Rules with parameters in modal logic II
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00524632" target="_blank" >RIV/67985840:_____/20:00524632 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.apal.2020.102829" target="_blank" >https://doi.org/10.1016/j.apal.2020.102829</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apal.2020.102829" target="_blank" >10.1016/j.apal.2020.102829</a>
Alternative languages
Result language
angličtina
Original language name
Rules with parameters in modal logic II
Original language description
We analyze the computational complexity of admissibility and unifiability with parameters in transitive modal logics. The class of cluster-extensible (clx) logics was introduced in the first part of this series of papers [8]. We completely classify the complexity of unifiability or inadmissibility in any clx logic as being complete for one of Σ2 exp, NEXP, coNEXP, PSPACE, or Π2 p. In addition to the main case where arbitrary parameters are allowed, we consider restricted problems with the number of parameters bounded by a constant, and the parameter-free case. Our upper bounds are specific to clx logics, but we also include similar results for logics of bounded depth and width. In contrast, our lower bounds are very general: they apply each to a class of all transitive logics whose frames allow occurrence of certain finite subframes. We also discuss the baseline problem of complexity of derivability: it is coNP-complete or PSPACE-complete for each clx logic. In particular, we prove PSPACE-hardness of derivability for a broad class of transitive logics that includes all logics with the disjunction property.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA19-05497S" target="_blank" >GA19-05497S: Complexity of mathematical proofs and structures</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annals of Pure and Applied Logic
ISSN
0168-0072
e-ISSN
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Volume of the periodical
171
Issue of the periodical within the volume
10
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
59
Pages from-to
102829
UT code for WoS article
000568991900008
EID of the result in the Scopus database
2-s2.0-85084806006