Affiliation:
1. Institute for Information Transmission Problems of Russian Academy of Sciences, Moscow 127051, Russia
2. School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, WITS2050, South Africa
Abstract
Abstract
We study the algorithmic properties of first-order monomodal logics of frames $\langle {\textrm{I}\!\textrm{N}}, \leqslant \rangle $, $\langle {\textrm{I}\!\textrm{N}}, < \rangle $, $\langle \mathbb {Q}, \leqslant \rangle $, $\langle \mathbb {Q}, < \rangle $, $\langle {\textrm{I}\!\textrm{R}}, \leqslant \rangle $, $\langle {\textrm{I}\!\textrm{R}}, < \rangle $, as well as some related logics, in languages with restrictions on the number of individual variables as well as the number and arity of predicate letters. We show that the logics of frames based on $ {\textrm{I}\!\textrm{N}}$ are $\varPi ^1_1$-hard—thus, not recursively enumerable—in languages with two individual variables, one monadic predicate letter and one proposition letter. We also show that the logics of frames based on $\mathbb {Q}$ and ${\textrm{I}\!\textrm{R}}$ are $\varSigma ^0_1$-hard in languages with the same restrictions. Similar results are obtained for a number of related logics.
Publisher
Oxford University Press (OUP)
Subject
Logic,Hardware and Architecture,Arts and Humanities (miscellaneous),Software,Theoretical Computer Science
Cited by
9 articles.
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