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Learning Stochastic Logic Programs
, 2000
"... Stochastic Logic Programs (SLPs) have been shown to be a generalisation of Hidden Markov Models (HMMs), stochastic contextfree grammars, and directed Bayes' nets. A stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0,1] and C is a firstorder r ..."
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Cited by 1181 (79 self)
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Stochastic Logic Programs (SLPs) have been shown to be a generalisation of Hidden Markov Models (HMMs), stochastic contextfree grammars, and directed Bayes' nets. A stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0,1] and C is a firstorder rangerestricted definite clause. This paper summarises the syntax, distributional semantics and proof techniques for SLPs and then discusses how a standard Inductive Logic Programming (ILP) system, Progol, has been modied to support learning of SLPs. The resulting system 1) nds an SLP with uniform probability labels on each definition and nearmaximal Bayes posterior probability and then 2) alters the probability labels to further increase the posterior probability. Stage 1) is implemented within CProgol4.5, which differs from previous versions of Progol by allowing userdefined evaluation functions written in Prolog. It is shown that maximising the Bayesian posterior function involves nding SLPs with short derivations of the examples. Search pruning with the Bayesian evaluation function is carried out in the same way as in previous versions of CProgol. The system is demonstrated with worked examples involving the learning of probability distributions over sequences as well as the learning of simple forms of uncertain knowledge.
The WellFounded Semantics for General Logic Programs
 Journal of the ACM
, 1991
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SSemantics Approach: Theory and Applications
, 1994
"... The paper is a general overview of an approach to the semantics of logic programs whose aim is finding notions of models which really capture the operational semantics, and are therefore useful for defining program equivalences and for semanticsbased program analysis. The approach leads to the intr ..."
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Cited by 126 (28 self)
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The paper is a general overview of an approach to the semantics of logic programs whose aim is finding notions of models which really capture the operational semantics, and are therefore useful for defining program equivalences and for semanticsbased program analysis. The approach leads to the introduction of extended interpretations which are more expressive than Herbrand interpretations. The semantics in terms of extended interpretations can be obtained as a result of both an operational (topdown) and a fixpoint (bottomup) construction. It can also be characterized from the modeltheoretic viewpoint, by defining a set of extended models which contains standard Herbrand models. We discuss the original construction modeling computed answer substitutions, its compositional version and various semantics modeling more concrete observables. We then show how the approach can be applied to several extensions of positive logic programs. We finally consider some applications, mainly in the area of semanticsbased program transformation and analysis.
A Survey of Research on Deductive Database Systems
 JOURNAL OF LOGIC PROGRAMMING
, 1993
"... The area of deductive databases has matured in recent years, and it now seems appropriate to re ect upon what has been achieved and what the future holds. In this paper, we provide an overview of the area and briefly describe a number of projects that have led to implemented systems. ..."
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Cited by 121 (8 self)
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The area of deductive databases has matured in recent years, and it now seems appropriate to re ect upon what has been achieved and what the future holds. In this paper, we provide an overview of the area and briefly describe a number of projects that have led to implemented systems.
A General Framework for Semanticsbased Bottomup Abstract Interpretation of Logic Programs
 ACM Transactions on Programming Languages and Systems
, 1993
"... Interpretation of Logic Programs Roberto Barbuti , Roberto Giacobazzi , Giorgio Levi Dipartimento di Informatica Universit`a di Pisa Corso Italia 40, 56125 Pisa fbarbuti,giaco,levig@di.unipi.it in ACM Transactions on Programming Languages and Systems Vol 15, January 1993 Abstract The theory ..."
