A Semantic Approach to Non-Monotonic Entailments
Any inferential system in which the addition of new premises can lead to the retraction of previous conclusions is a non-monotonic logic. Classical conditional probability provides the oldest and most widely respected example of non-monotonic inference. This paper presents a semantic theory for a unified approach to qualitative and quantitative non-monotonic logic. The qualitative logic is unlike most other nonmonotonic logics developed for AI systems. It is closely related to classical (i.e., Bayesian) probability theory. The semantic theory for qualitative non-monotonic entailments extends in a straightforward way to a semantic theory for quantitative partial entailment relations, and these relations turn out to be the classical probability functions.
Keywords: Inferential Systems, Non-Monotonic Logic, Probability Theory
PDF Link: /papers/86/p251-hawthorne.pdf
AUTHOR = "James Hawthorne
TITLE = "A Semantic Approach to Non-Monotonic Entailments",
BOOKTITLE = "Uncertainty in Artificial Intelligence 2 Annual Conference on Uncertainty in Artificial Intelligence (UAI-86)",
PUBLISHER = "Elsevier Science",
ADDRESS = "Amsterdam, NL",
YEAR = "1986",
PAGES = "251--262"