Towards Formalizing Non-Monotonic Reasoning in Physics: Logical Approach Based on Physical Induction and Its Relation to Kolmogorov Complexity

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

3-2012

Comments

Technical Report: UTEP-CS-11-60a

To appear in: Esra Erdem, Joohyung Lee, Yuliya Lierler, and David Pearce (eds.), Vladimir Lifschitz FestSchrift, Springer Lecture Notes on Computer Science.

Abstract

To formalize some types of non-monotonic reasoning in physics, researchers have proposed an approach based on Kolmogorov complexity. Inspired by Vladimir Lifschitz's belief that many features of reasoning can be described on a purely logical level, we show that an equivalent formalization can be described in purely logical terms: namely, in terms of physical induction.

One of the consequences of this formalization is that the set of not-abnormal states is (pre-)compact. We can therefore use Lifschitz's result that when there is only one state that satisfies a given equation (or system of equations), then we can algorithmically find this state. In this paper, we show that this result can be extended to the case of approximate uniqueness.