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

@inproceedings{Conradie2016CategoriesHI, title={Categories: How I Learned to Stop Worrying and Love Two Sorts}, author={Willem Conradie and Sabine Frittella and Alessandra Palmigiano and Michele Piazzai and Apostolos Tzimoulis and Nachoem M. Wijnberg}, booktitle={WoLLIC}, year={2016} }

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.
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## 41 Citations

Logical foundations of categorization theory Lecture 5

- Philosophy
- 2021

In this lecture, based on [7, Section 4], we discuss possible interpretations of the basic normal modal logic of categories, and related to this, some of its axiomatic extensions, and…

Algorithmic Correspondence and Canonicity for Possibility Semantics (Abstract)

- Computer ScienceSOQE
- 2017

A uniform and modular theory which subsumes the above results and extends them to logics with a non-classical propositional base has emerged, and has been dubbed unified correspondence.

Reconciliation of Approaches to the Semantics of Logics without Distribution

- Computer Science
- 2021

It is shown that, despite rejecting the additional frame restrictions, all the main ideas and results of the RS-frames approach relating to the semantics of non-distributive logics are captured in this simpler framework.

Toward an Epistemic-Logical Theory of Categorization

- PhilosophyTARK
- 2017

This paper introduces a sound and complete epistemic logic of categories and agents' categorical perception and proposes logic-based formalizations of some core concepts from psychological, sociological, and organizational research in categorization theory.

Sahlqvist theory for impossible worlds

- PhilosophyJ. Log. Comput.
- 2017

Unified correspondence theory is extended to Kripke frames with impossible worlds and their associated regular modal logics and it is shown that additivity and multiplicativity turn out to be key to extend Jonsson’s original proof of canonicity to the full Sahlqvist class of certain regular distributives naturally generalizing distributive modal logic.

A non-distributive logic for semiconcepts of a context and its modal extension with semantics based on Kripke contexts

- Computer Science
- 2022

A non-distributive two-sorted hypersequent calculus PDBL and its modal extension MPDBL are proposed for the classes of pure double Boolean algebras and puredouble Boolean algeses with operators respectively and it is demonstrated that, using PDBL, the basic notions and relations of conceptual knowledge can be expressed and inferences involving negations can be obtained.

THE LOGIC OF RESOURCES AND CAPABILITIES

- Computer ScienceThe Review of Symbolic Logic
- 2018

A number of properties enjoyed by LRC (soundness, completeness, canonicity, and disjunction property) and its associated analytic calculus (conservativity, cut elimination, and subformula property) are proved.

Compatibility and accessibility: lattice representation for semantics of non-classical and modal logics

- Computer ScienceArXiv
- 2022

The three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Ploˇsˇcica generalize possibility semantics for classical modal logics to non-classical modalLogics, motivated by a recent application of modal orthologic to natural language semantics.

Unified Correspondence as a Proof-Theoretic Tool

- Computer ScienceJ. Log. Comput.
- 2018

The present paper aims at establishing formal connections between correspondence phenomena, well known from the area of modal logic, and the theory of display calculi, originated by Belnap, and applies unified correspondence theory, with its tools and insights, to extend Kracht's results and prove his claims in the setting of DLE-logics.

Algorithmic Correspondence , Canonicity and Completeness for Possibility Semantics

- Computer Science
- 2017

The present paper aims at giving a closer look at the aforementioned unsolved problems using the algebraic and order-theoretic insights from a current ongoing research project, namely unified correspondence.

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