Nonmonotonic inference operations

TL;DR

This paper explores nonmonotonic inference operations, extending traditional monotonic logic to model how humans and machines draw defeasible conclusions from incomplete information.

Contribution

It introduces a broader class of inference operations, generalizing monotonic consequence operations and analyzing their properties and families.

Findings

Identifies interesting families of nonmonotonic inference operations

Extends the study of infinitary consequence operations beyond monotonic cases

Provides a self-contained framework inspired by prior finitary nonmonotonic logic results

Abstract

A. Tarski 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 infering defeasible information from incomplete knowledge. We single out a number of interesting families of inference operations. This study of infinitary inference operations is inspired by the results of Kraus, Lehmann and Magidor on finitary nonmonotonic operations, but this paper is self-contained.