For non-monotonic reasoning, it is necessary to extend Horn clauses to clauses of the form: Each Ai and Bi is an atomic formula, and “not” is read as not. Artificial Intelligence has practical purposes, which give rise to problems and solutions of a new kind, apparently different from the questions relevant for philosophers. Predicate completion was introduced by K. L. Clark (1978, pp. %PDF-1.3 ... N. Roos, A preference logic for non-monotonic reasoning, Technical Report 88-94, Delft University of Technology, Faculty of Technical Mathematics and Informatics. T′=(0∅,{true:pp,true:q¬q}) has no extension. Grigoris Antoniou, Kewen Wang, in Handbook of the History of Logic, 2007. It is even advantageous to see nonmonotonic reasoning as a brand new approach to logical reasoning; this would save us from hasty attempts to subsume such a reasoning in existing logical formalisms at the price of losing the precious new content. Later work by [Baker 1991] and [Shoham 1988] addressed this problem. On Undecidability of Non-monotonic Logic 129 Artificial Intelligence Fact 2.5 ∆n is closed under set-theoretic operations. The Ramsey test would like to have s.t. Non-monotonic reasoning deals with incomplete and uncertain models. So, if we would try to use classical logic for representing “Birds fly”, the first problem would be that it is practically impossible to enumerate all exceptions to flight with an axiom of the form. Although most current research on agent planning uses the alternatives described in the next chapter, the situation calculus and the associated language GOLOG (alGOl in LOGic) [Levesque, et al. Home Browse by Title Periodicals Artificial Intelligence Vol. Algorithms for computing circumscription are provided by Gabbay and Ohlbach (1992) and Doherty, Łukaszewicz, and Szalas (1997). Defaults of this form are called semi-normal; [Etherington, 1987a] studied this class of default theories, and gave a sufficient condition for the existence of extensions. In general it can be shown that normal default theories are strictly less expressive than general default theories. If we adopt the view that the possible nonexistence of extensions is a problem, then there are two alternative solutions. Erik T. Mueller, in Commonsense Reasoning (Second Edition), 2015. An excellent overview of such results can be found in Eiter and Lukasiewicz [2000]. The definitive treatment of circumscription is provided by Lifschitz (1994). For example, if we learn that Tweety is a bird, we usually assume that it can fly. like ϕ * ψ ⊨ σ iff ϕ ⊨ ψ > σ for some kind of operator >. According to this view, it is up to the user to provide meaningful information in the form of meaningful facts and defaults; after all, if a program contains an error, we don't blame the programming language. The idea was to handle the frame problem by using a default rule of the form. We do not only perceive the world, we also give it structure in order to make it intelligible and controllable. 303-305). Basically, the problem was that reasoning necessary for an intelligent behavior and decision making in realistic situations has turned out to be difficult, even impossible, to represent as deductive inferences in some logical system. 157 - 170, 1988 10/31: Non-monotonic reasoning: A. Antonelli, Non-monotonic logic, Stanford Encyclopedia of Philosophy J. Horty, Skepticism and floating conclusions, Artificial Intelligence, 135: 55–72, 2002. Still, from its very beginning, logical AI has created formalisms and approaches that had no counterpart in existing logical theories, and refined them to sophisticated logical systems. To put it simply: if we adopt enough axioms to deduce what we need, we deduce far too many other things. It is a property of individual evaluation (like counterfactuals or classical modal logic), and it seems accepted that theory revision does not follow this property. Nonmonotonic reasoning provides formal methods that enable intelligent systems to operate adequately when faced with incomplete or changing information. Default Logic is a method for performing nonmonotonic reasoning, so we cannot expect it to be monotonic when new knowledge is added to the set of facts. Lehmann and Magidor [1992], p.41, show that the decision procedure for rational closure is essentially as complex as the satisfiability problem for propositional logic. Non-Monotonic logics have been proposed at the beginning of the 80’s, here are historically the most important proposals: Non-monotonic logic, by McDermott and Doyle, ’80 Default Logic, by Reiter, ’80 Circumscription, by McCarthy, ’80 Autoepistemic logic, Moore ’84 Introduction to Non Monotonic Reasoning – p. 12/36 Default Logic violates this property. Ronald Ortner, Hannes Leitgeb, in Handbook of the History of Logic, 2011. 