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Modal Equivalence and Bisimilarity in Many-valued Modal Logics with Many-valued Accessibility Relations

Diaconescu Denisa

Fundamenta Informaticae

2020

Vol. 173, nr 2-3

177--189

In this paper we investigate the Hennessy-Milner property for models of many-valued modal logics defined based on complete MTL-chains having many-valued accessibility relations. Our main result gives a necessary and sufficient algebraic condition for the class of image-finite models for such modal logics to admit the Hennessy-Milner property.

Counterpart Semantics for a Second-Order μ-Calculus

Gadducci F., Lafuente A. L., Vandin A.

Fundamenta Informaticae

2012

Vol. 118, nr 1-2

177-205

Quantified &mi;-calculi combine the fix-point and modal operators of temporal logics with (existential and universal) quantifiers, and they allow for reasoning about the possible behaviour of individual components within a software system. In this paper we introduce a novel approach to the semantics of such calculi: we consider a sort of labeled transition systems called counterpart models as semantic domain, where states are algebras and transitions are defined by counterpart relations (a family of partial homomorphisms) between states. Then, formulae are interpreted over sets of state assignments (families of partial substitutions, associating formula variables to state components). Our proposal allows us to model and reason about the creation and deletion of components, as well as the merging of components. Moreover, it avoids the limitations of existing approaches, usually enforcing restrictions of the transition 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. The paper is rounded up with some considerations about expressiveness and decidability aspects.

Separability, Expressiveness, and Decidability in the Ambient Logic

Hirschkoff D.

Schedae Informaticae

2003

Vol. 12

77-84

The Ambient Logic (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. We study some basic questions concerning the descriptive and discriminating power of AL, focusing on the equivalence on processes induced by the logic (= L ). We consider MA, and two Turing complete subsets of it, MA IF and MA synIF , respectively defined by imposing a semantic and a syntactic constraint on process prefixes. The main contributions include: coinductive and inductive operational characterisations of = L on MA synIF; an axiomatisation of = L on MA IF ; the construction of characteristic formulas for the processes in with respect to = L; the decidability of = L on MA IF and on MAsynIF , and its undecidability on MA.