Nonmonotonic reasoning: From finitary relations to infinitary inference operations
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, the monotonicity requirement is weakened and one considers more general operations, inference operations. These operations describe the nonmonotonic logics both humans and machines seem to use when inferring defeasible information from incomplete knowledge. Some interesting families of inference operations are singled out and discussed. This study of infinitary inference operations is inspired by the results obtained in the case of nonmonotonic inference relations.
scientific article; zbMATH DE number 590918