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From Rough Sets to Rough Knowledge Bases

Vitória A., Damásio C. V., Małuszyński J.

Fundamenta Informaticae

2003

Vol. 57, nr 2-4

215--246

This paper presents an expressive language for representing knowledge about vague concepts. It is based on the rough set formalism and it caters for implicit definition of rough relations by combining different regions (e.g. upper approximation, lower approximation, boundary) of other rough relations. The semantics of the proposed language is obtained by translating it to the language of extended logic programs whose meaning is captured by paraconsistent stable models. A query language is also discussed to retrieve information about the defined rough relations. Motivating examples illustrating the use of the language are described.

Processing Indefinite Deductive Databases under the Possible Model Semantics

Johnson C.A.

Fundamenta Informaticae

2002

Vol. 49, nr 4

325-347

The relationship between possible and supported models of unstratified indefinite deductive databases is studied, when disjunction is interpreted inclusively. Possible and supported models are shown to coincide under a suitable definition of supportedness, and the concept of a supported cover is introduced and shown to characterise possible models and facilitate top-down query processing and compilation under the possible model semantics. The properties and query processing of deductive databases under the possible model semantics is compared and contrasted with the perfect model semantics.

Stable models for stubborn sets

Varpaaniemi K.

Fundamenta Informaticae

2000

Vol. 43, Nr 1-4

355-375

The stubborn set method is one of the methods that try to relieve the state space explosion problem that occurs in state space generation. Spending some time in looking for "good'" stubborn sets can pay off in the total time spent in generating a reduced state space. This article shows how the method can exploit tools that solve certain problems of logic programs. The restriction of a definition of stubbornness to a given state can be translated into a variable-free logic program. When a stubborn set satisfying additional constraints is wanted, the additional constraints should be translated, too. It is easy to make the translation in such a way that each acceptable stubborn set of the state is represented by at least one stable model of the program, each stable model of the program represents at least one acceptable stubborn set of the state, and for each pair in the representation relation, the number of certain atoms in the stable model is equal to the number of enabled transitions of the represented stubborn set. So, in order to find a stubborn set which is good w.r.t. the number of enabled transitions, it suffices to find a stable model which is good w.r.t. the number of certain atoms. The article also presents a new NP-completeness result concerning stubborn sets.