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31
Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
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Cited by 224 (21 self)
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In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
Extending Classical Logic with Inductive Definitions
, 2000
"... The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of nonmonotonic reasoning, logic programming and deductiv ..."
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Cited by 58 (38 self)
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The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of nonmonotonic reasoning, logic programming and deductive databases, and to show its application for knowledge representation by giving a typology of definitional knowledge.
Nested Abnormality Theories
 Artificial Intelligence
, 1995
"... We propose a new approach to the use of circumscription for representing knowledge. Nested abnormality theories are similar to simple abnormality theories introduced by McCarthy, except that their axioms may have a nested structure, with each level corresponding to another application of the circ ..."
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Cited by 47 (5 self)
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We propose a new approach to the use of circumscription for representing knowledge. Nested abnormality theories are similar to simple abnormality theories introduced by McCarthy, except that their axioms may have a nested structure, with each level corresponding to another application of the circumscription operator. The new style of applying circumscription sometimes leads to more economical and elegant formalizations. Mathematical properties of nested abnormality theories may be easier to investigate. These advantages are demonstrated by recasting several familiar applications of circumscription in the new format, including some examples of inheritance hierarchies, the domain closure assumption and causal minimization. Nested abnormality theories provide also a convenient representation for the explanation closure approach to the frame problem developed by Schubert.
On the expressive power of database queries with intermediate types
 Journal of Computer and System Sciences
, 1991
"... The setheight of a complex object type is defined to be its level of nesting of the set construct. In a query of the complex object calculus which maps a database D to an output type T,anintermediate type is a type which is used by some variable of the query, but which is not present in D or T.Fore ..."
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Cited by 44 (2 self)
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The setheight of a complex object type is defined to be its level of nesting of the set construct. In a query of the complex object calculus which maps a database D to an output type T,anintermediate type is a type which is used by some variable of the query, but which is not present in D or T.Foreachk, i ≥ 0 we define CALCk,i to be the family of calculus queries mapping from and to types with setheight ≤ k and using intermediate types with setheight ≤ i. In particular, CALC0,0 is the classical relational calculus, and CALC0,1 is equivalent to the family of secondorder (relational) queries. Several results concerning these families of languages are obtained. A primary focus is on the families CALC0,i, which map relations to relations. Upper and lower bounds in terms of hyperexponential time and space on the complexity of these families are provided. The CALC0,i hierarchy does not collapse with respect to expressive power. The union ∪0≤iCALC0,i is exactly the family of elementary queries, i.e., queries with hyperexponential complexity. The expressive power of queries from the complex object calculus interpreted using semantics based on the use of arbitrarily large finite or infinite set of invented values is studied. Under these semantics, the expressive power of the relational calculus is not increased, and the CALC0,i hierarchy collapses at CALC0,1. In general, queries with these semantics may not be computable. We also consider an alternative semantics which yields a family of queries equivalent to the computable queries. 1
A logic of nonmonotone inductive definitions
 ACM transactions on computational logic
, 2007
"... Wellknown principles of induction include monotone induction and different sorts of nonmonotone induction such as inflationary induction, induction over wellfounded sets and iterated induction. In this work, we define a logic formalizing induction over wellfounded sets and monotone and iterated i ..."
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Cited by 28 (16 self)
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Wellknown principles of induction include monotone induction and different sorts of nonmonotone induction such as inflationary induction, induction over wellfounded sets and iterated induction. In this work, we define a logic formalizing induction over wellfounded sets and monotone and iterated induction. Just as the principle of positive induction has been formalized in FO(LFP), and the principle of inflationary induction has been formalized in FO(IFP), this paper formalizes the principle of iterated induction in a new logic for NonMonotone Inductive Definitions (IDlogic). The semantics of the logic is strongly influenced by the wellfounded semantics of logic programming. This paper discusses the formalisation of different forms of (non)monotone induction by the wellfounded semantics and illustrates the use of the logic for formalizing mathematical and commonsense knowledge. To model different types of induction found in mathematics, we define several subclasses of definitions, and show that they are correctly formalized by the wellfounded semantics. We also present translations into classical first or second order logic. We develop modularity and totality results and demonstrate their use to analyze and simplify complex definitions. We illustrate the use of the logic for temporal reasoning. The logic formally extends Logic Programming, Abductive Logic Programming and Datalog, and thus formalizes the view on these formalisms as logics of (generalized) inductive definitions. Categories and Subject Descriptors:... [...]:... 1.
Largescale deduplication with constraints using dedupalog
 in: Proceedings of the 25th International Conference on Data Engineering (ICDE
"... Abstract — We present a declarative framework for collective deduplication of entity references in the presence of constraints. Constraints occur naturally in many data cleaning domains and can improve the quality of deduplication. An example of a constraint is “each paper has a unique publication v ..."
