Modal Operators for Coequations

Modal Operators for Coequations

We present the dual to Birkhoff’s variety theorem in terms of predicates over the carrier of a cofree coalgebra (i.e., in terms of “coequations”). We then discuss the dual to Birkhoff’s completeness theorem, showing how closure under deductive rules dualizes to yield two modal operators acting on coequations. We discuss the properties of these operators and show, given a familiar condition on t...

Bilattices and Modal Operators

A bilattice is a set equipped with two partial orders and a negation operation that inverts one of them while leaving the other unchanged; it has been suggested that the truth values used by inference systems should be chosen from such a structure instead of the two-point set {t, f}. Given such a choice, we redefine a modal operator to be a function on the bilattice selected, and show that this...

Deriving Inverse Operators for Modal Logic

Spatial constraint systems are algebraic structures from concurrent constraint programming to specify spatial and epistemic behavior in multi-agent systems. We shall use spatial constraint systems to give an abstract characterization of the notion of normality in modal logic and to derive right inverse/reverse operators for modal languages. In particular, we shall identify the weakest condition...

Parameter Structures for Parametrized Modal Operators

The parameters of the parametrized modal operators [p] and 〈p〉 usually represent agents (in the epistemic interpretation) or actions (in the dynamic logic interpretation) or the like. In this paper the application of the idea of parametrized modal operators is extended in two ways: First of all a modified neighbourhood semantics is defined which permits among others the interpretation of the pa...

Modal operators for meet-complemented lattices