Abstract
Building on previous work on Weighted Description Logic (WDL), we present and assess an algorithm for concept combination grounded in the experimental research in cognitive psychology. Starting from two WDL formulas representing concepts in a way similar to Prototype Theory and a knowledge base (KB) modelling background knowledge, the algorithm outputs a new WDL formula which represent the combination of the input concepts. First, we study the logical properties of the operator defined by our algorithm. Second, we collect data on the prototypical representation of concepts and their combinations and learn WDL formulas from them. Third, we evaluate our algorithm and the role of the KB by comparing the algorithm’s outputs with the learned WDL formulas.
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Notes
- 1.
This algorithm revises the original one [35].
- 2.
Similar weighted accounts can be introduced in languages other than DL [29].
- 3.
The algorithm can however accept more general inputs.
- 4.
The algorithm guarantees that \({\mathbf {\bar{sft}}(\mathbb {K}{:}{\textsf{M}}{\circ }{\textsf{H}}) = \textbf{snc}(\mathbb {K}{:}{\textsf{M}}{\circ }{\textsf{H}})}\), see Phase 3.
- 5.
We also dropped the feature Are of different sizes that applies to the whole concept and would have been tricky in the extensional evaluation of the weights, see below.
- 6.
“The model first proposes that the intension of a conjunction is formed as the union of the constituent attribute sets” [20, p.56].
- 7.
We add 1 to both counts to avoid potential infinities.
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Righetti, G., Galliani, P., Masolo, C. (2023). Concept Combination in Weighted DL. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_27
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