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arXiv · 1604.00777

Categories: How I Learned to Stop Worrying and Love Two Sorts

Willem Conradie·Sabine Frittella·Michele Piazzai·Apostolos Tzimoulis·Alessandra Palmigiano·Nachoem M. Wijnberg
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Abstract

RS-frames were introduced by Gehrke as relational semantics for substructural logics. They are two-sorted structures, based on RS-polarities with additional relations used to interpret modalities. We propose an intuitive, epistemic interpretation of RS-frames for modal logic, in terms of categorization systems and agents' subjective interpretations of these systems. Categorization systems are a key to any decision-making process and are widely studied in the social and management sciences. A set of objects together with a set of properties and an incidence relation connecting objects with their properties forms a polarity which can be `pruned' into an RS-polarity. Potential categories emerge as the Galois-stable sets of this polarity, just like the concepts of Formal Concept Analysis. An agent's beliefs about objects and their properties (which might be partial) is modelled by a relation which gives rise to a normal modal operator expressing the agent's beliefs about category membership. Fixed-points of the iterations of the belief modalities of all agents are used to model categories constructed through social interaction.

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Willem Conradie, Sabine Frittella, Michele Piazzai, Apostolos Tzimoulis, Alessandra Palmigiano, Nachoem M. Wijnberg. 2016-04-04. Categories: How I Learned to Stop Worrying and Love Two Sorts. https://doi.org/10.1007/978-3-662-55386-2%5C_7

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