Nonmonotonic inference operations

Nonmonotonic inference operations

A. Tarski [21] proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and consider more general operations, inference operations. These operations describe the nonmonotonic logics both humans and machines seem to be using when inf...

Deductive Nonmonotonic Inference Operations: Antitonic Representations

We provide a characterization of those nonmonotonic inference operations C for which C(X) may be described as the set of all logical consequences of X together with some set of additional assumptions S(X) that depends anti-monotonically on X (i.e., X ⊆ Y implies S(Y ) ⊆ S(X)). The operations represented are exactly characterized in terms of properties most of which have been studied in [3]. Sim...

A Semantic Approach to Nonmonotonic Reasoning: Inference Operations and Choice

This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premisses. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set o...

Nonmonotonic Modes of Inference

In this paper we investigate nonmonotonic ‘modes of inference’. Our approach uses modal (conditional) logic to establish a uniform framework in which to study nonmonotonic consequence. We consider a particular mode of inference which employs a majority-based account of default reasoning—one which differs from the more familiar preferential accounts—and show how modal logic supplies a framework ...

Credulous Nonmonotonic Inference