A two-level approach to logics of data and information

Presented at the First Workshop on the Philosophy of Information and Logic (Oxford, UK)

Abstract. Cognitive states like knowledge and belief, as well as cognitive commodities like evidence, justification, or proof play a central role in our epistemological theories. Being attentive to the way such states and commodities interact in these theories is particularly important. This is even more so if, besides knowledge, we also want to reason about how data and information improve our overall epistemic position. This is mainly due to the fact that being informed is itself ambiguous between the predominantly syntactic relation of holding a piece of data that qualifies as genuine information and the largely semantic relation of being in a state which satisfies certain conditions. In this paper we argue that getting the relation between states and commodities “right” is a first prerequisite for the choice of bridge axioms in a combined logic of data and information with theoretical virtues similar to the existing combined logics of knowledge and belief. To start with, we formalise the intuitively valid principles that “being informed involves holding data,” and “being informed involves holding a piece of information.” Subsequently, we check how these necessary conditions for being informed constrain the set of plausible bridge axioms, and then outline a generic combined system. To conclude, a number of broader methodological considerations are introduced and related to the specificity of introducing informational considerations into the practice of formal modelling.