of the ACM Symposium on the Principles of Database Systems (PODS
, 1989
"... This paper examines an extension of Horn logic in which rules can add entries to a database hypothetically. Several researchers have developed logical systems along these lines, but the complexity and expressibility of such logics is only now being explored. It has been shown, for instance, that the ..."
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Cited by 11 (7 self)
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This paper examines an extension of Horn logic in which rules can add entries to a database hypothetically. Several researchers have developed logical systems along these lines, but the complexity and expressibility of such logics is only now being explored. It has been shown, for instance, that the datacomplexity of these logics is PSPACEcomplete in the functionfree, predicate case. This paper extends this line of research by developing syntactic restrictions with lower complexity. These restrictions are based on two ideas from Hornclause logic: linear recursion and stratified negation. In particular, a notion of stratification is developed in which negationasfailure alternates with linear recursion. The complexity of such rulebases depends on the number of layers of stratification. The result is a hierarchy of syntactic classes which corresponds exactly to the polynomialtime hierarchy of complexity classes. In particular, rulebases with k strata are datacomplete for \Sigma P...