Blending margins: The modal logic K has nullary unification type
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Blending margins: The modal logic K has nullary unification type
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Logic and Computation
ISSN
0955-792X
e-ISSN
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Volume of the periodical
25
Issue of the periodical within the volume
5
Country of publishing house
GB - UNITED KINGDOM
Number of pages
10
Pages from-to
1231-1240
UT code for WoS article
000363212100004
EID of the result in the Scopus database
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