Toward Formalizing Non-Monotonic Reasoning In Physics: The Use of Kolmogorov Complexity

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

7-2008

Comments

UTEP-CS-04-02c.

Short version published in: Leonid Sheremetov and Matias Alvarado (eds.), Proceedings of the Workshops on Intelligent Computing WIC'04 associated with the Mexican International Conference on Artificial Intelligence MICAI'04, Mexico City, Mexico, April 26-27, 2004, pp. 187-194; a detailed version to appear in Revista Iberoamericana de Inteligencia Artificial.

Abstract

When a physicist writes down equations, or formulates a theory in any other terms, he usually means not only that these equations are true for the real world, but also that the model corresponding to the real world is "typical" among all the solutions of these equations. This type of argument is used when physicists conclude that some property is true by showing that it is true for "almost all" cases. There are formalisms that partially capture this type of reasoning, e.g., techniques based on the Kolmogorov-Martin-Lof definition of a random sequence. The existing formalisms, however, have difficulty formalizing, e.g., the standard physicists' argument that a kettle on a cold stove cannot start boiling by itself, because the probability of this event is too small.

We present a new formalism that can formalize this type of reasoning. This formalism also explains "physical induction" (if some property is true in sufficiently many cases, then it is always true), and many other types of physical reasoning.