Possible World Partition Sequences: A Unifying Framework for Uncertain Reasoning

TL;DR

This paper introduces a unifying framework called possible world partition sequences that integrates various uncertain reasoning formalisms, facilitating combined analysis and understanding of their behavior.

Contribution

It proposes a common semantic framework for diverse uncertainty formalisms, enabling their integration and comparison within a unified structure.

Findings

Incorporates default logic, autoepistemic logic, probabilistic conditioning, and possibility theory into the framework.

Provides a semantics for combining different uncertain reasoning formalisms.

Establishes a basis for building integrated systems handling multiple uncertainty formalisms.

Abstract

When we work with information from multiple sources, the formalism each employs to handle uncertainty may not be uniform. In order to be able to combine these knowledge bases of different formats, we need to first establish a common basis for characterizing and evaluating the different formalisms, and provide a semantics for the combined mechanism. A common framework can provide an infrastructure for building an integrated system, and is essential if we are to understand its behavior. We present a unifying framework based on an ordered partition of possible worlds called partition sequences, which corresponds to our intuitive notion of biasing towards certain possible scenarios when we are uncertain of the actual situation. We show that some of the existing formalisms, namely, default logic, autoepistemic logic, probabilistic conditioning and thresholding (generalized conditioning), and possibility theory can be incorporated into this general framework.