The basic goal of context-aware systems is to make software aware of the environment and to adapt to their changing context. For that purpose, the core problem is to have a powerful context model. While significative formalizations have been proposed, context models are either expressed through logical formalisms or with ontology-based approaches. The major problem with all that approaches is that they suffer from the chronic insufficiency of first-order logic to cope with dynamic change and especially, to solve the frame problem. Therefore, building context-aware software is a complex task due to a lack of appropriate formal models in dynamic environments. In this paper, we propose a model which combines the strengths of both approaches while trying not to carry their specific weaknesses into the resulting formal framework. For this purpose, the formal model relies both on a knowledge representation with ontologies and on a logical reasoning with Dependent Record Types (DRT) based on Intuitionistic Type Theory and the Curry-Howard isomorphism. This logic modelling aims to be applied to any kind of process-based applications.