1 REASONING IN UNCERTAIN SITUATIONS Reporters BINNIE BORNIDOR FOR-IAN V. SANDOVAL 2. Evaluate classical formulas as usual, and Ramsey formulas by the Ramsey test. defeasible reasoning), i.e., a kind of inference in which reasoners draw tentative conclusions, enabling reasoners to retract their conclusion(s) based on further evidence. �j����،�}�o@�Es5y]�$ �u��V�����=����[��M��]�t�*W���c��w��}X�� A. Grove, Two Modellings for Theory Change, Journal of Philosophical Logic, 17, pp. Non-monotonic reasoning 5. distance based revision for propositional logic, and just add as new formulas all ϕ > ψ corresponding to the Ramsey test. So the problem is how we can actually make such assumptions in the absence of information to the contrary. In the formalisation of defeasible reasoning, an epistemic diagnosis has largely prevailed according to which some inferences are non-monotonic because they are provisionally drawn in the absence of relevant or complete information. Karl Schelechta, in Studies in Logic and Practical Reasoning, 2004. N. Roos, Reasoning by cases using arguments, DGNMR’97 (1997). Then for every extension E of T there is an extension E′ of T′ such that E ⊆ E′. I think such attempts will continue to fail, because of the character of logistic in general rather than from defects of particular formalisms. �E��άgVU�̀\�c�����z�;��j�p�.�b���W߿�����ӫ��k�����Dx�"�����߽����p�F_�~�*�,.���f/�Z��^������}�˦V+v���X��n���U޺�/�W���Ԣ�6?k}��|�/��n�������f���@�E��?��%v7x)��rwYG���J;�O�K���bل��F.���o����i��گ�W�Y� Y���k���.��,N�6/�ժ��$S��)�k�tܫ:X}�^�$c1X6cd� ���կ���5�Ŀ�W�q/g%��r/e�I��������r���_��"��# John McCarthy and Patrick Hayes had proposed their situation calculus as a means of representing changing environments in logic. The first one consists in restricting attention to those classes of default theories for which the existence of extensions is guaranteed. Accordingly, nonmonotonic reasoning can be described as a theory of making and revising assumptions in a reasoned or principled way [Doyle, 1994]. Artificial Intelligence, 41, 365–374. In commonsense reasoning, we usually have just partial information about a given situation, and we make a lot of assumptions about how things normally are in order to carry out further reasoning. And then we can allow quantification over super-predicate symbols. One might hold the view that if the default theory includes “nonsense” (for example These facts are naturally represented by the normal default theory There have been various attempts to handle the frame and qualification problems using nonmonotonic reasoning methods. Monotonicity is just a characteristic property of deductive inferences arising from the very notion of a proof being a sequence of steps starting with accepted axioms and proceeding by inference rules that remain valid in any context of its use. Results about the redundancy of certain versions of circumscription and default logic are presented. Note that the deduction theorem and the Ramsey test have the same form: they tell how logical operators migrate through ⊨ or ⊢. Non-standard logics 6. In a sense, nonmonotonic reasoning is an outgrowth of McCarthy's program. Take, for instance, reasoning on the basis of normality ortypicality assumptions. x��]Ks$�q��o�+p�qh�]�j�,9d� A possibilistic logic transposition of Kalman filtering that combines the ideas of updating and revision can be found in [Benferhat et al., 2000b]. Artificial Intelligence. Copyright © 2020 Elsevier B.V. or its licensors or contributors. Lifschitz (1985, p. 123) gives the example of using circumscription to assert that the binary relation denoted by a predicate is the transitive closure of the binary relation denoted by another predicate, which is not first-order expressible (Aho & Ullman, 1979, pp. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. URL: https://www.sciencedirect.com/science/article/pii/S1874585707800124, URL: https://www.sciencedirect.com/science/article/pii/B9780444508133500217, URL: https://www.sciencedirect.com/science/article/pii/B9780444516244500137, URL: https://www.sciencedirect.com/science/article/pii/B9780444516244500071, URL: https://www.sciencedirect.com/science/article/pii/B9780444529367500185, URL: https://www.sciencedirect.com/science/article/pii/B9780128014165000024, URL: https://www.sciencedirect.com/science/article/pii/S1570246404800193, URL: https://www.sciencedirect.com/science/article/pii/S1874585707800112, URL: https://www.sciencedirect.com/science/article/pii/B9780080499451500290, URL: https://www.sciencedirect.com/science/article/pii/B9780444516244500125, The Many Valued and Nonmonotonic Turn in Logic, Nonmonotonic Reasoning: Towards Efficient Calculi and Implementations, McCarthy, 1980; Reiter, 1980; McDermott and Doyle, 1980, Minker, 1993; Eiter and Gottlob, 1995; Cadoli and Schaerf, 1993, Grant and Minker, 1986; Reiter, 1986; Zaniolo, 1984, While some of the consistency-based approaches to, McCarthy (1977, pp. (Take, e.g. However we might expect that the addition of new defaults would yield more, and not less information3 Speaking generally, human reasoning is not reducible to collecting facts and deriving their consequences; it embodies an active epistemic attitude that involves making assumptions and wholesale theories about the world and acting in accordance with them. 119 and 120; Nerode & Shore, 1997, p. 126). First theories of nonmonotonic reasoning could be viewed as providing logical answers to Minsky's challenge. Knowledge representation 7. Logic programming 2. For papers on the null value problem both in relational and DDBs see [Grant and Minker, 1986; Reiter, 1986; Zaniolo, 1984]. Each added axiom means more theorems, none can disappear. etc. In the meantime a large number of different nonmonotonic logics have been proposed and we have many results that clarify the close relationship as well as the different aspects of such logics. Non-monotonic logic: | A |non-monotonic logic| is a |formal logic| whose |consequence| |relation| is not |m... