# General Concept Inclusions inFluzzy Description Logics

@inproceedings{Stoilos2006GeneralCI, title={General Concept Inclusions inFluzzy Description Logics}, author={Giorgos Stoilos and Umberto Straccia and G. Stamou and Jeff Z. Pan}, booktitle={ECAI}, year={2006} }

Fuzzy Description Logics (fuzzy DLs) have been proposed as a language to describe structured knowledge with vague concepts. A major theoretical and computational limitation so far is the inability to deal with General Concept Inclusions (GCIs), which is an important feature of classical DLs. In this paper, we address this issue and develop a calculus for fuzzy DLs with GCIs.

## 81 Citations

Mixed Integer Programming, General Concept Inclusions and Fuzzy Description Logics

- Mathematics, Computer ScienceEUSFLAT Conf.
- 2007

This paper develops a calculus for fuzzy DLs with GCIs under various semantics: classical logic, \Zadeh semantics", and Lukasiewicz logic.

A Fuzzy Description Logic with Product T-norm

- Computer Science2007 IEEE International Fuzzy Systems Conference
- 2007

This work proposes a novel semantics combining the common product t-norm with the standard negation, and shows some interesting properties of the logic and proposes a reasoning algorithm based on a mixture of tableaux rules and the reduction to mixed integer quadratically constrained programming.

Fuzzy description logics with general t-norms and datatypes

- Mathematics, Computer ScienceFuzzy Sets Syst.
- 2009

This work proposes a semantics based on the use of a general left-continuous t-norm and an involutive negation and shows how to handle functional concrete roles relating individuals of the domain and strings, real or integer numbers.

How Fuzzy Is My Fuzzy Description Logic?

- Mathematics, Computer ScienceIJCAR
- 2012

This work provides a class of t-norms and an expressive fuzzy DL for which ontology consistency is linearly reducible to crisp reasoning, and thus has its same complexity.

Handling Imprecise Knowledge with Fuzzy Description Logic

- Computer ScienceDescription Logics
- 2006

The syntax and semantics of fuzzy SHOIQ are presented, investigating several properties of the semantics of transitivity, qualified cardinality restrictions and reasoning capabilities.

The limits of decidability in fuzzy description logics with general concept inclusions

- Mathematics, Computer ScienceArtif. Intell.
- 2015

This paper presents a proof framework that allows for a near-universal classification of fuzzy DLs according to the decidability of their consistency problem, and provides matchingDecidability results for most of the remaining logics.

Consistency in Fuzzy Description Logics over Residuated De Morgan Lattices

- 2012

Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based…

On the Undecidability of Fuzzy Description Logics with GCIs with Lukasiewicz t-norm

- Mathematics, Computer ScienceArXiv
- 2011

Analysis of Fuzzy Description Logics with General Concept Inclusions with GCIs shows that knowledge base satisfiability is also an undecidable problem for Lukasiewicz Logic.

Reasoning with qualified cardinality restrictions in fuzzy Description Logics

- Computer Science2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence)
- 2008

This paper investigates on the problem of reasoning with qualified cardinality restrictions (QCRs) in fuzzy DLs, extending previous results on simple number restrictions, and presents a tableaux algorithm for the the fuzzy-DL fKD-ALCIQ.

Are fuzzy description logics with general concept inclusion axioms decidable?

- Mathematics, Computer Science2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011)
- 2011

This paper shows that an algorithm that was claimed to answer the question affirmatively for this logic is actually incorrect, and proves undecidability of a variant of this logic.

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