Resolving Zadehs Paradox Axiomatic Possibility Theory as a Foundation for Reliable Artificial Intelligence

TL;DR

This paper advocates for possibility theory as a robust axiomatic foundation for handling uncertainty in AI, resolving Zadeh's paradox and improving reasoning with contradictory data.

Contribution

It develops a rigorous axiomatic framework for possibility theory, demonstrating its advantages over probabilistic and evidential paradigms in AI reasoning.

Findings

Possibility theory effectively resolves Zadeh's paradox.

It enables correct processing of contradictory information.

The approach aligns formal reasoning with natural intelligence logic.

Abstract

This work advances and substantiates the thesis that the resolution of this crisis lies in the domain of possibility theory, specifically in the axiomatic approach developed in Bychkovs article. Unlike numerous attempts to fix Dempster rule, this approach builds from scratch a logically consistent and mathematically rigorous foundation for working with uncertainty, using the dualistic apparatus of possibility and necessity measures. The aim of this work is to demonstrate that possibility theory is not merely an alternative, but provides a fundamental resolution to DST paradoxes. A comparative analysis of three paradigms will be conducted probabilistic, evidential, and possibilistic. Using a classic medical diagnostic dilemma as an example, it will be shown how possibility theory allows for correct processing of contradictory data, avoiding the logical traps of DST and bringing formal reasoning closer to the logic of natural intelligence.