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Knowledge-driven versus data-driven logics. (English) Zbl 0942.03023
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.

03B42 Logics of knowledge and belief (including belief change)
68T30 Knowledge representation
03B45 Modal logic (including the logic of norms)
03B52 Fuzzy logic; logic of vagueness
68T27 Logic in artificial intelligence
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