Antitonic Representations for Nonmonotonic Inference Operations

Title: Antitonic Representations for Nonmonotonic Inference Operations

Abstract: This research article explores the characterization of nonmonotonic inference operations that can be represented as a set of assumptions that depend antitonically on the given set of facts. The study provides a satisfactory notion of pseudo-compactness and an alternative, more elegant, and more general proof of the existence of an infinitary deductive extension for any finitary deductive operation.

Research Question: How can we characterize nonmonotonic inference operations that have an antitonic representation?

Methodology: The study uses logical reasoning and the language of set theory to characterize nonmonotonic inference operations. It builds on previous research in the field and provides a more general and elegant proof of the existence of an infinitary deductive extension for any finitary deductive operation.

Results: The research provides a characterization of those nonmonotonic inference operations C for which C(X) can be described as the set of all logical consequences of X together with some set of additional assumptions S(X) that depends antitonically on X. The study also discusses extending finitary operations to infinitary operations and provides an alternative proof of the existence of an infinitary deductive extension.

Implications: The research provides a more general and satisfactory notion of pseudo-compactness for nonmonotonic operations. It also offers an alternative proof of the existence of an infinitary deductive extension, which is of interest to the field of artificial intelligence and logic programming. Additionally, the study shows that many nonmonotonic systems can be presented in an antitonic way, even if they were not originally designed that way.

Link to Article: https://arxiv.org/abs/0203003v1 Authors: arXiv ID: 0203003v1