Frontiers integrating nonmonotonic logical reasoning and. Nonmonotonic logics exhibit these abilities and allow to model nonmonotonic reasoning nmr. Is human reasoning about nonmonotonic conditionals. Knowledge representation and nonmonotonic reasoning. Artificial intelligence foundations of computational. The topic soon aroused the interest of the logic programming. In this paper, we concentrate on nonmonotonic rule sets 2,17. Nonmonotonic formalizations of reasoning deal with the problem of drawing conclusions when the description of either a situation or a problem is incomplete. Some wellknown approaches to non monotonic reasoning are. Default and nonmonotonic aspects of qualitative spatial. Non monotonic spatial reasoning with answer set programming modulo theories. Non monotonic reasoning is useful for representing defaults.
This suppositional character of commonsense reasoning conflicts with the monotonic character of logical derivations. Second, the rules of the nonmonotonic system p guiding a jsb allow for withdrawing conclusions in the light of new premises. Nonmonotonic logic stanford encyclopedia of philosophy. Nonmonotonic reasoning introduction motivation different forms of reasoning different formalizations default logic complexity approaches to non monotonic reasoning consistencybased. Analytic tableaux calculi for klm logics of nonmonotonic reasoning. In addition, in the case of poor quality data, monotonic logics such as rdfs cause an explosion of trivial and often useless derivations, as also. The original article of thomason pursues two goals. Research on argumentation and non monotonic reasoning began in full force in the early eighties. Nonmonotonic spatial reasoning with answer set programming. When monotonic solutions to the frame problem were found reiter 1991. Historical remarks on nonmonotonic reasoning, especially. Monotonic and non monotonic reasoning in artificial. These benchmarks formalized types of non monotonic reasoning and specified the answers generally accepted by researchers in the area.
This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. Benchmark problems for formal nonmonotonic reasoning. This appendix will follow up on thomasons second goal and show that linguists have taken up his invitation to use nonmonotonic logic as a formal tool. This volume contains the papers that will be presented at the first international workshop on argumentation and non monotonic reasoning argnmr 2007 on may 14, 2007 in tempe, arizona, us. Defeasible reasoning, a member of the non monotonic reasoning family, offers the extra capability of dealing with conflicting informa. Roos, preferential model semantics, argumentation frameworks and closure properties, nmr 2012 2012 8 pages. Pdf logic in nonmonotonic reasoning semantic scholar.
This is because the well known systems of mathemattal logic have the following monotonicity property. Logical systems provide only a more or less tight frame. Nerode classical logic is the study of safe formal reasoning. On the other hand, default logic exemplifies monotonic ity of the first kind and nonmonotonicity of the second kind. If there were no model in which the premises are true and the conclusion false, the reasoning would be valid according to a standard, deductive, monotonic logic, and would not be an. Indeed, most proposals for structured argumentation use a monotonic base logic e. Non monotonic logics result from associating a standard logic with a preference relation on models. Non monotonic inference is inference that is defeasible. Non monotonic logics exhibit these abilities and allow to model nonmonotonic reasoning nmr. Deductive reasoning is deducing new information from logically related known. The second argument against classical logic is the socalled monotonicity argument. A nonmonotonic logic is a formal logic whose conclusion relation is not monotonic. F or this e w consider a sequence of generalizations of the pioneering orks w of gabba y, kraus, lehmann, magidor and makinson.
In other words, nonmonotonic logics are devised to capture and represent. Thielscher 1999, non monotonic reasoning again seemed to be obsolete. Although several non monotonic formalisms have been proposed antoniou, 1997, pl is the only. If there were no model in which the premises are true and the conclusion false, the reasoning would be valid according to a standard, deductive, monotonic logic, and. This contrasts with the general idea that nmr can be used to make knowledge representation and reasoning simpler, not harder. Before we turn to probabilistic inference and parameter estimation, we introduce our new language for probabilistic nonmonotonic logic programming, called. Riley h and sridharan m 2019 integrating non monotonic logical reasoning and inductive learning with deep learning for explainable visual question answering. Is intractability of nonmonotonic reasoning a real drawback. Introduction to non monotonic reasoning cnu 27 marseille. The logic of definite clauses with negation as failure is non monotonic.
Non monotonic logics non monotonic reasoning has been studied in detail in ai and various non monotonic logics have been invented. Pdf argumentation and nonmonotonic reasoning paolo. By contrast, ilp realizes inductive machine learning while most techniques have been developed under the classical monotonic logic. Nonmonotonic reasoning and logic nonmonotonic reasoning changes the ways logic is used.
Nonmonotonic reasoning provides formal methods that enable intelligent systems to operate adequately when faced with incomplete or changing information. Artificial intelligence foundations of computational agents. A non monotonic logic is a formal logic whose conclusion relation is not monotonic. Nonmonotonic reasoning an overview sciencedirect topics. Nonmonotonic spatial reasoning with answer set programming modulo theories. Nonmonotonic reasoning in deductive argumentation deepai. Circumscription formalizes such conjectural reasoning.
