Categories

How I learned to stop worrying and love two sorts

Conference paper (2016)

Authors

Willem Conradie University of Johannesburg

S.S.A. Frittella

A. Palmigiano University of Johannesburg,

M. Piazzai

A. Tzimoulis

Nachoem Wijnberg Universiteit van Amsterdam

Categorization theory Epistemic logic Formal concept analysis Lattice-based modal logic RS-frames

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http://resolver.tudelft.nl/uuid:345f7dda-70fe-4a0e-be8f-b3639021ce4d

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Published Date

2016

Language

English

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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.