Gadducci, Fabio and Lluch-Lafuente, Alberto and Vandin, Andrea
Counterpart semantics for a second-order mu-calculus.
Graph Transformations (ICGT 2010).
Lecture Notes in Computer Science, 6372
Springer, pp. 282-297.
We propose a novel approach to the semantics of quantified μ-calculi, considering models where states are algebras; the evolution relation is given by a counterpart relation (a family of partial homomorphisms), allowing for the creation, deletion, and merging of components; and formulas are interpreted over sets of state assignments (families of substitutions, associating formula variables to state components). Our proposal avoids the limitations of existing approaches, usually enforcing restrictions of the evolution relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of.
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