Inquisitive Heyting Algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F21%3A00546145" target="_blank" >RIV/67985955:_____/21:00546145 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s11225-020-09936-9" target="_blank" >https://doi.org/10.1007/s11225-020-09936-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11225-020-09936-9" target="_blank" >10.1007/s11225-020-09936-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Inquisitive Heyting Algebras

Popis výsledku v původním jazyce

In this paper we introduce a class of inquisitive Heyting algebras as algebraic structures that are isomorphic to algebras of finite antichains of bounded implicative meet semilattices. It is argued that these structures are suitable for algebraic semantics of inquisitive superintuitionistic logics, i.e. logics of questions based on intuitionistic logic and its extensions. We explain how questions are represented in these structures (prime elements represent declarative propositions, non-prime elements represent questions, join is a question-forming operation) and provide several alternative characterizations of these algebras. For instance, it is shown that a Heyting algebra is inquisitive if and only if its prime filters and filters generated by sets of prime elements coincide and prime elements are closed under relative pseudocomplement. We prove that the weakest inquisitive superintuitionistic logic is sound with respect to a Heyting algebra iff the algebra is what we call a homomorphic p-image of some inquisitive Heyting algebra. It is also shown that a logic is inquisitive iff its Lindenbaum–Tarski algebra is an inquisitive Heyting algebra.

Název v anglickém jazyce

Inquisitive Heyting Algebras

Popis výsledku anglicky

In this paper we introduce a class of inquisitive Heyting algebras as algebraic structures that are isomorphic to algebras of finite antichains of bounded implicative meet semilattices. It is argued that these structures are suitable for algebraic semantics of inquisitive superintuitionistic logics, i.e. logics of questions based on intuitionistic logic and its extensions. We explain how questions are represented in these structures (prime elements represent declarative propositions, non-prime elements represent questions, join is a question-forming operation) and provide several alternative characterizations of these algebras. For instance, it is shown that a Heyting algebra is inquisitive if and only if its prime filters and filters generated by sets of prime elements coincide and prime elements are closed under relative pseudocomplement. We prove that the weakest inquisitive superintuitionistic logic is sound with respect to a Heyting algebra iff the algebra is what we call a homomorphic p-image of some inquisitive Heyting algebra. It is also shown that a logic is inquisitive iff its Lindenbaum–Tarski algebra is an inquisitive Heyting algebra.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

60301 - Philosophy, History and Philosophy of science and technology

Projekt

<a href="/cs/project/GA20-18675S" target="_blank" >GA20-18675S: Povaha logických forem a moderní logika</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Studia Logica

ISSN

0039-3215

e-ISSN

1572-8730

Svazek periodika

109

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

23

Strana od-do

995-1017

Kód UT WoS článku

000619395100002

EID výsledku v databázi Scopus

2-s2.0-85101209895