We endeavor to increase our knowledge, even if it complicates some. In this paper we introduce nonmonotonic reasoning and the attempts at formalizing it using nonmonotonic logics. In other words, adding information never invalidates any conclusions. Is human reasoning about nonmonotonic conditionals. This is called default or non monotonic reasoning and cannot be formalized directly in pure fol in general. Researchers in non monotonic logic are adamant about disassociating default reasoning from any statistical or empirical interpretation.
I then provide a summary which includes an assessment of the field and what must be done to further research in nonmonotonic reasoning and logic programming. Nonmonotonic reasoning is a pattern of reasoning that allows an agent to make and retract tentative conclusions from inconclusive evidence. On the links between argumentationbased reasoning and. On natural deduction system for nonmonotonic reasoning. However, the base logic does not need to be nonmonotonic.
Circumscription a form of nonmonotonic reasoning was published in artificial intelligence in 1980. Several paraphrases of this pattern are commonly accepted. What is monotonic and nonmonotonic reasoning in artificial. A non monotonic logic is a formal logic whose consequence relation is not monotonic. This means that whenever t is a set of sentences in such a logic and w is a sentence, then t w. Nonmonotonic reasoning is a subfield of artificial intelligence trying to find more realistic formal models of reasoning than classical logic. In this paper, we are presenting a scalable method for nonmonotonic. Scalable nonmonotonic reasoning over rdf data using. Rational nonmonotonic reasoning microsoft research. The field of nonmonotonic reasoning is now an essential part of the logical approach to artificial intelligence ai. Nonmonotonic reasoning nmr addresses a fundamental problem that classical logic methods in computer science encounter when modelling realworld. In other words, non monotonic logics are devised to capture and represent defeasible inferences cf. The present study2 pertains mainly to two approaches to nonmonotonic reasoning. We describe the relations between nmr and logic, and two main paradigms of nmr, preferential and explanatory one.
Nonmonotonic reasoning this is a practical problem for development of expert system due to revising a conclusion belief revision, other conclusions may also depend on it, and this may set off a chain reaction. Circumscription formalizes such conjectural reasoning. As we will see, the resulting nonmonotonicformalism will form a most natural and immediate generalization of classical logic that allows for nonmonotonic reasoning. The logic of definite clauses with negation as failure is non monotonic. However, to model commonsense reasoning, it is necessary to be able to jump to plausible conclusions from the given knowledge. Non monotonic reasoning is based on default reasoning or most probabilistic choice. To draw plausible conclusions it is necessary to make assumptions.
Nonmonotonic reasoning and the reversibility of belief change. A rule like ps are normally, usually qs is commonly referred to as a default, and the goal is to account for default reasoning not to be confused with default logic, which is a speci c approach. Judea pearl, in probabilistic reasoning in intelligent systems, 1988. The overview includes the major results developed including complexity results that are known about the various theories.
It admits various in terpretations, but the most popular is that it assigns meaning to the quanti. Logical foundations of commonsense gerhard brewka gmd, sankt augustin, germany the right of the university 0 cambridge to print and self. We think that the truth conditions of generic sentences can be captured by using ordinary quantification and a non monotonic conditional operator. A default is a rule that can be used unless it overridden by. This is called default or non monotonic reasoning and cannot be. We show that the nonmonotonicity of common sense reasoning is a function of the way we use logic, not a function of the logic we use. Pdf argumentation and nonmonotonic reasoning paolo. This paper gives a possibleworlds interpretation of the nonmonotonic reasoning problem based on standard decision theory and the emerging probability logic. Pdf argumentation, nonmonotonic reasoning and logic.
Classical logics share a common property of being monotonic. If the notion of nonmonotonic reasoning is understood in a broad sense, then probabilistic reasoning can also be subsumed. Monotonic and nonmonotonic reasoning in artificial. You j, wang x and yuan l 2001 nonmonotonic reasoning as prioritized argumentation, ieee transactions on knowledge and data engineering. The set of conclusions thus does not grow monotonically with the given information. Theorem proving techniques for these logics are also described. Pdf we present a conceptual description of nonmonotonic formalisms as essentially twolayered reasoning systems consisting of a monotonic logical. The default case reasoning of many computer programs reiter 1980 and the use of thnot in microplanner sussman, et. Analysis of algorithms for monotonic and nonmonotonic. A logic is nonmonotonic if some conclusions can be invalidated by adding more knowledge. Elsevier artificial intelligence 77 1995 3257 artificial intelligence on the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and nperson games phan minh dung division of computer science, asian institute of technology, gpo box 2754, bangkok 10501, thailand.
