Search results
Results From The WOW.Com Content Network
A non-monotonic logic is a formal logic whose entailment relation is not monotonic.In other words, non-monotonic logics are devised to capture and represent defeasible inferences, i.e., a kind of inference in which reasoners draw tentative conclusions, enabling reasoners to retract their conclusion(s) based on further evidence. [1]
Monotonicity of entailment is a property of many logical systems such that if a sentence follows deductively from a given set of sentences then it also follows deductively from any superset of those sentences.
Deductive inference is monotonic: if a conclusion is reached on the basis of a certain set of premises, then that conclusion still holds if more premises are added. By contrast, everyday reasoning is mostly non-monotonic because it involves risk: we jump to conclusions from deductively insufficient premises.
Defeasible logic is a non-monotonic logic proposed by Donald Nute to formalize defeasible reasoning. In defeasible logic, there are three different types of propositions: strict rules specify that a fact is always a consequence of another; defeasible rules specify that a fact is typically a consequence of another; undercutting defeaters
The accounts discussed above all yield monotonic consequence relations, i.e. ones such that if is a consequence of , then is a consequence of any superset of . It is also possible to specify non-monotonic consequence relations to capture the idea that, e.g., 'Tweety can fly' is a logical consequence of
About this time, researchers in artificial intelligence became interested in non-monotonic reasoning and its semantics. With philosophers such as Pollock and Donald Nute (e.g., defeasible logic), dozens of computer scientists and logicians produced complex systems of defeasible reasoning between 1980 and 2000. No single system of defeasible ...
The following result is a generalisation of the monotone convergence of non negative sums theorem above to the measure theoretic setting. It is a cornerstone of measure and integration theory with many applications and has Fatou's lemma and the dominated convergence theorem as direct consequence.
Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions.. Default logic can express facts like “by default, something is true”; by contrast, standard logic can only express that something is true or that something is false.