We consider 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: bisimulation invariance, uniform interpolation, and expressive power. In particular: – we discuss the relation between bisimulation invariance of bisimulation quantifiers and the semantical notion of amalgamation of the class of frames; – we consider a strong form of interpolation, uniform interpolation, and its relation with the closure under bisimulation quantifiers; – we compare bisimulation quantifiers logic with the better known extension of modal logic with extremal fixed points. In this article we show that the answers to these questions that are valid for the class of all frames do not generalize to arbitrary classes, but they do generalize if we restrict to classes of (finite) transitive or (finite) transitive and reflexive frames.

A note on bisimulation quantifiers and fixed points over transitive frames

LENZI, Giacomo;
2008-01-01

Abstract

We consider 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: bisimulation invariance, uniform interpolation, and expressive power. In particular: – we discuss the relation between bisimulation invariance of bisimulation quantifiers and the semantical notion of amalgamation of the class of frames; – we consider a strong form of interpolation, uniform interpolation, and its relation with the closure under bisimulation quantifiers; – we compare bisimulation quantifiers logic with the better known extension of modal logic with extremal fixed points. In this article we show that the answers to these questions that are valid for the class of all frames do not generalize to arbitrary classes, but they do generalize if we restrict to classes of (finite) transitive or (finite) transitive and reflexive frames.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/1954286
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 6
social impact