Abstract

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 nonmonotonic 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 nonmonotonic systems, in particular to minimal reasoning in propositional calculus and predicate calculus, and to propositional Poole systems. keywords : nonmonotonic inference, compactness, model theory 1 Introduction Given a language L a logic can be described on an abstract level by a functor C : 2 L ! 2 L such that for every set X ` L, C(X) is understood to be the set of all the consequences of the set X of premises. If ...

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