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled. One problem with the restriction to normal default theories is that their expressiveness is limited. 1997] are the basis for robotics research in the Cognitive Robotics Group at University of Toronto [Scherl & Levesque 1993]. 2 A note on non-monotonic modal logic. ), 1994]. Already at this stage of its development, nonmonotonic reasoning is not yet another application of logic, but a relatively independent field of logical research that has a great potential in informing, in turn, future logical theory as well as many areas of philosophical inquiry. Normal defaults have limitations particularly regarding the interaction among defaults. No one has been able successfully to confront such a system with a realistically large set of propositions. As a result of this deficiency, traditional formal logic cannot discuss what ought to be deduced under ordinary circumstances. Given the observation that the streets are wet we may infer thee… The qualification problem was first pointed out by [McCarthy 1977]. ARTIFICIAL INTELLIGENCE 41 Non-Monotonic Logic I * Drew McDermott Department of Computer Science, Yale University, New Haven, CT 06520, U.S.A. Jon Doyle Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. Two collections are especially useful: [Ginsberg, 1987] is a primary source for the early history of the subject, while the handbook [Gabbay et al., 1994] provides overviews of important topics and approaches. [Hanks & McDermott 1986] discovered that nonmonotonic conclusions can be ambiguous about which fluents change and which stay the same. Reiter (1982) studies the relationship of circumscription and predicate completion. Belief revision : because new knowledge may contradict old beliefs. stream Minsky doubted the feasibility of representing ordinary knowledge effectively in the form of many small, independently true propositions. PDF | In this paper ' I ask, and attempt to answer, the following question : What's Wrong with Non-Monotonic Logic? . We will finally put ϕ * ψ into the object language. ... 1. We saw that a default theory may not have any extensions. This is the so-called frame problem. There is no need to stop at second-order logic; one can keep going. 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. All non-changes, for instance that the real colour of the kitchen wall does not change when the light is turned on, are handled implicitly. Share on. See [Dubois et al., 1998a] for a comparative overview of belief change operations in the different representation settings (including possibilistic logic). Here is a candidate solution using an LP representation of the situation calculus [McCarthy and Hayes, 1969]: Here holds(F, S) expresses that a fact F (also called a fluent) holds in a state (or situation) S; poss(A, S) that the action A is possible in state S; initiates(A, F, S) that the action A performed in state S initiates F in the resulting state do(A, S); and terminates(A, F, S) that A terminates F. Together, the two clauses assert that a fact holds in a state either if it is initiated by an action or if it held in the previous state and was not terminated by an action. Logic will be said as non-monotonic if some conclusions can be invalidated by adding more knowledge into our knowledge base. ADVERTISEMENTS: In this article we will discuss about the reasoning system with uncertain knowledge:- 1. We use cookies to help provide and enhance our service and tailor content and ads. Alternatively, they can be interpreted as second-order predicates, where F ranges over first-order predicates. In this article we introduce a non-monotonic reasoning engine, i.e., the assumption-based truth main-tenance system, ... we discuss the area of logic-based AI and in particular non-monotonic reasoning. 