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Zbl 0942.03023
Dubois, Didier; Hájek, Petr; Prade, Henri
Knowledge-driven versus data-driven logics. (English)
[J] J. Logic Lang. Inf. 9, No.1, 65-89 (2000). ISSN 0925-8531; ISSN 1572-9583/e

Summary: The starting point of this work is the gap between two distinct traditions in information engineering: knowledge representation and data-driven modelling. The first tradition emphasizes logic as a tool for representing beliefs held by an agent. The second tradition claims that the main source of knowledge is made of observed data, and generally does not use logic as a modeling tool. However, the emergence of fuzzy logic has blurred the boundaries between these two traditions by putting forward fuzzy rules as a Janus-faced tool that may represent knowledge, as well as approximate nonlinear functions representing data. This paper lays bare logical foundations of data-driven reasoning whereby a set of formulas is understood as a set of observed facts rather than a set of beliefs. Several representation frameworks are considered from this point of view: classical logic, possibility theory, belief functions, epistemic logic, fuzzy rule-based systems. Mamdani's fuzzy rules are recovered as belonging to the data-driven view. In possibility theory a third set-function, different from possibility and necessity plays a key role in the data-driven view, and corresponds to a particular modality in epistemic logic. A bi-modal logic system is presented which handles both beliefs and observations, and for which a completeness theorem is given. Lastly, our results may shed new light in deontic logic and allow for a distinction between explicit and implicit permission that standard deontic modal logics do not often emphasize.

MSC 2000:: *03B42 Logic of knowledge and belief
68T30 Knowledge representation
03B45 Modal logic, etc.
03B52 Fuzzy logic
68T27 AI logics

Keywords: possibility theory; knowledge representation; data-driven modelling; fuzzy logic; data-driven reasoning; epistemic logic; deontic logic

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