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Blending margins: The modal logic K has nullary unification type
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SYSNO ASEP 0453140 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Blending margins: The modal logic K has nullary unification type Author(s) Jeřábek, Emil (MU-W) RID, SAI, ORCID Source Title Journal of Logic and Computation - ISSN 0955-792X
Roč. 25, č. 5 (2015), s. 1231-1240Number of pages 10 s. Language eng - English Country GB - United Kingdom Keywords modal logic ; unification type ; rule of margins Subject RIV BA - General Mathematics R&D Projects IAA100190902 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) 1M0545 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support MU-W - RVO:67985840 UT WOS 000363212100004 DOI 10.1093/logcom/ext055 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2016
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