Information types in intuitionistic predicate logic with constant domains

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F26%3A00645874" target="_blank" >RIV/67985955:_____/26:00645874 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1093/jigpal/jzaf057" target="_blank" >https://doi.org/10.1093/jigpal/jzaf057</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/jigpal/jzaf057" target="_blank" >10.1093/jigpal/jzaf057</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Information types in intuitionistic predicate logic with constant domains

Popis výsledku v původním jazyce

In this paper, we study two operators, inquisitive disjunction and inquisitive existential quantifier, in the context of first-order intuitionistic logic with constant domains. We explain that these operators allow us to express types of intuitionistic propositions. We first provide this language with a relational semantics and formulate a sound axiomatic system. Completeness of the system for the full language is presented as an open problem but we prove completeness for a rich fragment of the language adapting the methods developed by Gianluca Grilleti in the context of classical inquisitive logic. We also develop a general algebraic framework in which we characterize the class of “Kripkean algebras” generated by the relational semantics. In this way, we obtain our first algebraic characterization of the logic of intuitionistic types. We further characterize the class of all homomorphic images of “Kripkean algebras” that we call “inquisitive algebras”, thus obtaining a second, more general algebraic semantics for this logic.

Název v anglickém jazyce

Information types in intuitionistic predicate logic with constant domains

Popis výsledku anglicky

In this paper, we study two operators, inquisitive disjunction and inquisitive existential quantifier, in the context of first-order intuitionistic logic with constant domains. We explain that these operators allow us to express types of intuitionistic propositions. We first provide this language with a relational semantics and formulate a sound axiomatic system. Completeness of the system for the full language is presented as an open problem but we prove completeness for a rich fragment of the language adapting the methods developed by Gianluca Grilleti in the context of classical inquisitive logic. We also develop a general algebraic framework in which we characterize the class of “Kripkean algebras” generated by the relational semantics. In this way, we obtain our first algebraic characterization of the logic of intuitionistic types. We further characterize the class of all homomorphic images of “Kripkean algebras” that we call “inquisitive algebras”, thus obtaining a second, more general algebraic semantics for this logic.

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

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2026

Kód důvěrnosti údajů

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

Název periodika

Logic Journal of the IGPL

ISSN

1367-0751

e-ISSN

1368-9894

Svazek periodika

34

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

jzaf057

Kód UT WoS článku

001676419400001

EID výsledku v databázi Scopus

2-s2.0-105029514173