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Algorithmic complexity of monadic multimodal predicate logics with equality over finite Kripke frames
P. 13–17.
Publication based on the results of:
Rybakov M., / Series arXiv "math". 2025. No. 2505.00524.
The paper considers algorithmic properties of classical and non-classical first-order logics and theories in bounded languages. The main idea is to prove the undecidability of various fragments of classical and non-classical first-order logics and theories indirectly — by extracting it as a consequence of the recursive inseparability of special problems associated with them. First, we ...
Added: May 21, 2025
Агаджанян И. А., Rybakov M., Шкатов Д. П., / Series arXiv "math". 2023.
The paper investigates algorithmic complexity of monadic multimodal predicate logics with equality over finite Kripke frames or classes of finite Kripke frames. Precise complexity bounds for monadic logics of classes of Kripke frames with finitely many possible worlds are obtained. ...
Added: July 7, 2023
Shehtman V. B., Annals of Pure and Applied Logic 2023 Vol. 174 No. 2 Article 103202
The paper studies completeness and incompleteness of modal predicate logics in
Kripke semantics, especially for logics of the form QL, minimal predicate extensions
of modal propositional logics. We show that QL is incomplete for a continual family
of logics above K + \Box(\Box p \rigtharrow p), in particular for well-known K5 and K45. On
the other hand, in some cases ...
Added: January 30, 2023
Rybakov M., Shkatov D., Journal of Logic and Computation 2020 Vol. 30 No. 7 P. 1305–1329
We study the effect of restricting the number of individual variables, as well as the number and arity of predicate letters, in languages of first-order predicate modal logics of finite Kripke frames on the logics’ algorithmic properties. A finite frame is a frame with a finite set of possible worlds. The languages we consider have ...
Added: August 27, 2020
Shehtman V. B., , in: Advances in Modal LogicVol. 12.: College Publications, 2018. P. 559–575.
We prove completeness for some normal modal predicate logics in the standard Kripke semantics with expanding domains. We consider quantified versions of propositional logics with the axiom of density plus some others (transitivity, confluence). The method of proof modifies the technique developed for other cases
(without density) by S. Ghilardi, G. Corsi and D. Skvorstov; but now we arrange the ...
Added: September 20, 2018