[2405.00912] Unification in the description logic $\mathcal{FL}_\bot$
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Computer Science > Symbolic Computation

arXiv:2405.00912 (cs)
[Submitted on 1 May 2024 (v1), last revised 13 Nov 2024 (this version, v3)]

Title:Unification in the description logic $\mathcal{FL}_\bot$

Authors:Barbara Morawska
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Abstract:Description Logics are a formalism used in the knowledge representation, where the knowledge is captured in the form of concepts constructed in a controlled way from a restricted vocabulary. This allows one to test effectively for consistency of and the subsumption between the concepts. Unification of concepts may likewise become a useful tool in analysing the relations between concepts. The unification problem has been solved for the description logics $\mathcal{FL}_0$ and $\mathcal{EL}$. These small logics do not provide any means to express negation. Here we show an algorithm solving unification in $\mathcal{FL}_\bot$, the logic that extends $\mathcal{FL}_0$ with the bottom concept. Bottom allows one to express that two concepts are disjoint. Our algorithm runs in exponential time, with respect to the size of the problem.
Subjects: Symbolic Computation (cs.SC); Logic in Computer Science (cs.LO)
Cite as: arXiv:2405.00912 [cs.SC]
  (or arXiv:2405.00912v3 [cs.SC] for this version)
  https://doi.org/10.48550/arXiv.2405.00912

Submission history

From: Barbara Morawska [view email]
[v1] Wed, 1 May 2024 23:53:34 UTC (170 KB)
[v2] Fri, 10 May 2024 15:43:11 UTC (201 KB)
[v3] Wed, 13 Nov 2024 10:32:29 UTC (206 KB)
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