Development of the logics required for modelling mathematical practice

To develop a formal approach to the study of mathematical practice, needed to make comparisons possible with foundational studies, we shall focus on the development of two separate features of the formalisms we believe are needed. One aspect is fairly general, and focuses on the need to model the processes whereby we share and communicate mathematical knowledge. This approach is continuous with recent research in dynamic epistemic and dynamic doxastic logic (including belief revision), and should allow us to model the information flow within as well as between different mathematical communities, see, e.g., Van Benthem (2007); Van Ditmarsch et al. (2007). A second aspect is more specific, as it relates to the specificity of what mathematicians really communicate. This means that we should be interested in “real” rather than in idealized proofs. To incorporate these features, we shall have to go beyond existing formal approaches.