Formal Mechanisms for Reduction in Science

Abstract

The paper presents a formal way of looking at the reduction in science by exhibiting
among others the cases of Newtonian and Hamiltonian formulations of Classical
mechanics. The cases are discussed in a framework con¬sidering a scientific theory as
consisting of the juxtaposition of two languages, the object language used to express
empirical statement about systems and the property language used to express
statements about the properties of systems. Both of these languages are ideally based
on the syntax of first order predicate logic and endowed with a semantic structure
expressed by ontologies. In this framework the notion of reduction can be referred to
the axiom system constituting the core of the ontologies. Reduction corresponds to
the extension of the axiom system and thus of the ontology. The reason is that the
ontology then contains more contextual knowledge and less data is needed to describe
a system.