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Cited by 28 (2 self)
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Abstract — We present a declarative framework for collective deduplication of entity references in the presence of constraints. Constraints occur naturally in many data cleaning domains and can improve the quality of deduplication. An example of a constraint is “each paper has a unique publication venue”; iftwo paper references are duplicates, then their associated conference references must be duplicates as well. Our framework supports collective deduplication, meaning that we can dedupe both paper references and conference references collectively in the example above. Our framework is based on a simple declarative Datalogstyle language with precise semantics. Most previous work on deduplication either ignore constraints or use them in an adhoc domainspecific manner. We also present efficient algorithms to support the framework. Our algorithms have precise theoretical guarantees for a large subclass of our framework. We show, using a prototype implementation, that our algorithms scale to very large datasets. We provide thorough experimental results over realworld data demonstrating the utility of our framework for highquality and scalable deduplication. I.
ON REPRESENTATIONAL ISSUES ABOUT COMBINATIONS OF CLASSICAL THEORIES WITH NONMONOTONIC RULES
, 2006
"... In the context of current efforts around SemanticWeb languages, the combination of classical theories in classical firstorder logic (and in particular of ontologies in various description logics) with rule languages rooted in logic programming is receiving considerable attention. Existing approach ..."
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Cited by 19 (13 self)
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In the context of current efforts around SemanticWeb languages, the combination of classical theories in classical firstorder logic (and in particular of ontologies in various description logics) with rule languages rooted in logic programming is receiving considerable attention. Existing approaches such as SWRL, dlprograms, and DL+log, differ significantly in the way ontologies interact with (nonmonotonic) rules bases. In this paper, we identify fundamental representational issues which need to be addressed by such combinations and formulate a number of formal principles which help to characterize and classify existing and possible future approaches to the combination of rules and classical theories. We use the formal principles to explicate the underlying assumptions of current approaches. Finally, we propose a number of settings, based on our analysis of the representational issues and the fundamental principles underlying current approaches.
Reasoning in Open Domains
 In Logic Programming and NonMonotonic Reasoning
, 1993
"... In this paper we modify the semantics of epistemic specifications (and hence the answer set semantics of extended logic program and disjunctive databases) to allow for reasoning in the absence of domainclosure assumption. This modification increases the expressive power of the language and allows ..."
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Cited by 18 (1 self)
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In this paper we modify the semantics of epistemic specifications (and hence the answer set semantics of extended logic program and disjunctive databases) to allow for reasoning in the absence of domainclosure assumption. This modification increases the expressive power of the language and allows one to explicitly state the domainclosure and other assumptions about the domain of discourse in the language of epistemic specifications. The power of the language is demonstrated by way of examples. In particular we show how open domain assumption can be used to formalize default reasoning in the presence of anonymous exceptions to defaults. 1 Introduction Epistemic specifications were introduced in [4] as a tool for knowledge representation. They can be viewed as a generalization of "extended disjunctive databases" from [6] capable of expressing powerful forms of introspection. The semantics of an epistemic specification 5 has been given via the notion of a world view of 5  a collect...
Updating Knowledge Bases with Disjunctive Information
 Proceedings of Thirteenth National Conference on Artificial Intelligence (AAAI96
, 1996
"... It is well known that the minimal change principle was widely used in knowledge base updates. However, recent research has shown that the conventional minimal change methods, eg. the PMA [11], were generally problematic for updating knowledge bases with disjunctive information. In this paper, we ..."
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Cited by 17 (5 self)
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It is well known that the minimal change principle was widely used in knowledge base updates. However, recent research has shown that the conventional minimal change methods, eg. the PMA [11], were generally problematic for updating knowledge bases with disjunctive information. In this paper, we propose two different approaches to deal with this problem  one is called the minimal change with exceptions (the MCE), the other is called the minimal change with maximally disjunctive inclusions (the MCD). The first method is syntaxdependent, while the second is modelbased. We show that these two approaches are equivalent for propositional knowledge base updates, and the second method is also appropriate for the first order knowledge base update. We then prove that our new update approaches still satisfy the standard Katsuno and Mendelzon's update postulates. Key words: knowledge base upate, knowledge representation, minimal change, disjunctive information 1 Introduction Th...
Decomposition of Database Classes under Path Functional Dependencies and Onto Constraints
 In Foundations of Information and Knowledge Systems
, 2000
"... Based on Flogic, we specify an advanced data model with objectoriented and logicoriented features that substantially extend the relational approach. For this model we exhibit and study the counterpart to the wellknown decomposition of a relation scheme according to a nontrivial nonkey functio ..."
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Cited by 17 (2 self)
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Based on Flogic, we specify an advanced data model with objectoriented and logicoriented features that substantially extend the relational approach. For this model we exhibit and study the counterpart to the wellknown decomposition of a relation scheme according to a nontrivial nonkey functional dependency. For decomposing a class of a database schema the transformation of pivoting is used. Pivoting separates apart some attributes of the class into a newly generated class. This new class is declared to be a subclass of the result class of the socalled pivot attribute. Moreover the pivot attribute provides the link between the original class and the new subclass. We identify the conditions for the result of pivoting being equivalent with its input: the expressive power of path functional dependencies, the validity of the path functional dependency between the pivot attribute and the transplanted attributes, and the validity of the ontoconstraint guaranteeing that value...