On Completeness of Logics Enriched with Transitive Closure Modality

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On Completeness of Logics Enriched with Transitive Closure Modality

P. 1–3.

Shapirovsky I., Zolin E.

We give a sufficient condition for Kripke completeness of the extension of a modal logic with the transitive closure modality. More precisely, we show that if a logic is canonical and admits what we call definable filtration (ADF), then such an extension is complete (and again ADF).

Language: English

Keywords: Kripke completeness

In book

7th International Conference on Topology, Algebra and Categories in Logic (TACL 2015)

[б.и.], 2015.

Predicate counterparts of modal logics of provability: High undecidability and Kripke incompleteness

Rybakov M., Logic Journal of the IGPL 2024 Vol. 32 No. 3 P. 465–492

In this paper, the predicate counterparts, defined both axiomatically and semantically by means of Kripke frames, of the modal propositional logics GL, Grz, wGrz and their extensions are considered. It is proved that the set of semantical consequences on Kripke frames of every logic between QwGrz and QGL.3 or between QwGrz and QGrz.3 is Pi-1-1-hard even in languages with ...

Added: July 7, 2023

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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 ...

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Rybakov M., Котикова Е. А., Logical Investigations 2015 Vol. 21 No. 1 P. 86–99

For an infinite class of calculi containing CTL and QCL, it is proved that they are Kripke incomplete. ...

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Rybakov M., Shkatov D., , in: Десятые Смирновские чтения: материалы Междунар. науч. конф., Москва, 15–17 июня 2017 г.: М.: Современные тетради, 2017. P. 45–45.

We discuss an example of recursively-enumerable Kripke-complete first-order modal logics that are not Kripke complete with respect to a first-order definable class of frames. ...

Added: October 7, 2019

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Rybakov M., Shkatov D., , in: Advances in Modal LogicVol. 12.: College Publications, 2018. P. 531–539.

It is well-known that every quantied modal logic complete with respect to a first-order definable class of Kripke frames is recursively enumerable. Numerous examples are also known of natural quantied modal logics complete with respect to a class of frames dened by an essentially second-order condition which are not recursively enumerable. It is not, however, known if these ...

Added: October 6, 2019

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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