Nonmonotonic reasoning

Abstract

The research on nonmonotonic reasoning includes several attempts to formalize reasoning that refuse to acknowledge one of the fundamental properties of classical logic: monotonicity. Nonmonotonic formalizations of reasoning deal with the problem of drawing conclusions when the description of either a situation or a problem is incomplete. Such incompleteness can be justified not only by epistemological reasons, since the knowledge about a situation can often be partial, but also by engineering reasons, as the need arises to avoid the explicit recording of a huge amount of information. In this paper we describe the main formalizations of nonmonotonic reasoning with the aim to present a coherent overview of the research in this field, and therefore we pay special attention to the problem of establishing relationships among different proposals.

Ecological non-monotonicity and its effects on complexity and stability of populations, communities and ecosystems

“…In human society, non-monotonicity can refer to boom and bust market crises in economics or to the rise and fall of dynasties. The non-monotonicity in logic or reasoning has attracted very much attention in social and computer sciences (Bidoit and Hull, 1989;Donini et al, 1990).…”

Inference enterprise models: An approach to organizational performance improvement

“…Methods for inductive reasoning have been developed in the areas of logic and expert systems (Groarke, ), inferential statistics (both frequentist and Bayesian philosophies of probability) (Box & Tiao, ; DeGroot, ; Fisher, ; Jaynes, ; Neyman, ; Reid & Cox, ), fuzzy inference (Cherkassky, ; Mamdani & Assilian, ; Sugeno, ), and nonmonotonic logics (in contrast to traditional logic and expert systems) (Donini, Lenzerini, Nardi, Pirri, & Schaerf, ; Ginsberg, ). Given our focus on the prediction problem within inductive inference, we address only methods that produce probabilities, including: a subset of frequentist‐oriented statistical inference methods (e.g., logistic regression), Bayesian inference that produces probabilities (e.g., Bayes rule), and a range of machine‐learning methods that are undeclared in the frequentist‐Bayesian debates but are routinely trained to produce probabilities as outputs (e.g., random forests and neural networks).…”