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18
SLDNFA: an abductive procedure for normal abductive programs
 Proc. of the International Joint Conference and Symposium on Logic Programming
, 1992
"... A family of extensions of SLDNFresolution for normal abductive programs is presented. The main difference between our approach and existing procedures is the treatment of nonground abductive goals. A completion semantics is given and the soundness and completeness of the procedures has been proven ..."
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Cited by 65 (15 self)
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A family of extensions of SLDNFresolution for normal abductive programs is presented. The main difference between our approach and existing procedures is the treatment of nonground abductive goals. A completion semantics is given and the soundness and completeness of the procedures has been proven. The research presented here, provides a simple framework of abductive procedures, in which a number of parameters can be set, in order to fit the abduction procedure to the application under consideration.
Representing Incomplete Knowledge in Abductive Logic Programming
 In Proc. of the International Symposium on Logic Programming
, 1993
"... Recently, Gelfond and Lifschitz presented a formal language for representing incomplete knowledge on actions and states, and a sound translation from this language to extended logic programming. We present an alternative translation to abductive logic programming with integrity constraints and prove ..."
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Cited by 61 (10 self)
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Recently, Gelfond and Lifschitz presented a formal language for representing incomplete knowledge on actions and states, and a sound translation from this language to extended logic programming. We present an alternative translation to abductive logic programming with integrity constraints and prove the soundness and completeness. In addition, we show how an abductive procedure can be used, not only for explanation, but also for deduction and proving satisfiability under uncertainty. From a more general perspective, this work can be viewed as asuccessfulexperiment in the declarative representation of and automated reasoning on incomplete knowledge using abductive logic programming. 1
SLDNFA: an abductive procedure for abductive logic programs
, 1997
"... We present SLDNFA, an extension of SLDNFresolution for abductive reasoning on abductive logic programs. SLDNFA solves the floundering abduction problem: nonground abductive atoms can be selected. SLDNFA provides also a partial solution for the floundering negation problem. Different abductive a ..."
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Cited by 54 (13 self)
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We present SLDNFA, an extension of SLDNFresolution for abductive reasoning on abductive logic programs. SLDNFA solves the floundering abduction problem: nonground abductive atoms can be selected. SLDNFA provides also a partial solution for the floundering negation problem. Different abductive answers can be derived from an SLDNFArefutation; these answers provide different compromises between generality and comprehensibility. Two extensions of SLDNFA are proposed which satisfy stronger completeness results. The soundness of SLDNFA and its extensions is proven. Their completeness for minimal solutions with respect to implication, cardinality and set inclusion is investigated. The formalisation of SLDNFA presented here is an update of an older version presented in [13] and does not rely on skolemisation of abductive atoms. 1
The Wellfounded Semantics Is the Principle of Inductive Definition
 Logics in Arti Intelligence
, 1998
"... . Existing formalisations of (transfinite) inductive definitions in constructive mathematics are reviewed and strong correspondences with LP under least model and perfect model semantics become apparent. I point to fundamental restrictions of these existing formalisations and argue that the wellfou ..."
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Cited by 45 (29 self)
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. Existing formalisations of (transfinite) inductive definitions in constructive mathematics are reviewed and strong correspondences with LP under least model and perfect model semantics become apparent. I point to fundamental restrictions of these existing formalisations and argue that the wellfounded semantics (wfs) overcomes these problems and hence, provides a superior formalisation of the principle of inductive definition. The contribution of this study for LP is that it (re )introduces the knowledge theoretic interpretation of LP as a logic for representing definitional knowledge. I point to fundamental differences between this knowledge theoretic interpretation of LP and the more commonly known interpretations of LP as default theories or autoepistemic theories. The relevance is that differences in knowledge theoretic interpretation have strong impact on knowledge representation methodology and on extensions of the LP formalism, for example for representing uncertainty. Keywo...
A terminological interpretation of (Abductive) Logic Programming
 International Conference on Logic Programming and Nonmonotonic Reasoning
, 1995
"... The logic program formalism is commonly viewed as a modal or default logic. In this paper, we propose an alternative interpretation of the formalism as a terminological logic. A terminological logic is designed to represent two different forms of knowledge. A TBox represents definitions for a set of ..."