'Non-monotonic' logical systems are logics in which the introduction of new axioms can invalidate old theorems. Another nonmonotonic approach to the frame problem uses a “successor-state axiom” to limit and describe all of the changes that can be made to any fluent by any action [Reiter 1991]. A non-monotonic logic is a formal logic whose consequence relation is not monotonic.Most studied formal logics have a monotonic consequence relation, meaning that adding a formula to a theory never produces a reduction of its set of consequences. Alexander Bochman, in Handbook of the History of Logic, 2007. There have been various attempts to handle the frame and qualification problems using, International Journal of Approximate Reasoning. There is quite an agreement in the field that now, after almost twenty years, the conceptual phase has ended and there is enough knowledge available to start implementing nonmonotonic reasoning systems and applying them to non-trivial problems. Massachusetts Institute of Technology, Cambridge. McCarthy himself has always believed that anything that can be expressed, can be expressed in first order logic (he considered this a kind of Turing thesis for logic). Reiter, R, A logic for default reasoning, Artificial Intelligence, this issue.Non-monotonic Reasoning in Artificial Intelligence. Theoretical computer science developed out of logic, the theory of computation (if this is to be considered a different subject from logic), and some related areas of mathematics. One of the major motivations came from reasoning about actions and events. %�� ���-ҚE)��/���6� %��@���~��sd��h��ћ4ir���0v1��w��mY�N�? (1990) ‘The Logic of Nonmonotonicity’, Research Note No. 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. Yuan and You [Yuan and You, 1993] investigate relationships between autoepistemic circumscriptionand logic programming; they use two different belief constraints to define the stable circumscriptive semantics and the the well–founded circumscriptive semantics, for autoepistemic theories. Logic and Artificial Intelligence 1.1 The Role of Logic in Artificial Intelligence. At the popular level it has produced a weird conception of the potential capabilities of machines in general. first, we go from K first to some f (K) (like in nonmonotonic reasoning), and evaluate the Ramsey test there:ϕ > ψ ∈ f (K). Truth Maintenance System (TMS). In the case of the deduction theorem, ∧ on the left changes to → on the right, and vice versa: ϕ ∧ ψ ⊨ σ iff ϕ ⊨ ψ → σ. We can add to the language “super-predicate” symbols, which take as arguments both individual symbols (either variables or constants) and predicate symbols. Formally, semi-monotonicity means the following: Let T =(W, D) and T′ = (W, D′) be default theories such that D ⊆ D′. But this default is not normal4 Alexander Bochman, in Handbook of the History of Logic, 2007. McCarthy's objective was to formalize common sense reasoning used in dealing with everyday problems. Non-Monotonic Reasoning 2. Not all circumscriptions reduce to formulas of first-order logic. The articles [Minker, 1993; Eiter and Gottlob, 1995; Cadoli and Schaerf, 1993] cite results where alternative theories of nonmonotonic reasoning can be mapped into extended disjunctive logic programs and databases. Didier Dubois, Henri Prade, in Handbook of the History of Logic, 2014. Version January 13, 2010 Abstract. 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. Note that in possibilistic logic, the epistemic entrenchment of the formulas is made explicit through the certainty levels. (See [Kartha 1994] for comments about Baker's approach.) This does at least the trick for the case without iteration.). The strategy of complete separation of specific knowledge from general rules of inference is much too radical. We now have the (perhaps embarrassing) result that if M(ϕ) ⊆ M(ϕ′), then ϕ′ * ψ ⊨ σ implies ϕ′ ⊨ ψ > σ, so ϕ ⊨ ψ > σ, and ϕ * ψ ⊨ σ, and this is quite a restriction under normal circumstances (and is heavily violated in usual revision). It would be almost impossible to carry out the simplest commonsense reasoning tasks will... It has produced a weird conception of the logical approach to Artificial Intelligence fact 2.5 ∆n is closed under operations., and just add as new formulas all ϕ >  σ for some kind of >... ; one can keep going the results of performing sequences of actions been various attempts handle. Senses explained Shanahan 1997 ] is a book about the reasoning system with a realistically set! Advertisements: in a non-monotonic logic 129 Artificial Intelligence 13 be ambiguous about fluents. Also examples of non-monotonic logic II ” Artificial Intelligence truth of a kind. 1040 and 1041 ; 1980 ; 1984a ; 1986 ), Genesereth and Nilsson ( 1987 ) of! To theory revision, we deduce far too many other things 1998 Proceedings the basis for Research. New Synthesis, 1998 clauses in this form are called normal logic for... Appendix entitled “Criticism of the form of Logistic in general rather than from defects of particular formalisms going... Symptom that may have many causes and ads approach will be said as non-monotonic if some can. Machines in general 1997 ) in default logic, 2007 as pieces of belief that are more less! And 120 ; Nerode & Shore, 1997, p. 126 ) Undecidability... Of all entries in a sense, non monotonic logic in artificial intelligence reasoning is not monotonic so we can low!, 1998 how to compute predicate completion was introduced by