Blending margins: The modal logic K has nullary unification type

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F15%3A00453140" target="_blank" >RIV/67985840:_____/15:00453140 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1093/logcom/ext055" target="_blank" >http://dx.doi.org/10.1093/logcom/ext055</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/logcom/ext055" target="_blank" >10.1093/logcom/ext055</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Blending margins: The modal logic K has nullary unification type

Popis výsledku v původním jazyce

We investigate properties of the formula p->[]p in the basic modal logic K. We show that K satisfies an infinitary weaker variant of the rule of margins A->[]A / A,A, and as a consequence, we obtain various negative results about admissibility and unification in K. We describe a complete set of unifiers (i.e., substitutions making the formula provable) of p->[]p, and use it to establish that K has the worst possible unification type: nullary. In well-behaved transitive modal logics, admissibility and unification can be analyzed in terms of projective formulas, introduced by Ghilardi; in particular, projective formulas coincide for these logics with formulas that are admissibly saturated (i.e., derive all their multiple-conclusion admissible consequences) or exact (i.e., axiomatize a theory of a substitution). In contrast, we show that in K, the formula p->[]p is admissibly saturated, but neither projective nor exact. All our results for K also apply to the basic description logic ALC.

Název v anglickém jazyce

Blending margins: The modal logic K has nullary unification type

Popis výsledku anglicky

We investigate properties of the formula p->[]p in the basic modal logic K. We show that K satisfies an infinitary weaker variant of the rule of margins A->[]A / A,A, and as a consequence, we obtain various negative results about admissibility and unification in K. We describe a complete set of unifiers (i.e., substitutions making the formula provable) of p->[]p, and use it to establish that K has the worst possible unification type: nullary. In well-behaved transitive modal logics, admissibility and unification can be analyzed in terms of projective formulas, introduced by Ghilardi; in particular, projective formulas coincide for these logics with formulas that are admissibly saturated (i.e., derive all their multiple-conclusion admissible consequences) or exact (i.e., axiomatize a theory of a substitution). In contrast, we show that in K, the formula p->[]p is admissibly saturated, but neither projective nor exact. All our results for K also apply to the basic description logic ALC.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Journal of Logic and Computation

ISSN

0955-792X

e-ISSN

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Svazek periodika

25

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

10

Strana od-do

1231-1240

Kód UT WoS článku

000363212100004

EID výsledku v databázi Scopus

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