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Cited by 23 (16 self)
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The logic program formalism is commonly viewed as a modal or default logic. In this paper, we propose an alternative interpretation of the formalism as a terminological logic. A terminological logic is designed to represent two different forms of knowledge. A TBox represents definitions for a set of concepts. An ABox represents the assertional knowledge of the expert. In our interpretation, a logic program is a TBox providing definitions for all predicates; this interpretation is present already in Clark's completion semantics. We extend the logic program formalism such that some predicates can be left undefined and use classical logic as the language for the ABox. The resulting logic can be seen as an alternative interpretation of abductive logic program formalism. We study the expressivity of the formalism for representing uncertainty by proposing solutions for problems in temporal reasoning, with null values and open domain knowledge. 1 Introduction The logic program formalism is c...
An Inductive Definition Approach to Ramifications
 IN ELECTRONIC TRANSACTIONS ON ARTIFICIAL INTELLIGENCE
, 1998
"... ..."
Coherent Integration of Databases by Abductive Logic Programming
 Journal of Artificial Intelligence Research
, 2004
"... We introduce an abductive method for a coherent integration of independent datasources. ..."
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Cited by 13 (5 self)
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We introduce an abductive method for a coherent integration of independent datasources.
A Strong Correspondence between Description Logics and Open Logic Programming
 In Proc. of ICLP’97
, 1997
"... This paper formally investigates the relationship between Open Logic Programming (OLP) and Description Logics (DL). A description logic is designed to represent two different forms of knowledge. A TBox represents definitional knowledge, i.e. definitions for a set of concepts. An ABox represents a ..."
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Cited by 8 (1 self)
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This paper formally investigates the relationship between Open Logic Programming (OLP) and Description Logics (DL). A description logic is designed to represent two different forms of knowledge. A TBox represents definitional knowledge, i.e. definitions for a set of concepts. An ABox represents assertional knowledge about specific domain objects. OLP is a declarative, terminological interpretation of the formalism of Abductive Logic Programming. In this interpretation, an abductive logic program is considered to consist of a TBox providing definitions for nonabducible predicates and an ABox providing assertional knowledge in the form of first order logic axioms. We define a provably correct mapping of DL theories to open logic programs, and identify sublanguages of OLP corresponding to several description logics. We also show strong correspondences between derivations produced by a typical DL algorithm and an abductive resolution procedure. The correspondences clarify longquesti...
Compositionality of Normal Open Logic Programs
, 1997
"... Compositionality of programs is an important concern in knowledge representation and software development. In the context of Logic Programming, up till now, the issue has mostly been studied for definite programs only. Here, we study compositionality in the context of normal open logic programming. ..."
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Cited by 8 (6 self)
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Compositionality of programs is an important concern in knowledge representation and software development. In the context of Logic Programming, up till now, the issue has mostly been studied for definite programs only. Here, we study compositionality in the context of normal open logic programming. This is a very expressive logic for knowledge representation of uncertainty and incomplete knowledge on concepts and on problem domain, in which the compositionality issue turns up very naturally. The semantics of the logic is a generalisation (allowing nonHerbrand interpretations) of the wellfounded semantics. We provide a number of results which offer different sufficient conditions under which the models of the composition of two theories can be related to the intersection of the models of the composing theories. In particular, under these conditions, logical consequence will be preserved under composition. Keywords : Logic Programming, Knowledge representation. CR Subject Classific...
Satisfiability checking for PC(ID)
, 2005
"... The logic FO(ID) extends classical first order logic with inductive definitions. This paper studies the satisifiability problem for PC(ID), its propositional fragment. We develop a framework for model generation in this logic, present an algorithm and prove its correctness. As FO(ID) is an integrati ..."
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Cited by 7 (2 self)
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The logic FO(ID) extends classical first order logic with inductive definitions. This paper studies the satisifiability problem for PC(ID), its propositional fragment. We develop a framework for model generation in this logic, present an algorithm and prove its correctness. As FO(ID) is an integration of classical logic and logic programming, our algorithm integrates techniques from SAT and ASP. We report on a prototype system, called MidL, experimentally validating our approach.