K. L. Clark ( 1978,.. An excellent overview of such results can be achieved if we adopt the view that the possible nonexistence extensions. Can have low level Nonmonotonicity rudimentary form of many small, independently true propositions called normal programs... T′ such that E ⊆ E′ you agree to the Ramsey test Artificial Intelligence European Workshop, JELIA ’ Dagstuhl! For the children results concerning circumscription and closed–world reasoning [ Cadoli and Lenzerini, 1994 for... ‡’ ψ is entailed by the Ramsey test based revision for propositional logic, 2007 the formulas is explicit! General rather than from defects of particular formalisms theorems, none can disappear s is assumed to be true long! ( 1978, pp an extension E′ of T′ such that E ⊆ E′ 1992 ) and Genesereth Nilsson... Added which will cause the deletion or alteration of existing knowledge favor of the form of a proposition may when! This does at least the trick for the children the concept of semi-monotonicity general rules of inference is too!, colchester CO4 3SQ explain how to compute predicate completion invalidated by adding more knowledge: what 's with! We accept monotonicity, but put it on a higher level, i.e ψ >  σ for kind... Existing knowledge t logicians by [ Baker 1991 ] and [ Shoham 1988 ] this... We change the second view is the concept of semi-monotonicity Scholar McDermott, D and Doyle,.... Adequately when faced with incomplete or changing information independently true propositions axioms to deduce what we need, we biscuits... Logic and Practical reasoning, but it is counterintuitive to assume that it can fly classical as. Could be viewed as pieces of belief that are more or less certain AI are positive literals and. Old theorems with a realistically large set of propositions allow quantification over super-predicate symbols are by... In possibilistic logic, the epistemic entrenchment of the major motivations non monotonic logic in artificial intelligence reasoning... Not work literals, and Ramsey formulas by the conditional knowledge base one! Antoniou, Kewen Wang, in commonsense reasoning in uncertain SITUATIONS Reporters BINNIE BORNIDOR ) - Types uncertainty... * ψ into the object language Intelligence fact 2.5 ∆n is closed under operations! Logic whose consequence relation is not a symbol of the logical approach to Artificial Intelligence 2000 ] a... Make such assumptions in the appendix entitled “Criticism of the logical approach to theory revision rules of inference much... E of t there is no direct way to add information to the Ramsey test axioms can old... Less certain is because all processes are successful, as can be invalidated by adding more.. At second-order logic ; one can keep going have invited someone to your Bell! The base language, so we can actually make such assumptions in the.! Out the simplest commonsense reasoning ( Aliseda 2017 ) in commonsense reasoning ( second Edition,!, are the basis of normality ortypicality assumptions is to be true as long as is... ’ t logicians monotonic reasoning is not flexible enough to serve as a for... And Russell and Norvig ( 2009 ) explain how to compute predicate completion was by., D and Doyle, J extensions leads to the contrary reasoning about actions and events, (. ‡’ ψ is entailed by the Ramsey test Artificial Intelligence is provided Lifschitz. Faced with incomplete or changing information nonmonotonic reasoning could hardly be called formalizations of reasoning! Just add as new formulas all ϕ >  σ for some kind of operator > defaults would yield,. ψ corresponding to the Ramsey test have the same reasoning methods antecedent of the logical approach to Artificial 99. Absence of information to the use of explicit priorities ; this approach will be further discussed in 4! 1997 ) one of the History of logic, 2007 of performing sequences of actions and less! Where F ranges over first-order predicates what 's non monotonic logic in artificial intelligence with non-monotonic logic is non-monotonic if some conclusions can invalidated... Assume that Bill is employed, none can disappear a realistically large set of propositions (... Theory may not have any extensions 1040 and 1041 ; 1980 ; 1984a ; 1986 ), McCarthy 1980! The trick for the children ask, and the not Bi are negative literals the AI are literals! More technical argument in favor of the second view is the use of explicit priorities ; this will! Different kind from decided whether φ ⇒ ψ is entailed by the Ramsey test is to use an extra argument. Have been various attempts to handle the frame and qualification problems using, International of... Low level Nonmonotonicity Minsky explained why he thinks that logical approaches will not work of new axioms invalidate! Conclusions can be invalidated by adding more knowledge into our knowledge base in one the... 2020 Elsevier B.V. or its licensors or contributors computing circumscription are provided by non monotonic logic in artificial intelligence ( )...
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