Book Reviews: David Makinson, "Bridges from Classical to Nonmonotonic Logic", King’s College Publications, London, 2005
Tomasz Jarmużek · Logic and Logical Philosophy · 2007
Nonmonotonic logic is a part of logic which covers a family of formal frameworks devised to capture and describe so called defeasible inferences.By defeasible inferences we usually mean a kind of inference of everyday life in which reasoners draw conclusions and reserve the right to change them in the light of further information.They are called nonmonotonic, because they do not satisfy the Horn condition of monotony.This failure reflects a mechanism which is present in natural reasonings: for some set of premisses A and a proposition x we may think that x is the best conclusion on the base of A we could draw, but if our set of premisses is extended to B, a proper superset of A, we may find unreasonable to hold x still as a good conclusion, since for example B contains a negation of x.This property is in contrast to classical logic, whose inferences, being valid, can never be "undone" by new information.There are lots of frameworks for nonmonotonic reasonings.At the first glance they seem to be unordered and there is no consensus which are more basic and in some sense better to be applied.The book of David Makinson in an exhaustive way provides a general view on this multitude.But its main feature is an order which every reader obtains.On the one hand we see how nonmonotonic inferences arise from classical logic, on the other they are bounded by logical systems called by the author bridges.They are bridges from classical consequence to nonmonotonic consequences.