Introduction to non monotonic reasoning lsis pdf book. Monotonic reasoning can be defined in artificial intelligence. Classical logic is monotonic in the following sense. Nonmonotonic reasoning provides formal methods that enable intelligent systems to operate adequately when faced with incomplete or changing information. Abstract we present a conceptual description of nonmonotonic formalisms as essentially twolayered reasoning systems consisting of a monotonic log ical system, coupled with a mechanism of a reasoned choice of default assumptions. The book begins with a discussion of the various types of nonmonotonic reasoning, their applications and their logics. This short paper relates the conditional objectbased and possibility theorybased approaches for reasoning with conditional statements pervaded with exceptions, to other methods in nonmonotonic reasoning which have been independently proposed. 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.
Western philosophers developed classical logic over a period of thirtythree centuries after its introduction in. Difference between monotonic and nonmonotonic reasoning. The objective behind the area is the use of logic for knowledge representation and reasoning. Nonmonotonic reasoning is useful for representing defaults. A default is a rule that can be used unless it overridden by an exception. Practical non monotonic reasoning guido governatori knowledge techniques week 2012 nicta members nicta partners au from imagination to impact 2. The term nonmonotonic logic in short, nml covers a family of formal frameworks devised to capture and represent defeasible inference. Declarativism if we made nml inference procedure based. An overview of nonmonotonic reasoning and logic programming. In nonmonotonic theories, an inference may depend on lack of information. Default logic is one of the better understoo d formalisms in nonmonotonic reasoning.
In this paper, we outline the prototype of an automated inference tool, called quip, which provides a uniform implementation for several nonmonotonic reasoning formalisms. Chapter 4 nonmonotonic reasoning alexander bochman abstract nonmonotonic reasoning is a theory of the rational use of assumptions. We provide a conceptual description of the field of nonmonotonic reasoning as comprising two essentially different theories, preferential and explanatory nonmonotonic reasoning. Analysis of algorithms for monotonic and non monotonic reasoning john franco, john schlipf, and sean weaver. A non monotonic reasoning is a heuristic inference which can be invalidated or retracted further by adding more pieces. Logical foundations of commonsense cambridge tracts in theoretical computer science brewka, gerhard on. Nonmonotonic formalizations of reasoning deal with the problem of drawing conclusions when the description of either a situation or a problem is incomplete.
With this background, some researchers attempt to combine techniques in the context of nonmonotonic inductive logic programming nmilp. It is job of belief revision system truth maintenance system tms to establish the state which would have occurred due to. Pdf in this study, we will explore the respective roles of logic and non monotonic reasoning in argumentation. The first attempts showed how argumentation results in a very natural way of conceptualizing commonsense reasoning, appropriately reflecting its. Non monotonic reasoning this is a practical problem for development of expert system due to revising a conclusion belief revision, other conclusions may also depend on it, and this may set off a chain reaction. Virtually every example in ai that calls upon such reasoning fits the following pattern. Non monotonic logic nml motivation to define a strong yet flexible system to deal. Pdf two paradigms of nonmonotonic reasoning semantic. But, of course, such reasoning must be nonmonotonic, as additional things could change by unrelated reasons.
In other words, a nonmonotonic consequence relation that corresponds to universal principles of rational belief is impossible. In this work, nonmonotonic computational logic, answer set programming in particular, is applied to industrialscale automotive product configuration problems. Nonmonotonic reasoning, nonmonotonic logics and reasoning. A nonmonotonic logic is a formal logic whose consequence relation is not monotonic.
By contrast, ilp realizes inductive machine learning while most techniques have been developed under the classical monotonic logic. Adding knowledge in monotonic reasoning does not reduce the set of prepositions that arise. In nonmonotonic theories, an inference may depend on a lack of information. This study reports a series of three experiments on reasoning with inference rules about nonmonotonic conditionals in the framework of coherence. A decision method for nonmonotonic reasoning based on autoepistemic logic ilkka niemeli helsinki university of technology department of computer science digital systems laboratory otakaari 1, 02150 espoo, finland emaih ilkka. A decision method for nonmonotonic reasoning based on. Tu dresden, ws 201718 introduction to nonmonotonic reasoning slide 34 introducing defaults and default logics. Non monotonic spatial reasoning with answer set programming modulo theories. Ta non monotonic a system which violates the monotonic property.
Is intractability of nonmonotonic reasoning a real drawback. Nonmonotonic reasoning an overview sciencedirect topics. For nonmonotonic reasoning we will have to alter the classical notions of logical entailment and of proof. Nonmonotonic reasoning, conditional objects and possibility. Non monotonic logics deal with non monotonic reasoning, that involves adopting assumptions that may have to be abandoned in the light of new 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. It is the aim of the proposed monograph to present. Anything can end before a clause is added, even after it is added. Non monotonic reasoning has standard applications in areas such as diagnosis and logic programming.
