Knowledge-Driven versus Data-Driven Logics

  • Authors:

  • Didier Dubois;Petr Hájek;Henri Prade

  • Affiliations:

  • Institut de Recherche en Informatique de Toulouse (IRIT), Université Paul Sabatier, CNRS, 118 route de Narbonne, 31062 Toulouse Cedex, France;Institute of Computer Science, Academy of Sciences, 18207 Prague, Czech Republic;Institut de Recherche en Informatique de Toulouse (IRIT), Université Paul Sabatier, CNRS, 118 route de Narbonne, 31062 Toulouse Cedex, France

  • Venue:
  • Journal of Logic, Language and Information
  • Year:
  • 2000

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Abstract

The starting point of this work is the gap between two distincttraditions in information engineering: knowledge representation anddata-driven modelling. The first tradition emphasizes logic as a toolfor representing beliefs held by an agent. The second tradition claimsthat the main source of knowledge is made of observed data, andgenerally does not use logic as a modelling tool. However, the emergenceof fuzzy logic has blurred the boundaries between these two traditionsby putting forward fuzzy rules as a Janus-faced tool that may representknowledge, as well as approximate non-linear functions representingdata. This paper lays bare logical foundations of data-driven reasoningwhereby a set of formulas is understood as a set of observed factsrather than a set of beliefs. Several representation frameworks areconsidered from this point of view: classical logic, possibility theory,belief functions, epistemic logic, fuzzy rule-based systems. Mamdani‘sfuzzy rules are recovered as belonging to the data-driven view. Inpossibility theory a third set-function, different from possibility andnecessity plays a key role in the data-driven view, and corresponds to aparticular modality in epistemic logic. A bi-modal logic system ispresented which handles both beliefs and observations, and for which acompleteness theorem is given. Lastly, our results may shed new light indeontic logic and allow for a distinction between explicit and implicitpermission that standard deontic modal logics do not often emphasize.