Implementation of nonmonotonic logics by Fourier holography technique

Many modern applications of description logics (DLs, for short), such as biomedical ontologies and semantic web policies, provide compelling motivations for extending DLs with an overriding mechanism analogous to the homonymous feature of object-oriented programming. Rational closure (RC) is one of the candidate semantics for such extensions, and one of the most intensively studied. So far, however, it has been limited to strict fragments of SROIQ(D) – the logic on which OWL2 is founded. In this paper we prove that RC cannot be extended to logics that do not satisfy the disjoint model union property, including SROIQ(D). Then we introduce a refinement of RC called stable rational closure that overcomes the dependency on the disjoint model union property. Our results show that stable RC is a natural extension of RC. However, its positive features come at a price: stable RC re-introduces one of the undesirable features of other nonmonotonic logics, namely, deductive closures may not exist and may not be unique.

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Preferences and Nonmonotonic Reasoning

AI Magazine ◽

10.1609/aimag.v29i4.2179 ◽

2008 ◽

Vol 29 (4) ◽

pp. 69 ◽

Cited By ~ 24

Author(s):

Gerhard Brewka ◽

Ilkka Niemela ◽

Miroslaw Truszczynski

Keyword(s):

Logic Programming ◽

Nonmonotonic Reasoning ◽

Nonmonotonic Logic ◽

Preference Information ◽

The World ◽

Extended Logic Programming ◽

Answer Set Semantics ◽

Nonmonotonic Logics ◽

Answer Set

We give an overview of the multifaceted relationship between nonmonotonic logics and preferences. We discuss how the nonmonotonicity of reasoning itself is closely tied to preferences reasoners have on models of the world or, as we often say here, possible belief sets. Selecting extended logic programming with the answer-set semantics as a "generic" nonmonotonic logic, we show how that logic defines preferred belief sets and how preferred belief sets allow us to represent and interpret normative statements. Conflicts among program rules (more generally, defaults) give rise to alternative preferred belief sets. We discuss how such conflicts can be resolved based on implicit specificity or on explicit rankings of defaults. Finally, we comment on formalisms which explicitly represent preferences on properties of belief sets. Such formalisms either build preference information directly into rules and modify the semantics of the logic appropriately, or specify preferences on belief sets independently of the mechanism to define them.

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