Abstract
Types are fundamental for conceptual domain modeling and knowledge representation in computer science. Frequently, monadic types used in domain models have as their instances objects (endurants, continuants), i.e., entities persisting in time that experience qualitative changes while keeping their numerical identity. In this paper, I revisit a philosophically and cognitively well-founded theory of object types and propose a system of modal logics with restricted quantification designed to formally characterize the distinctions and constraints proposed by this theory. The formal system proposed also addresses the limitations of classical (unrestricted extensional) modal logics in differentiating between types that represent mere properties (or attributions) ascribed to individual objects from types that carry a principle of identity for those individuals (the so-called sortal types). Finally, I also show here how this proposal can complement the theory of conceptual spaces by offering an account for kind-supplied principles of cross-world identity. The account addresses an important criticism posed to conceptual spaces in the literature and is in line with a number of empirical results in the literature of cognitive psychology.
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Notes
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What are termed classes in UML are akin to what I name types here, not to the well-known set-theoretical notion of classes. In other words, classes in UML are intensional not extensional entities.
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Guizzardi, G. (2015). Logical, Ontological and Cognitive Aspects of Object Types and Cross-World Identity with Applications to the Theory of Conceptual Spaces. In: Zenker, F., Gärdenfors, P. (eds) Applications of Conceptual Spaces. Synthese Library, vol 359. Springer, Cham. https://doi.org/10.1007/978-3-319-15021-5_9
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