Abstract
Types are a crucial concept in conceptual modelling, logic, and knowledge representation as they are an ubiquitous device to understand and formalise the classification of objects. We propose a logical treatment of types based on a cognitively inspired modelling that accounts for the amount of information that is actually available to a certain agent in the task of classification. We develop a predicative modal logic whose semantics is based on conceptual spaces that model the actual information that a cognitive agent has about objects, types, and the classification of an object under a certain type. In particular, we account for possible failures in the classification, for the lack of sufficient information, and for some aspects related to vagueness.
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Notes
- 1.
\(*\) means here that a certain quality is not applicable to a certain object.
- 2.
Since we deal with restricted quantification, we define the predicative language without open formulas.
- 3.
Note that we are using a concept of intension that differs from the standard view of modal logics, i.e. the Carnap view of intensions as functions form possible worlds to extensions of predicates. Here the intension of a type, in a Fregean perspective, is the relevant information associated to the type. This information may or may not change through possible worlds. This is an open question that requires further investigation. In this paper, we prefer not to commit to either assumption.
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Porello, D., Guizzardi, G. (2017). Towards a Cognitive Semantics of Types. In: Esposito, F., Basili, R., Ferilli, S., Lisi, F. (eds) AI*IA 2017 Advances in Artificial Intelligence. AI*IA 2017. Lecture Notes in Computer Science(), vol 10640. Springer, Cham. https://doi.org/10.1007/978-3-319-70169-1_32
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