Equilibria und weiteres Heiteres II

TL;DR

This paper explores the concept of independence as a ternary relation within non-monotonic logic, extending previous probabilistic studies and demonstrating the impossibility of finite characterization while providing methods to construct valid rules.

Contribution

It advances the understanding of independence in non-monotonic logic by analyzing product functions and showing finite characterization is impossible, offering ways to generate all valid rules.

Findings

Finite characterization of independence is impossible.

Methods to construct all valid rules for independence.

Extension of probabilistic independence concepts to non-monotonic logic.

Abstract

We investigate several technical and conceptual questions. Our main subject is the investigation of independence as a ternary relation in the context of non-monotonic logic. In the context of probability, this investigation was started by W.Spohn et al., and then followed by J.Pearl. We look at products of function sets, and thus continue our own investigation of independence in non-monotonic logic. We show that a finite characterization of this relation in our context is impossible, and indicate how to construct all valid rules.