Abstract
Generally, mereological relations are modeled using fragments of first-order logic(FOL) and difficulties arise when meta-reasoning is done over their properties, leading to reason outside the logic. Alternatively, classical languages for conceptual modeling such as UML lack of formal foundations resulting in ambiguous interpretations of mereological relations. Moreover, they cannot prove that a given specification is correct from a logical perspective. In order to address all these problems, we suggest a formal framework using a dependent (higher-order) type theory such as those used in program checking and theorem provers (e.g., Coq). It is based on constructive logic and allows reasoning in different abstraction levels within the logic. Furthermore, it maximizes the expressiveness while preserving decidability of type checking and results in a coherent theory with a powerful sub-typing mechanism.
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Dapoigny, R., Barlatier, P. (2009). Towards an Ontological Modeling with Dependent Types: Application to Part-Whole Relations. In: Laender, A.H.F., Castano, S., Dayal, U., Casati, F., de Oliveira, J.P.M. (eds) Conceptual Modeling - ER 2009. ER 2009. Lecture Notes in Computer Science, vol 5829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04840-1_13
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DOI: https://doi.org/10.1007/978-3-642-04840-1_13
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