Towards a logic of epistemic theory of measurement

Abstract

We propose a logic to reason about data collected by a number of measurement systems. The semantic of this logic is grounded on the epistemic theory of measurement that gives a central role to measurement devices and calibration. In this perspective, the lack of evidences (in the available data) for the truth or falsehood of a proposition requires the introduction of a third truth-value (the undetermined). Moreover, the data collected by a given source are here represented by means of a possible world, which provide a contextual view on the objects in the domain. We approach (possibly) conflicting data coming from different sources in a social choice theoretic fashion: we investigate viable operators to aggregate data and we represent them in our logic by means of suitable (minimal) modal operators.