All

What are you looking for?

All
Projects
Results
Organizations

Quick search

  • Projects supported by TA ČR
  • Excellent projects
  • Projects with the highest public support
  • Current projects

Smart search

  • That is how I find a specific +word
  • That is how I leave the -word out of the results
  • “That is how I can find the whole phrase”

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

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

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

  • 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