An abstraction mapping over clausal form theories in first-order predicate calculus is presented that involves the renaming of predicate symbols. This renaming is not 1-1, in the sense that several predicate symbols Ri,.. . , Rn from the original theory are all replaced by a single symbol R in the abstract theory. In order to preserve consistency, however, the clauses that distinguish the Rj's ...

This paper summarizes the current state of the art in the topics of rst-order theory revision and theory restructuring. The various tasks involved in rst-order theory reenement (revision vs. restructuring) are deened and then discussed in turn. For theory revision, the issue of minimality is discussed in detail, and a general outline algorithm is given which identiies the major places of diiere...

We offer a view on how probability is related to logic. Specifically, we argue against the widely held belief that standard classical logics have no direct way of modelling the certainty of assumptions in theories and no direct way of stating the certainty of theorems proved from these (uncertain) assumptions. The argument rests on the observation that probability densities, being functions, ca...

I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must include axioms for the mathematics used in the scientific theories. Next, I contend that models are...

A theory is called κ-categorical, or categorical in power κ, if it has one model up to isomorphism of cardinality κ. Morley’s Categoricity Theorem states that if a theory of first order logic is categorical in some uncountable power κ, then it is categorical in every uncountable power. We provide an elementary exposition of this theorem, by showing that a theory is categorical in some uncountab...