Logic and Language

Alessandro Giordani (Catholic University of Milan): An Evidence-based logic of Acceptance and Rejection

Speaker: Alessandro Giordani (Catholic University of Milan)
Title: An Evidence-based logic of Acceptance and Rejection
Time: 15:30 - 17:30
Location: ILLC seminar room, F1.15


In this paper, I am going to present logics of acceptance and rejection based on the idea that these epistemic states are frame-dependent, where a frame for an epistemic state is assumed to consist of a triple (Σ,I,S), where (i) Σ is a set of subject matters, (ii) I is a set of sources of justi cation, and (iii) S is a set of reference epistemic standards. The central intuition underlying such an approach is that states of acceptance and rejection are connected to epistemic justi cations, where a justi cation is intended as a subjective ground for assuming a proposition p as a solution to a speci c problem relative to subject matter σ ∈ Σ, a solution that derives from a source i ∈ I and satis es a standard s ∈ S. In modeling this kind of states, I will extend the usual systems of epistemic logic in two directions: (i) by introducing a partition of the epistemic space into cells, corresponding to di erent conceptual frames; (ii) by making explicit the reference to justi ers, corresponding to elements of evidence for asserting propositions. The rst step allows us to introduce a local approach to the epistemic space, thus generalizing the standard global approach. The second step allows us to generalize the constructive approach according to which assertibility has to be intended as having a procedure to obtain a proof of a proposition. As we will see, the resulting system is extremely powerful from an analytical point of view. In particular, within the system, it is possible both to provide an intuitive interpretation of the phenomena of para-completeness and para-consistency connected to rejection and to assume an intermediate standpoint on the problem as to whether rejection is to be intended as having a proof of the negation of a proposition or rather as not having a proof of the proposition.