Realist Consequence, Epistemic Inference, Computational Correctness

Standard views on logical consequence stem historically fromthe propositions as truth-bearers tradition on the one hand, and fromthe assertoric standpoint on truth for propositions by proof-objects. Afurther step in the evolution of the notion of logical validity is repre-sented by formulation of correctness on computational processes, as sug-gested by the proofs-as-programs interpretation. We analyse this fairlyrecent computational interpretation of logic in view of the new princi-ples it offers to characterize the notion of validity: execution conditions;resources accessibility; local validity; error-handling. In this new andextended sense, logical validity significantly improves the simple asser-toric interpretation of correctness of non-realistic philosophies of logic.We set explicitly the connection to the notion of eventual consistencythat holds for computational systems in a distributed setting.