Categories: How I learned to stop worrying and love two sorts

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

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

17 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationProceedings of 23rd International Workshop, WoLLIC 2016
Subtitle of host publicationLogic, Language, Information, and Computation
PublisherSpringer
Pages145-164
Number of pages20
Volume9803
ISBN (Print)9783662529201
DOIs
Publication statusPublished - 2016
Event23rd International Workshop on Logic, Language, Information, and Computation, WoLLIC 2016 - Puebla, Mexico
Duration: 16 Aug 201619 Aug 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9803
ISSN (Print)03029743
ISSN (Electronic)16113349

Conference

Conference23rd International Workshop on Logic, Language, Information, and Computation, WoLLIC 2016
CountryMexico
CityPuebla
Period16/08/1619/08/16

Keywords

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

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