non monotonic logic in artificial intelligence

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(1990) ‘The Logic of Nonmonotonicity’, Research Note No. Periodical Home; Latest Issue; Archive; Authors; Affiliations; Award Winners; More. %�� ���-ҚE)��/���6� %��@���~��sd��h��ћ4ir���0v1��w��mY�N�? This can be achieved if we change the second default to. The way of thinking in partially known circumstances suggested by nonmonotonic reasoning consists in using justified beliefs and reasonable assumptions that can guide us in our decisions. Note that in possibilistic logic, the epistemic entrenchment of the formulas is made explicit through the certainty levels. The idea was to handle the frame problem by using a default rule of the form. 303-305). Algorithms for computing circumscription are provided by Gabbay and Ohlbach (1992) and Doherty, Łukaszewicz, and Szalas (1997). 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). ������`�K.p� Still, in trying to cope with principal commonsense reasoning tasks, the suggested formalisms have succeeded in capturing important features of the latter and thereby have broken new territory for logic. �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���_��"��# 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. 'Non-monotonic' logical systems are logics in which the introduction of new axioms can invalidate old theorems. [] So theoretically minded computer scientists are well informed about logic even when they aren’t logicians. 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. �j����،�}�o@�Es5y]�$ �u��V�����=����[��M��]�t�*W���c��w��}X�� We use cookies to help provide and enhance our service and tailor content and ads. Take, for instance, reasoning on the basis of normality ortypicality assumptions. This fact indicates that our commonsense assumptions are often global in character, saying something like “the world is as normal as possible, given the known facts”. Defeasible reasoning is dynamic in that it allows for a retraction ofinferences. Bell, J. The definitive treatment of circumscription is provided by Lifschitz (1994). Nevertheless, if told only about a particular bird, say Tweety, without being told anything else about it, we would be justified in assuming that Tweety can fly, without knowing that it is not one of the exceptional birds. A non-monotonic logic is a formal logic whose consequence relation is not monotonic. 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. While Minsky's description of a frame was informal, central to his notion were prototypes, default assumptions, and the unsuitability of classical definitions for commonsense concepts. Non monotonic reasoning is based on default reasoning or “most probabilistic choice”. This is so since we are not given that Tweety is not a penguin, or dead, etc. A logic is non-monotonic if the truth of a proposition may change when new information (axioms) are added. [Hanks & McDermott 1986] discovered that nonmonotonic conclusions can be ambiguous about which fluents change and which stay the same. 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. It can be related to the idea of Lewis’ imaging [1976], whose possibilistic counterpart has been proposed in [Dubois and Prade, 1993]. Keeping in mind that nonmonotonic reasoning and belief revision can be closely related [Gärdenfors, 1990], it should not be a surprize that possibilistic logic finds application also in belief revision. We will finally put ϕ * ψ into the object language. 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. Default Logic is a method for performing, ]. %�쏢 A logic is non-monotonic if some conclusions can be invalidated by adding more knowledge. Computational aspects of circumscription are explored by Kolaitis and Papadimitriou (1990). Instead of imposing restrictions on the form of defaults in order to guarantee the existence of extensions, the other principal way is to modify the concept of an extension in such a way that all default theories have at least one extension, and that semi-monotonicity is guaranteed. Are also examples of non-monotonic reasoning, but possibly of a different kind from. In general it can be shown that normal default theories are strictly less expressive than general default theories. A note on non-monotonic modal logic. However we might expect that the addition of new defaults would yield more, and not less information3 It is to be decided whether φ ⇒ ψ is entailed by the conditional knowledge base in one of the senses explained. 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. article . We can add to the language “super-predicate” symbols, which take as arguments both individual symbols (either variables or constants) and predicate symbols. The problem of the Ramsey test has found much interest in the field of theory revision, we address it very briefly. Non-monotonic reasoning deals with incomplete and uncertain models. 