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

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

*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review

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 publicationLogic, Language, Information, and Computation - 23rd International Workshop, WoLLIC 2016, Proceedings
EditorsJouko Väänänen, Åsa Hirvonen, Ruy de Queiroz
PublisherSpringer Verlag
Pages145-164
Number of pages20
ISBN (Print)9783662529201
DOIs
Publication statusPublished - 1 Jan 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 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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

Fingerprint

Dive into the research topics of 'Categories: How I learned to stop worrying and love two sorts'. Together they form a unique fingerprint.

Cite this