Resolving Zadehs Paradox Axiomatic Possibility Theory as a Foundation for Reliable Artificial Intelligence
This work addresses a foundational problem in AI for researchers and practitioners dealing with uncertainty, offering a mathematically rigorous alternative to existing paradigms.
The paper tackles the foundational crisis in uncertainty reasoning by proposing axiomatic possibility theory as a solution to Zadeh's paradox, demonstrating through a medical diagnostic example that it correctly processes contradictory data and avoids logical traps of Dempster-Shafer theory.
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.