Description Logics (DLs) supporting uncertainty are not as well studied and developed as their crisp counterparts, thereby limiting their practical use in real world domains. The Bayesian DL BEL and its extensions have been introduced to deal with uncertain knowledge without assuming (probabilistic) independence between axioms. In this paper we combine the classical DL ALC with Bayesian Networks to define a new DL known as BALC. BALC includes a solution to the consistency checking problem and changes to the tableaux algorithm that are not a part of BEL. Furthermore, BALC also supports probabilistic assertional information which was not studied for BEL. We present algorithms for four categories of reasoning problems for our logic; two versions of concept satisfiability (referred to as total concept satisfiability and partial concept satisfiability respectively), knowledge base consistency, subsumption, and instance checking. We show that all reasoning problems in BALC are in the same complexity class as their classical variants, provided that the size of the Bayesian Network is included in the size of the knowledge base.

Botha, L., Meyer, T., Penaloza, R. (2018). The Bayesian description logic BALC. Intervento presentato a: International Workshop on Description Logics, DL 2018, USA.

The Bayesian description logic BALC

Penaloza R.
2018

Abstract

Description Logics (DLs) supporting uncertainty are not as well studied and developed as their crisp counterparts, thereby limiting their practical use in real world domains. The Bayesian DL BEL and its extensions have been introduced to deal with uncertain knowledge without assuming (probabilistic) independence between axioms. In this paper we combine the classical DL ALC with Bayesian Networks to define a new DL known as BALC. BALC includes a solution to the consistency checking problem and changes to the tableaux algorithm that are not a part of BEL. Furthermore, BALC also supports probabilistic assertional information which was not studied for BEL. We present algorithms for four categories of reasoning problems for our logic; two versions of concept satisfiability (referred to as total concept satisfiability and partial concept satisfiability respectively), knowledge base consistency, subsumption, and instance checking. We show that all reasoning problems in BALC are in the same complexity class as their classical variants, provided that the size of the Bayesian Network is included in the size of the knowledge base.
paper
probabilistic reasoning, description logics
English
International Workshop on Description Logics, DL 2018
2018
2018
2211
http://ceur-ws.org/Vol-2211/paper-09.pdf
open
Botha, L., Meyer, T., Penaloza, R. (2018). The Bayesian description logic BALC. Intervento presentato a: International Workshop on Description Logics, DL 2018, USA.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/267809
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