FO(ID) as an Extension of DL with Rules

Vennekens, Joost; Denecker, Marc

doi:10.1007/978-3-642-02121-3_30

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…Our deductive calculus and the completeness result for a fragment of FO(ID), can be viewed as a step in developing tools similar as in the field of description logics. In a similar aim, a decidable guarded fragment of FO(ID) was described recently in [20].…”

Section: ∀X Y T Ranscl(x Y) ← Edge(x Y) ∀X Y T Ranscl(x Y) ← (∃Zmentioning

confidence: 99%

A Deductive System for FO(ID) Based on Least Fixpoint Logic

Hou

Denecker

2009

Logic Programming and Nonmonotonic Reasoning

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Abstract. The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. The goal of this paper is to extend Gentzen's sequent calculus to obtain a deductive inference method for FO(ID). The main difficulty in building such a proof system is the representation and inference of unfounded sets. It turns out that we can represent unfounded sets by least fixpoint expressions borrowed from stratified least fixpoint logic (SLFP), which is a logic with a least fixpoint operator and characterizes the expressibility of stratified logic programs. Therefore, in this paper, we integrate least fixpoint expressions into FO(ID) and define the logic FO(ID,SLFP). We investigate a sequent calculus for FO(ID,SLFP), which extends the sequent calculus for SLFP with inference rules for the inductive definitions of FO(ID). We show that this proof system is sound with respect to a slightly restricted fragment of FO(ID) and complete for a more restricted fragment of FO(ID).

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Section: ∀X Y T Ranscl(x Y) ← Edge(x Y) ∀X Y T Ranscl(x Y) ← (∃Zmentioning

confidence: 99%

A Deductive System for FO(ID) Based on Least Fixpoint Logic

Hou

Denecker

2009

Logic Programming and Nonmonotonic Reasoning

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“…Monotone definitions in FO(ID) are a different rule-based syntactic sugar of the fixpoint formulas of Least Fixpoint Logic (LFP) (Park 1969). Last but not least, FO(ID), being a clear, well-founded integration of rules into classical logic, might play a unifying role in the current attempts of extending FO-based description logics with rules (Vennekens and Denecker 2009). It thus appears that FO(ID) occupies quite a central position in the spectrum of computational and knowledge representation logics.…”

Section: Introductionmentioning

confidence: 99%

FO(FD): Extending classical logic with rule-based fixpoint definitions

Hou¹,

Cat²,

Denecker³

2010

Theory and Practice of Logic Programming

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We introduce fixpoint definitions, a rule-based reformulation of fixpoint constructs. The logic FO(FD), an extension of classical logic with fixpoint definitions, is defined. We illustrate the relation between FO(FD) and FO(ID), which is developed as an integration of two knowledge representation paradigms. The satisfiability problem for FO(FD) is investigated by first reducing FO(FD) to difference logic and then using solvers for difference logic. These reductions are evaluated in the computation of models for FO(FD) theories representing fairness conditions and we provide potential applications of FO(FD).

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FO(ID) as an extension of DL with rules

Vennekens¹,

Denecker

Bruynooghe

2010

Ann Math Artif Intell

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There are many interesting Knowledge Representation questions surrounding rule languages for the Semantic Web. The most basic one is of course: which kind of rules should be used and how do they integrate with existing Description Logics? Similar questions have already been addressed in the field of Logic Programming, where one particular answer has been provided by the language of FO(ID). FO(ID) is an extension of first-order logic with a rule-based representation for inductive definitions. By offering a general integration of first-order logic and Logic Programs, it also induces a particular way of extending Description Logics with rules. The goal of this paper is to investigate this integration and discover whether there are interesting extensions of DL with rules that can be arrived at by imposing appropriate restrictions on the highly expressive FO(ID).

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FO(ID) as an Extension of DL with Rules

Cited by 3 publications

References 12 publications

A Deductive System for FO(ID) Based on Least Fixpoint Logic

A Deductive System for FO(ID) Based on Least Fixpoint Logic

FO(FD): Extending classical logic with rule-based fixpoint definitions

FO(ID) as an extension of DL with rules

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