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Etude de la connaissance dans le cadre d'observations partielles : La logique de l'observation

Olivier Brunet 1, 2
1 EXMO - Computer mediated exchange of structured knowledge
LIG - Laboratoire d'Informatique de Grenoble, Inria Grenoble - Rhône-Alpes
Abstract : We focus on the study of knowledge obtained by performing partial observations of a system. The result of those observations can be structured by comparing their informationalcontent, and this is how we define what we call representations. It is also possible to study the possible relationships existing between different observations methods, which leads to the existence of functions between representations. With this formalism, we make a logical study of the way information behaves in such a context. The first point which arises from this is that one has to use intuitionistic logic, since propositions are about facts and not beliefs, and the addition of information does not change their veracity. This logic is extended by adding “modal” operators, which correspond to different ways of observing a system and express the fact that a piece of information is accessible or not from a given point of view. Depending on the constraints which are applied to our structures, one gets several behaviors for those operators and as many logics, all similar to the modal logic IS4. The basic postulate, that is a system is studied by observing it, is extremely general. However, our study shows that this leads to a rather weak logic, since neither the excluded middle principle nor the modal axiom 5 can be verified, even if extra hypotheses are considered. This means that the only important elements are the results of observations, and any reasoning is done constructively from them. As a consequence, the non-observation of a fact can not be used as a proof of its negation. In conclusion, the only elements which have to be taken into account when observing and studying nature are the observations which can be done of it, and any knowledge is obtained deductively from it.
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Olivier Brunet. Etude de la connaissance dans le cadre d'observations partielles : La logique de l'observation. Logique en informatique [cs.LO]. Université Joseph Fourier, Grenoble I, 2002. Français. ⟨tel-01239149⟩

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