Nonmonotonic reasoning | SpringerLinkFull text of the second edition of Artificial Intelligence: foundations of computational agents, Cambridge University Press, is now available. The definite clause logic is monotonic in the sense that anything that could be concluded before a clause is added can still be concluded after it is added; adding knowledge does not reduce the set of propositions that can be derived. A logic is non-monotonic if some conclusions can be invalidated by adding more knowledge. The logic of definite clauses with negation as failure is non-monotonic. Non-monotonic reasoning is useful for representing defaults. A default is a rule that can be used unless it overridden by an exception. For example, to say that b is normally true if c is true, a knowledge base designer can write a rule of the form.
Defaults with Priorities. Ford pointed out that the order of strict and defeasible links in arguments matters. For normal default theories that only consist of normal defaultsi. Besnard, P.Considerations on default logic: an alternative approach. Artificial Intelligence"the truth of a proposition may change when new information axioms are added and a logic may be build to allows the statement to be retracted. The following Euler diagram illustrates the conditional arhificial in a possible probability distribution for the given statements.
Nonmonktonic says, T. Take the following example that is frequently discussed in the literature. R Examples Predicate logic and the inferences we perform on it. Google Scholar Prymusinski, "the truth of a proposition may change when new information axioms are added and a logic may be build to allows the statement to be retracted.
Lukaszewicz, W. But its salient feature is adescription of exciting recent results on Inference Relations, 92 1 : 1. Clearly, most forms of defeasible reasoning are externally dynamic and hence most logics for defeasible reasoning violate Monotony: they have non-monotonic consequence relations for which consequences may not persist when new information is obtained. Artificial MonoronicBeliefRevision and their relations.
Google Scholar Przymusinski, A. References : 72 02 3. Therefore we often revise our conclusions, when new information becomes available. Gelder, T.
Monotonic and nonmonotonic reasoning
A non-monotonic logic is a formal logic whose consequence relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences cf. Intuitively, monotonicity indicates that learning a new piece of knowledge cannot reduce the set of what is known. A monotonic logic cannot handle various reasoning tasks such as reasoning by default consequences may be derived only because of lack of evidence of the contrary , abductive reasoning consequences are only deduced as most likely explanations , some important approaches to reasoning about knowledge the ignorance of a consequence must be retracted when the consequence becomes known , and similarly, belief revision new knowledge may contradict old beliefs. Abductive reasoning is the process of deriving the most likely explanations of the known facts. An abductive logic should not be monotonic because the most likely explanations are not necessarily correct. For example, the most likely explanation for seeing wet grass is that it rained; however, this explanation has to be retracted when learning that the real cause of the grass being wet was a sprinkler.
DEON Artifical Intelligence48 2 : - The CCR application of one rule may thus block the application of another. Cognition31 1 : 61- Belief revision : because new knowledge may contradict old beliefs.
From Artificial Intelligence Series. Nonmonotonic reasoning provides formal methods that enable intelligent systems to operate adequately when faced with incomplete or changing information. In particular, it provides rigorous mechanisms for taking back conclusions that, in the presence of new information, turn out to be wrong and for deriving new, alternative conclusions instead. Nonmonotonic reasoning methods provide rigor similar to that of classical reasoning; they form a base for validation and verification and therefore increase confidence in intelligent systems that work with incomplete and changing information. Following a brief introduction to the concepts of predicate logic that are needed in the subsequent chapters, this book presents an in depth treatment of default logic. Other subjects covered include the major approaches of autoepistemic logic and circumscription, belief revision and its relationship to nonmonotonic inference, and briefly, the stable and well-founded semantics of logic programs. This book offers a very elegant introduction to nonmonotonic reasoning.
In: PODS, pp. SyntheseA. Prioritizing Default Logic.
A default is applied in case its precondition is implied by the current beliefs and its conclusion is consistent with the given beliefs, F, its own justificiation. How to cite this entry. Lin. This allows us to infer flies.