Realist Consequence, Epistemic Inference, Computational Correctness

Standard views on logical consequence stem historically from the propositions as truth-bearers tradition on the one hand, and from the assertoric standpoint on truth for propositions by proof-objects, on the other. A further step in the evolution of the notion of logical validity is represented by the formulation of correctness on computational processes, as suggested by the proofs-as-programs interpretation. We analyse this fairly recent computational interpretation of logic in view of the new principles it offers to characterize the notion of validity: execution conditions; resources accessibility; local validity; error-handling. In this new and extended sense, logical validity significantly improves the simple assertoric interpretation of correctness of non-realistic philosophies of logic. We set explicitly the connection to the notion of eventual consistency that holds for computational systems in a distributed setting.