The default nonmonotonic reasoning was formalised by a class of logical systems. Paraconsistent logic logic where it is not necessarily true that a a. A knowledge based approach to enable structural engineering design. Pdf nonmonotonic reasoning in interpretation semantic. This paper is an updated version of an invited banquet address, first international. Nonmonotonic logic an overview sciencedirect topics. This study reports a series of three experiments on reasoning with inference rules about nonmonotonic conditionals in the framework of coherence. Need for defaults and non monotonic reasoning classical approaches for dealing with defaults closed world reasoning circumscription default logic auto epistemic logic modal logic modern approaches for dealing with defaults prioritized rules argumentation theories example uses of defaults. Non monotonic reasoning is nowadays a hot topic in ai. With this background, some researchers attempt to combine techniques in the context of nonmonotonic inductive logic programming nmilp. In this paper an approach to the exhaustive interpretation of answers is developed. To begin with, there are many reasons to believe that non monotonic reasoning cannot be expressed in the form of a logical inference in some ingenious nonmonotonic logic.
Przemyslaw andrzej walega, carl schultz, mehul bhatt. Non monotonic reasoning constitutes an approach to reasoning with incomplete or changing information and is significantly more powerful than standard reasoning, which simply deals with universal statements. Jun, 1988 default reasoning, nonmonotonic logics, and the frame problem, proc. Western philosophers developed classical logic over a period of thirtythree centuries after its introduction in the form of syllogistic by aristotle 1 in the third century b. Before non monotonic logic hypothetical counterfactual reasoning what would be true in a world where we change the truth value of some predicates. In other words, non monotonic logics are devised to capture and represent defeasible inferences cf. In studying the classic nonmonotonic problems and developing this line of research, we were. Monotonic and nonmonotonic reasoning in artificial. Classical logics share a common property of being monotonic.
Let l be a first order language, let pred be the set of predicates of l. Non monotonic logics and reasoning biases catarina dutilh novaes illc and department of philosophy university of amsterdam. In this article we introduce a non monotonic reasoning engine, i. Pdf diagnostic expert system using nonmonotonic reasoning. These generalizatio ns w allo the use of monotonic nonclassical logics as the underlying logic up on whic h nonmonotonic reasoning y ma b e based. Further areas of application include reasoning about natural kinds, diagnostic reasoning, and natural language processing reiter 1987, mccarthy 1986. 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. It is general in that it can accommodate different preference criteria, thus generating different non monotonic logics. Humans have always done nonmonotonic reasoning, but rigorous monotonic reasoning in reaching given conclusions has been deservedly more respected and admired. Defeasible reasoning and non monotonic logic defeasible reasoning. Since firstorder predicate logic is itself monotonic, a variety of alternative logics have been put forward as candidates for implementing nonmonotonic reasoning.
On this surgery, the main features of a nonmonotonic formalism are determined by the interplay between its logical basis and the nonmonotonic overhead. A logic is non monotonic if some conclusions can be invalidated by adding more knowledge. The need for non monotonic reasoning we cannot get circumscriptive reasoningcapability by adding sentencesto an. Our motivation for this line of research is discussed extensively in 2,3,4. Non monotonic reasoning nonmonotonic reasoning deals with the problem of deriving plausible conclusions, but not infallible, from a knowledge base a set of formulas. The objective of the article is to present solutions for problems occurring in classical expert systems based on. The default case reasoning of many computer programs reiter 1980 and the use of thnot in microplanner sussman, et. Non monotone logics have been developed recently which describe commonsense reasoning which is neither a restriction nor an extension of classical logic. Non monotonic reasoning in deductive argumentation.
Nonmonotonic reasoning department of computer science at the. In this paper, we argue that utilizing default logic still is of use when reasoning about. The first attempts showed how argumentation results in a very natural way of conceptualizing commonsense reasoning, appropriately reflecting its. We present a conceptual description of nonmonotonic formalisms as essentially twolayered reasoning systems consisting of a monotonic logical system, coupled with a mechanism of a reasoned choice of default assumptions. The research on nonmonotonic reasoning includes several attempts to formalize reasoning that refuse to acknowledge one of the fundamental properties of classical logic. We present a conceptual description of nonmonotonic formalisms as essentially twolayered reasoning systems consisting of a monotonic logical system, coupled with a mechanism of a reasoned choice.
I propose that work on nonmonotonic reasoning can benefit from new notions of inference, logicality and reason. Much of our everyday reasoning is like this, and a non monotonic approach has applications to a number of technical problems in artificial intelligence. Circumscription a form of non monotonic reasoning john mccarthy abstract humans and intelligent computer programs must often jump to the conclusion that the objects they can determine to have certain properties or relations are the only objects that do. The case of exhaustive interpretation katrin schulz and robert van rooij abstract.
These include modal logics, default logics, support for abductive reasoning, modified inheritance schemes, and minimalist reasoning assumptions. I suspect that even euclid did nonmonotonic reasoning in arguing for the postulates. Roos, an argumentation system for reasoning with conflictminimal paraconsistent alc, non monotonic reasoning nmr 2014. We will argue using examples that humans use such \ nonmonotonic reasoning and that it is required for intelligent behavior. Several studies about computational complexity of nonmonotonic reasoning nmr showed that nonmonotonic inference is significantly harder than classical, monotonic inference. Since the conclusions are not certain, it must be possible to retract some of them if new information shows that they are wrong classical logic is inadequate since it is. Scalable nonmonotonic reasoning over rdf data using mapreduce.
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