Natasha Kurtonina
Bisimulations without Prejudices
In modal logic and process theory, bisimulation is the basic notion of semantic
equivalence (van Benthem & Bergstra 1993), van Benthem, van Eijck & Stebletsova
1994, Andreka, van Benthem & Nemeti 1995). This is a `process equivalence'
stating when two models represent the `same structure'. The present paper shows why
and how we should get rid of two prejudices about bisimulation. The first
prejudice: bisimulation is always a symmetric relation. The second prejudice states
that bisimulation always has to follow the pattern of evaluation function: for
example, if a valuation of formulas is carried out on points and not on tuples,
then bisimulation should link points with points and not tuples with tuples.
Reflecting on these prejudices helps us solve some open problems in model theoretic
analysis of *Since* and *Until* operators and Categorial Grammar
Connectives.
Paul Dekker, November 2, 1995