Routley Star in Information-Based Semantics

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F22%3A00559694" target="_blank" >RIV/67985955:_____/22:00559694 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4204/EPTCS.358.21" target="_blank" >https://doi.org/10.4204/EPTCS.358.21</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4204/EPTCS.358.21" target="_blank" >10.4204/EPTCS.358.21</a>

Result language

angličtina

Original language name

Routley Star in Information-Based Semantics

Original language description

It is common in various non-classical logics, especially in relevant logics, to characterize negation semantically via the operation known as Routley star. This operation works well within relational semantic frameworks based on prime theories. We study this operation in the context of “information-based” semantics for which it is characteristic that sets of formulas supported by individual information states are theories that do not have to be prime. We will show that, somewhat surprisingly, the incorporation of Routley star into the information-based semantics does not lead to a collapse or a trivialization of the whole semantic system. On the contrary, it leads to a technically elegant though quite restricted semantic framework that determines a particular logic. We study some basic properties of this semantics. For example, we show that within this framework double negation law is valid only in involutive linear frames. We characterize axiomatically the logic of all linear frames and show that the logic of involutive linear frames coincides with a system that Mike Dunn coined Kalman logic. This logic is the {∧, ∨, ¬}-fragment of the “semi-relevant” logic known as R-mingle. Finally, we characterize by a deductive system the logic of all information frames equipped with Routley star.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

60301 - Philosophy, History and Philosophy of science and technology

Project

<a href="/en/project/GM21-23610M" target="_blank" >GM21-23610M: Logical Structure of Information Channels</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2022

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Proceedings of the 10th International Conference on Non-Classical Logics. Theory and Applications, NCL 2022, Łódź, Poland, 14-18 March 2022

ISBN

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ISSN

2075-2180

e-ISSN

2075-2180

Number of pages

13

Pages from-to

285-297

Publisher name

Open Publishing Association

Place of publication

online

Event location

Łódź

Event date

Mar 14, 2022

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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