Routley Star in Information-Based Semantics

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Routley Star in Information-Based Semantics

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Routley Star in Information-Based Semantics

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

60301 - Philosophy, History and Philosophy of science and technology

Projekt

<a href="/cs/project/GM21-23610M" target="_blank" >GM21-23610M: Logická struktura informačních kanálů</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název statě ve sborníku

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

ISBN

—

ISSN

2075-2180

e-ISSN

2075-2180

Počet stran výsledku

13

Strana od-do

285-297

Název nakladatele

Open Publishing Association

Místo vydání

online

Místo konání akce

Łódź

Datum konání akce

14. 3. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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