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A note on bisimulation quantifiers and fixed points over transitive frames. (English) Zbl 1173.03018
Three basic questions regarding the extension of modal logic with a special kind of propositional quantifiers, known as bisimulation quantifiers, over arbitrary classes of frames, are addressed.
1.
The relation between bisimulation invariance of bisimulation quantifiers and the semantical notion of amalgamation of the class of frames is discussed.
2.
A strong form of interpolation, uniform interpolation, and its relation with the closure under bisimulation quantifiers is considered.
3.
Bisimulation quantifiers logic and modal logic with extremal fixed points are compared.
Moreover it is proved that the extensions of modal logic with bisimulation quantifiers and fixed points are equivalent over the class of K4 or S4 frames.

MSC:
03B45 Modal logic (including the logic of norms)
03B70 Logic in computer science
03C80 Logic with extra quantifiers and operators
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