Contributions to the Theory of Nonmonotonic Inference Systems

In the present paper an approach to nonmonotonic reasoning is discussed which is inspired by the paradigm of abstract model theory. The aim is to analyse non-monotonic reasoning within the framework of inference operations based on model operators. This is done by using the concept of a deductive frame and its semantical counterpart, a semantical frame. These are considered as a basis for nonmonotonic model theory. Then several representation theorems are proved and compactness properties are analysed in detail. These concepts are applied to classical nonmono-tonic systems, in particular to minimal reasoning in propositional calculus and predicate calculus, and to propositional Poole systems.