This paper continues the power ordering approach to verisimilitude. We define a parameterized verisimilar ordering of theories in the finite propositional case, both semantically and syntactically. The syntactic definition leads to an algorithm for computing verisimilitude. Since the power ordering approach to verisimilitude can be translated into a standard notion of belief revision, the algorithm thereby also allows the computation of membership of a belief-revised theory.

A metric approach to Popper's verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of the difficulties (...) arising from the known definitions of verisimilitude. (shrink)