Constructive Plausible Logic Is Relatively Consistent

Abstract

An implemented, efficient, propositional non-monotonic logic, called Constructive Plausible Logic, is defined and explained. Several important properties enjoyed by this logic are stated. The most important property, relative consistency, means that whenever the set of axioms is consistent so is the set of all formulas proved using defeasible information. Hence the non-monotonic deduction mechanism is trustworthy. This is the first Plausible Logic which has been proved to be relatively consistent. Constructive disjunction is characterised by the property that a disjunction can be proved if and only if at least one of its disjuncts can be proved. Constructive Plausible Logic uses constructive disjunction. Moreover the ambiguity propagating proof algorithm is simpler than the one in Billington and Rock [4].