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Cited by 79 (27 self)
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Interpretation of Logic Programs Roberto Barbuti , Roberto Giacobazzi , Giorgio Levi Dipartimento di Informatica Universit`a di Pisa Corso Italia 40, 56125 Pisa fbarbuti,giaco,levig@di.unipi.it in ACM Transactions on Programming Languages and Systems Vol 15, January 1993 Abstract The theory of abstract interpretation provides a formal framework to develop advanced dataflow analysis tools. The idea is to define a nonstandard semantics which is able to compute, in finite time, an approximated model of the program. In this paper we define an abstract interpretation framework based on a fixpoint approach to the semantics. This leads to the definition, by means of a suitable set of operators, of an abstract fixpoint characterization of a model associated with the program. Thus, we obtain a specializable abstract framework for bottomup abstract interpretations of definite logic programs. The specialization of the framework is shown on two examples, namely ground dependence analysis and depthk analysis.
A Procedural Semantics for Well Founded Negation in Logic Programs
 Journal of Logic programming
, 1989
"... We introduce global SLSresolution, a procedural semantics for wellfounded negation as defined by Van Gelder, Ross and Schlipf. Global SLSresolution extends Przymusinski 's SLSresolution, and may be applied to all programs, whether locally stratified or not. 1 Global SLSresolution is define ..."
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Cited by 61 (2 self)
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We introduce global SLSresolution, a procedural semantics for wellfounded negation as defined by Van Gelder, Ross and Schlipf. Global SLSresolution extends Przymusinski 's SLSresolution, and may be applied to all programs, whether locally stratified or not. 1 Global SLSresolution is defined in terms of global trees, a new data structure representing the dependence of goals on derived negative subgoals. We prove that global SLSresolution is sound with respect to the wellfounded semantics, and complete for nonfloundering queries. While not effective in general, global SLSresolution is effective for classes of "acyclic" programs, and can be augmented with a memoing device to be effective for all functionfree programs. This research was supported by the National Science Foundation under grant IRI8722886, by a grant from IBM Corporation, and by the United States Air Force Office of Scientific Research under contract AFOSR880266. A preliminary version of this paper was presen...
Uniform Equivalence of Logic Programs under the Stable Model Semantics
, 2003
"... In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P [ R and Q [ R have the same stable models for any other program R. This property strengthens equivalence of P and Q with respect to sta ..."
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Cited by 56 (14 self)
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In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P [ R and Q [ R have the same stable models for any other program R. This property strengthens equivalence of P and Q with respect to stable models (which is the particular case for R = ;), and has an application in program optimization. In this paper, we consider the more liberal notion of uniform equivalence, in which R ranges only over the sets of facts rather than all sets of rules. This notion, which is wellknown, is particularly useful for assessing whether programs P and Q are equivalent as components in a logic program which is modularly structured. We provide semantical characterizations of uniform equivalence for disjunctive logic programs and some restricted classes, and analyze the computational cost of uniform equivalence in the propositional (ground) case. Our results, which naturally extend to answer set semantics, complement the results on strong equivalence of logic programs and pave the way for optimizations in answer set solvers as a tool for inputbased problem solving.
Efficient BottomUp Evaluation Of Logic Programs
 THE STATE OF THE ART IN COMPUTER SYSTEMS AND SOFTWARE ENGINEERING
, 1992
"... In recent years, much work has been directed towards evaluating logic programs and queries on deductive databases by using an iterative bottomup fixpoint computation. The resulting techniques offer an attractive alternative to Prologstyle topdown evaluation in several situations. They are sound ..."
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Cited by 43 (4 self)
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In recent years, much work has been directed towards evaluating logic programs and queries on deductive databases by using an iterative bottomup fixpoint computation. The resulting techniques offer an attractive alternative to Prologstyle topdown evaluation in several situations. They are sound and complete for positive Horn clause programs, are wellsuited to applications with large volumes of data (facts), and can support a variety of extensions to the standard logic programming paradigm. We present the basics of database query evaluation and logic programming evaluation, and then discuss bottomup fixpoint evaluation. We discuss an approach based upon using a program transformation ("Magic Templates") to restrict search, followed by fixpoint computation using a technique ("Seminaive evaluation") that avoids repeated inferences. The program transformation technique focuses the fixpoint evaluation, which is a forwardchaining strategy, by propagating bindings in the goal in a ma...