Knowledge-driven versus data-driven logics
Journal of Logic, Language and Information 9 (1):65--89 (2000)
| Abstract | 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 modelling 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 non-linear 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. | |||||||||
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Richard DeWitt (2005). On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics. Journal of Philosophical Logic 34 (5-6):545 - 560.
Thomas Vetterlein (2008). A Way to Interpret Łukasiewicz Logic and Basic Logic. Studia Logica 90 (3):407 - 423.
Petr Hájek & Petr Cintula (2006). On Theories and Models in Fuzzy Predicate Logics. Journal of Symbolic Logic 71 (3):863 - 880.
Henri Prade (1996). New Trends and Open Problems in Fuzzy Logic and Approximate Reasoning. Theoria 11 (3):109-121.
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