Undefinability of propositional quantifiers in the modal system S4

Ghilardi, Silvio; Zawadowski, Marek

doi:10.1007/bf01061237

Cited by 54 publications

(41 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since then, uniform interpolation has been established for various other logics, including the modal logics K and KT [1,9,10]. Intriguingly, the modal logics K4 and S4 do not have uniform interpolation [1,3]. As there are only seven propositional intermediate logics with interpolation [5], the number of intermediate logics with uniform interpolation is necessarily bounded by that number.…”

Section: Introductionmentioning

confidence: 99%

Uniform interpolation and sequent calculi in modal logic

Iemhoff

2018

Arch. Math. Logic

View full text Add to dashboard Cite

A method is presented that connects the existence of uniform interpolants to the existence of certain sequent calculi. This method is applied to several modal logics and is shown to cover known results from the literature, such as the existence of uniform interpolants for the modal logic K. New is the result that KD has uniform interpolation. The results imply that for modal logics K4 and S4, which are known not to have uniform interpolation, certain sequent calculi cannot exist.

show abstract

Section: Introductionmentioning

confidence: 99%

Uniform interpolation and sequent calculi in modal logic

Iemhoff

2018

Arch. Math. Logic

View full text Add to dashboard Cite

show abstract

“…It is known that uniform interpolation does not hold for all modal logics (it fails e.g. for the iterative logic S4 [14]), but we are unaware of an example of a noniterative modal logic for which (uniform) interpolation fails. We therefore leave the following to future research:…”

Section: Conclusion and Discussionmentioning

confidence: 97%

The Logic of Exact Covers: Completeness and Uniform Interpolation

Pattinson

2013

2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science

View full text Add to dashboard Cite

Abstract-We show that all (not necessarily normal or monotone) modal logics that can be axiomatised in rank-1 have the interpolation property, and that in fact interpolation is uniform if the logics just have finitely many modal operators. As immediate applications, we obtain previously unknown interpolation theorems for a range of modal logics, containing probabilistic and graded modal logic, alternating temporal logic and some variants of conditional logic.Technically, this is achieved by translating to and from a new (coalgebraic) logic introduced in this paper, the logic of exact covers. It is interpreted over coalgebras for an endofunctor on the category of sets that also directly determines the syntax. Apart from closure under bisimulation quantifiers (and hence interpolation), we also provide a complete tableaux calculus and establish both the Hennessy-Milner and the small model property for this logic.

show abstract

“…For many logical languages, it is known that uniform interpolants do not always exist; this is true for FO, but also for various modal logics [10,30]. Positive results are known for propositional intuitionistic logic [24] and the modal µ-calculus [7].…”

Section: Uniform Interpolationmentioning

confidence: 99%