On the relation between default and modal nonmonotonic reasoning. Nerode classical logic is the study of safe formal reasoning. This result suggests that the nonmonotonic community should study the issue of what kind of information is relevant to the application of a default rule elio and f. Despite the difference in motivation and technical construction there are strong similarities between these logics which are confirmed when they are finally shown to have a common basis.
Non monotonic reasoning on board a sony aibo 47 we propose to use non monotonic reasoning to accept the inconsistent information and resolve it to obtain the most plausible interpretation of the state of a robot and its environment. The present version has an addendum that was not in the published paper. Accordingly,the primary aim of our study will consist in laying down logical foundations for this kind of nonmonotonic reasoning. Intentional reasoning as nonmonotonic reasoning ceur. Second, the rules of the nonmonotonic system p guiding a jsb allow for withdrawing conclusions in the light of new premises. Research on argumentation and non monotonic reasoning began in full force in the early eighties.
Hanks and mcdermott 1987 describe anomalies in the application of default rules and circumscription to an intuitive case of non monotonic reasoning. The formalism of this paper is substantially superseded by that of applications of circumscription to formalizing common sense published in 1986. Nonmonotonic logic stanford encyclopedia of philosophy. In common sense reasoning one often draws conclusions that have to be withdrawn when further information is obtained. Non monotonic reasoning is useful for representing defaults. Hence a nonmonotonic inference may involve the theory as a whole. Nonmonotonic logic an overview sciencedirect topics. Introduction to non monotonic reasoning lsis pdf book online. Especially default and common sense reasoning is of interest. Can introduce abstract study of nonmonotonic consequence relations in same way as we study classical. We will argue using examples that humans use such onmonotonic reasoning and that it is required for intelligent behavior. The following chapters deal with formulations of nonmonotonic inheritance, and nonmonotonic reasoning based on nonmonotonic rules.
Commonsense reasoning 34 ent similarity between objects that might be governed by the same rules. Most studied formal logics have a monotonic consequence relation, meaning that. The application areas include diagnosis of hardware systems and even program debugging. In other words, nonmonotonic logics are devised to capture and represent defeasible inferences, i. Identifying this state is clearly a crucial initial step towards making a decision and then acting. Nonmonotonic reasoning is a particular kind of plausible reasoning. However, the current bdi models are monotonic and nonmonotonic logics are barely used to reason about time 11 or intentional states.
Alexander bochman computer science department, holon institute of technology hit israel. 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 knowledge base is of fixed size and can not be updated as in prologue file which is fixed during the clause checking and does not update that automatically. Non monotonic logic nml definition monotonic property for every theory t and t ta. Non monotonic reasoning in interpretation robert van rooij and katrin schulz 1 introduction the original article of thomason pursues two goals.
But monotonic systems are not good in real problem domains where the information is incomplete, situations change and new assumptions are generated while solving new problems. Default or non monotonic reasoning in the previous example we made an assumption in the absence of information to the contrary, and revised this assumption later when new knowledge became available. The systems central principle is that a tentative conclusion is a decision to make. The logic of definite clauses with negation as failure is nonmonotonic.
Nonmonotonic reasoning attempts to capture a form of commonsense reasoning nonmonotonic reasoning often deals with inferences based on defaults or what is usually the case belief change and nonmonotonic reasoning. Donini, marco schaerf 2 dipartimento di informatica e sistemistica, universitci di rome lo sapienza, via salaria 1, i00198 roma, italy received june 1995. We then consider the links between these axioms and the rationality postulates. Some key notions in nonmonotonic reasoning ceur workshop. Scalable nonmonotonic reasoning over rdf data using mapreduce ilias tachmazidis 1,2, grigoris antoniou 3, giorgos flouris, and spyros kotoulas4 1 institute of computer science, forth 2 department of computer science, university of crete 3 university of hudders. Laboratoire cnrs lsis 20102011a ai am indebted to laura giordano and alberto martelli for having provided me their course material. Reasoners draw conclusions defeasibly when they reserve the right to retract them in the light of further information. Pdf applications of nonmonotonic reasoning to automotive.
One is a default logic, suggested by raymond reiter in 25, the other is a modal approach to nonmonotonic reasoning, initiated by mcdermott and doyle in 221. Pdf quip a tool for computing nonmonotonic reasoning tasks. The many valued and nonmonotonic turn in logic sciencedirect. Non monotonic reasoning nonmonotonic reasoning deals with the problem of deriving plausible conclusions, but not infallible, from a knowledge base a set of formulas. Logic in nonmonotonic reasoning alexander bochman computer science department, holon institute of technology hit israel abstract 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.
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