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Constraint Logic Programming: A Survey
"... Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in differe ..."
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Cited by 791 (24 self)
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Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.
Theory of Generalized Annotated Logic Programming and its Applications
 Journal of Logic Programming
, 1992
"... Annotated logics were introduced in [43] and later studied in [5, 7, 31, 32]. In [31], annotations were extended to allow variables and functions, and it was argued that such logics can be used to provide a formal semantics for rulebased expert systems with uncertainty. In this paper we continue to ..."
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Cited by 180 (23 self)
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Annotated logics were introduced in [43] and later studied in [5, 7, 31, 32]. In [31], annotations were extended to allow variables and functions, and it was argued that such logics can be used to provide a formal semantics for rulebased expert systems with uncertainty. In this paper we continue to investigate the power of this approach. First, we introduce a new semantics for such programs based on ideals of lattices. Subsequently, some proposals for multivalued logic programming [5, 7, 32, 47, 40, 18] as well as some formalisms for temporal reasoning [1, 3, 42] are shown to fit into this framework. As an interesting byproduct of this investigation, we obtain a new result concerning multivalued logic programming: a model theory for Fitting's bilatticebased logic programming, which until now has not been characterized modeltheoretically. This is accompanied by a corresponding proof theory. 1 Introduction Large knowledge bases can be inconsistent in many ways. Nevertheless, certain...
Probabilistic Logic Programming
, 1992
"... Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming (cf. van Emden [51], Fitting [18, 19, 20], Blair and Subrahmanian ..."
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Cited by 139 (8 self)
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Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming (cf. van Emden [51], Fitting [18, 19, 20], Blair and Subrahmanian [5, 6, 49, 50], Kifer et al [29, 30, 31]) have restricted themselves to nonprobabilistic semantical characterizations. In this paper, we take a few steps towards rectifying this situation. We define a logic programming language that is syntactically similar to the annotated logics of [5, 6], but in which the truth values are interpreted probabilistically. A probabilistic model theory and fixpoint theory is developed for such programs. This probabilistic model theory satisfies the requirements proposed by Fenstad [16] for a function to be called probabilistic. The logical treatment of probabilities is complicated by two facts: first, that the connectives cannot be interpreted truth function...
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 114 (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.
Quantitative Deduction And Its Fixpoint Theory
 Journal of Logic Programming
, 1986
"... Logic programming provides a model for rulebased reasoning in expert systems. The advantage of this formal model is that it makes available many results from the semantics and proof theory of rstorder predicate logic. ..."
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Cited by 94 (0 self)
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Logic programming provides a model for rulebased reasoning in expert systems. The advantage of this formal model is that it makes available many results from the semantics and proof theory of rstorder predicate logic.
Hybrid Probabilistic Programs
 Journal of Logic Programming
, 1997
"... The precise probability of a compound event (e.g. e1 e2 ; e1 e2) depends upon the known relationships (e.g. independence, mutual exclusion, ignorance of any relationship, etc.) between the primitive events that constitute the compound event. To date, most research on probabilistic logic programmin ..."
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Cited by 73 (2 self)
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The precise probability of a compound event (e.g. e1 e2 ; e1 e2) depends upon the known relationships (e.g. independence, mutual exclusion, ignorance of any relationship, etc.) between the primitive events that constitute the compound event. To date, most research on probabilistic logic programming [20, 19, 22, 23, 24] has assumed that we are ignorant of the relationship between primitive events. Likewise, most research in AI (e.g. Bayesian approaches) have assumed that primitive events are independent. In this paper, we propose a hybrid probabilistic logic programming language in which the user can explicitly associate, with any given probabilistic strategy, a conjunction and disjunction operator, and then write programs using these operators. We describe the syntax of hybrid probabilistic programs, and develop a model theory and fixpoint theory for such programs. Last, but not least, we develop three alternative procedures to answer queries, each of which is guaranteed to be sound ...
A Parametric Approach to Deductive Databases with Uncertainty
, 1997
"... Numerous frameworks have been proposed in recent years for deductive databases with uncertainty. These frameworks differ in (i) their underlying notion of uncertainty, (ii) the way in which uncertainties are manipulated, and (iii) the way in which uncertainty is associated with the facts and rules o ..."
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Cited by 47 (6 self)
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Numerous frameworks have been proposed in recent years for deductive databases with uncertainty. These frameworks differ in (i) their underlying notion of uncertainty, (ii) the way in which uncertainties are manipulated, and (iii) the way in which uncertainty is associated with the facts and rules of a program. On the basis of (iii), these frameworks can be classified into implication based (IB) and annotation based (AB) frameworks. In this paper, we develop a generic framework called the parametric framework as a unifying umbrella for IB frameworks. We develop the declarative, fixpoint, and prooftheoretic semantics of programs in the parametric framework and show their equivalence. Using this framework as a basis, we study the query optimization problem of containment of conjunctive queries in this framework, and establish necessary and sufficient conditions for containment for several classes of parametric conjunctive queries. Our results yield tools for use in the query optimization for large classes of query programs in IB deductive databases with uncertainty.
Probabilistic Logic Learning
 ACMSIGKDD Explorations: Special issue on MultiRelational Data Mining
, 2004
"... The past few years have witnessed an significant interest in probabilistic logic learning, i.e. in research lying at the intersection of probabilistic reasoning, logical representations, and machine learning. A rich variety of di#erent formalisms and learning techniques have been developed. This pap ..."
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Cited by 36 (8 self)
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The past few years have witnessed an significant interest in probabilistic logic learning, i.e. in research lying at the intersection of probabilistic reasoning, logical representations, and machine learning. A rich variety of di#erent formalisms and learning techniques have been developed. This paper provides an introductory survey and overview of the stateof theart in probabilistic logic learning through the identification of a number of important probabilistic, logical and learning concepts.
Antitonic Logic Programs
, 2001
"... In a previous work we have de ned Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truthvalues with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, ..."
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Cited by 36 (10 self)
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In a previous work we have de ned Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truthvalues with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs and Fuzzy Logic Programming [3, 4]. However, none of these semantics define a form of nonmonotonic negation, which is fundamental for several knowledge representation applications. In the spirit of our previous work, we generalise our framework of Monotonic Logic Programs to allow for rules with arbitrary antitonic bodies over general complete lattices, of which normal programs are a special case. We then show that all the standard logic programming theoretical results carry over to Antitonic Logic Programs, defining Stable Model and Wellfounded Model alike semantics.
Loglinear models for firstorder probabilistic reasoning
 Proceedings of the 15th Annual Conference on Uncertainty in AI (UAI’99
, 1999
"... Recent work on loglinear models in probabilistic constraint logic programming is applied to firstorder probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic formulae themselves. We use Stochastic Logic Programs (SLPs) compo ..."
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Cited by 35 (5 self)
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Recent work on loglinear models in probabilistic constraint logic programming is applied to firstorder probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic formulae themselves. We use Stochastic Logic Programs (SLPs) composed of labelled and unlabelled definite clauses to define the proof probabilities. We have a conservative extension of firstorder reasoning, so that, for example, there is a oneone mapping between logical and random variables. We show how, in this framework, Inductive Logic Programming (ILP) can be used to induce the features of a loglinear model from data. We also compare the presented framework with other approaches to firstorder probabilistic reasoning.