Resource bisimilarity and graded bisimilarity coincide

Behavioural equivalences for coalgebras with unobservable moves

“…Corollary 4.10. For F N∪{∞} (A τ × Id)-coalgebras, weak behavioural equivalence coincides with weak resource bisimulation [1] for systems weighted over the (complete) arithmetic semiring of natural numbers (N ∪ {∞}, +, ·).…”

Neighbourhood Semantics for Graded Modal Logic

“…De Rijke [7] introduced graded tuple bisimulation for graded modal logic. Using this he proved the finite model property (which was first proved in Cerrato [3] via filtration) and that a first-order formula is invariant under graded bisimulation iff it is equivalent to a graded modal formula. Aceto, Ingolfsdottir and Sack [1] showed that resource bisimulation and graded bisimulation coincide over image-finite Kripke frames.…”

“…Van der Hoek [15] investigated the expressibility, decidability and definability of graded modal logic and also correspondence theory. Cerrato [3] proved the decidability by filtration for graded modal logic.…”

Dynamic Graded Epistemic Logic

“…It is therefore rather involved. Aceto, Ingólfsdóttir, & Sack (2010) showed a perfect correspondence between De Rijke's notion and a different notion called resource bisimulation, proposed by Corradini, De Nicola, & Labella (1999), that is rather elegant. Corradini et al,'s notion is what we will now define as graded bisimulation, although with a minor difference: in Aceto et al, (2010) and Corradini et al, (1999) agreement of propositional variables is not part of the definition.…”

“…The direction that bisimilarity implies modal equivalence also holds for models that are not image finite. We refer to Aceto et al, (2010) for proof details. THEOREM 2.10 ( Aceto et al, 2010, Prop.…”