Inquisitive split and structural completeness

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F25%3A00635847" target="_blank" >RIV/67985955:_____/25:00635847 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1017/S0960129525000118" target="_blank" >https://doi.org/10.1017/S0960129525000118</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S0960129525000118" target="_blank" >10.1017/S0960129525000118</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Inquisitive split and structural completeness

Popis výsledku v původním jazyce

In this paper, the notion of structural completeness is explored in the context of a generalized class of superintuitionistic logics involving also systems that are not closed under uniform substitution. We just require that each logic must be closed under D-substitutions assigning to atomic formulas only ∨-free formulas. For these systems we introduce four different notions of structural completeness and study how they are related. We focus on superintuitionistic inquisitive logics that validate a schema called Split and have the disjunction property. In these logics disjunction can be interpreted in the sense of inquisitive semantics as a question forming operator. It is shown that a logic is structurally complete with respect to D-substitutions if and only if it includes the weakest superintuitionistic inquisitive logic. Various consequences of this result are explored. For example, it is shown that every superintuitionistic inquisitive logic can be characterized by a Kripke model built up from D-substitutions. Additionally, we resolve a conjecture concerning superintuitionistic inquisitive logics due to Miglioli et al. and show that a false conjecture about superintuitionistic logics due to Minari and Wroński. becomes true in the broader space of regular generalized superintuitionistic logics.

Název v anglickém jazyce

Inquisitive split and structural completeness

Popis výsledku anglicky

In this paper, the notion of structural completeness is explored in the context of a generalized class of superintuitionistic logics involving also systems that are not closed under uniform substitution. We just require that each logic must be closed under D-substitutions assigning to atomic formulas only ∨-free formulas. For these systems we introduce four different notions of structural completeness and study how they are related. We focus on superintuitionistic inquisitive logics that validate a schema called Split and have the disjunction property. In these logics disjunction can be interpreted in the sense of inquisitive semantics as a question forming operator. It is shown that a logic is structurally complete with respect to D-substitutions if and only if it includes the weakest superintuitionistic inquisitive logic. Various consequences of this result are explored. For example, it is shown that every superintuitionistic inquisitive logic can be characterized by a Kripke model built up from D-substitutions. Additionally, we resolve a conjecture concerning superintuitionistic inquisitive logics due to Miglioli et al. and show that a false conjecture about superintuitionistic logics due to Minari and Wroński. becomes true in the broader space of regular generalized superintuitionistic logics.

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

2025

Kód důvěrnosti údajů

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

Název periodika

Mathematical Structures in Computer Science

ISSN

0960-1295

e-ISSN

1469-8072

Svazek periodika

—

Číslo periodika v rámci svazku

35

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

18

Strana od-do

e12

Kód UT WoS článku

001498096100001

EID výsledku v databázi Scopus

2-s2.0-105007136721