Abstract
We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of combining prototypical concepts, an open problem in the fields of AI and cognitive modelling. Our logic extends the logic of typicality \(\mathcal {ALC}+\mathbf{T}_\mathbf{R}\), based on the notion of rational closure, by inclusions \(p \ {::} \ \mathbf{T}(C) \sqsubseteq D\) (“we have probability p that typical Cs are Ds”), coming from the distributed semantics of probabilistic Description Logics. Additionally, it embeds a set of cognitive heuristics for concept combination. We show that the complexity of reasoning in our logic is ExpTime-complete as in \(\mathcal {ALC}\).
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Notes
- 1.
Here, we focus on the proposal of the formalism itself, therefore the machinery for obtaining probabilities from an application domain will not be discussed.
- 2.
Here we assume that some methods for the automatic assignment of the HEAD/MODIFER pairs are/may be available and focus on the discussion of the reasoning part.
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Acknowledgements
This work is partially supported by the project “ExceptionOWL”, Università di Torino and Compagnia di San Paolo, call 2014“Excellent (young) PI”, http://di.unito.it/exceptionowl.
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Lieto, A., Pozzato, G.L. (2018). A Description Logic of Typicality for Conceptual Combination. In: Ceci, M., Japkowicz, N., Liu, J., Papadopoulos, G., Raś, Z. (eds) Foundations of Intelligent Systems. ISMIS 2018. Lecture Notes in Computer Science(), vol 11177. Springer, Cham. https://doi.org/10.1007/978-3-030-01851-1_19
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