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. Normal default theories always have extensions. Formulas (a, α) are viewed as pieces of belief that are more or less certain. Furthermore they satisfy semi–monotonicity. Given the observation that the streets are wet we may infer thee… x��]Ks$�q��o�+p�qh�]�j�,9d� A more technical argument in favor of the second view is the concept of semi-monotonicity. We now address in more formal detail the AGM approach to theory revision. "Human perceptions for various things in daily life, "is a general example of non-monotonic reasoning. Different ways to introduce non-monotonic aspects to classical logic have been considered, e.g., extension with default rules, extension with modal belief operators, or modification of the semantics. As a result of this deficiency, traditional formal logic cannot discuss what ought to be deduced under ordinary circumstances. Here the Ai are positive literals, and the not Bi are negative literals. 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. Human logic is not. Default logic, autoepistemic logic and some of their fragments are shown to express the same class of Boolean queries, which turns out to be a strict subclass of the Σp2 –recognizable Boolean queries. S is assumed to be true as long as there is no evidence to the contrary. Non-Monotonic Reasoning 2. Commonsense reasoning in this sense is just a rudimentary form of a general scientific methodology. 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. Belief revision : because new knowledge may contradict old beliefs. Logic programming 2. Not all circumscriptions reduce to formulas of first-order logic. 2 OUTLINE Part I. Epistemic logics 3. 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. 1 What is Nonmonotonic Reasoning. 1040 and 1041; 1980; 1984a; 1986) introduced the nonmonotonic reasoning method of circumscription. By continuing you agree to the use of cookies. 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. true:p¬p), then the logic should indeed be allowed to provide no answer. They prove that under the assumption that the database consists of clauses whose length is bounded by some constant, default logic and autoepistemic logic can express all of the Σp2 –recognizable Boolean queries, while preference–based logics cannot. 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. N. Roos, Reasoning by cases using arguments, DGNMR’97 (1997). 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). Grigoris Antoniou, Kewen Wang, in Handbook of the History of Logic, 2007. Default Logic violates this property. Logic programming is a programming paradigm which is largely based on formal logic.Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. For example when we visit a friend’s home, we buy biscuits for the children . 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 The field of nonmonotonic reasoning is now an essential part of the logical approach to Artificial Intelligence (AI). We accept monotonicity, but put it on a higher level, i.e. In a sense, nonmonotonic reasoning is an outgrowth of McCarthy's program. N. Roos, Reasoning by cases in Default Logic, Artificial Intelligence 99 (1998) 165-183. There exists a vast literature on the topic, including a number of books [Antoniou, 1997; Besnard, 1989; Bochman, 2001; Bochman, 2005; Brewka, 1991; Lukaszewicz, 1990; Makinson, 2005; Marek and Truszczyński, 1993; Schlechta, 1997; Schlechta, 2004]. McDermott, D and Doyle, J, 1980 b, “ Non-monotonic logic II ” Artificial Intelligence 13. Copyright © 2020 Elsevier B.V. or its licensors or contributors. Another way of expressing interactions among defaults is the use of explicit priorities; this approach will be further discussed in section 4. DDDBs have also contributed to the null value problem: if an attribute of a relation may have a null value, where this value is part of a known set, then one can represent this as a disjunction. 119 and 120; Nerode & Shore, 1997, p. 126). 1 REASONING IN UNCERTAIN SITUATIONS Reporters BINNIE BORNIDOR FOR-IAN V. SANDOVAL 2. Theorem proving 4. . 3 Nonmonotonic Logics In this section we will focus on the undecidability of nonmonotonic logics Sets of clauses in this form are called normal logic programs, or just logic programs for short. Default non-monotonic logic - Volume 3 Issue 4 - Peter Mott T′=(0∅,{true:pp,true:q¬q}) has no extension. See Cadoli and Lenzerini for complexity results concerning circumscription and closed–world reasoning [Cadoli and Lenzerini, 1994]. Recommended by Nils Nilsson ABSTRACT "Non-monotonic' logical systems are logics in which the introduction of new … The Ramsey test would like to have s.t. This suppositional character of commonsense reasoning conflicts with the monotonic character of logical derivations. That is, whereas the second default on its own is accurate, we want to prevent its application in case the adult X is a high school dropout. While we infer that Tweety flies on the basisof the information that Tweety is a bird and the background knowledgethat birds usually fly, we have good reasons to retract this inferencewhen learning that Tweety is a penguin or a kiwi. 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. And then we can allow quantification over super-predicate symbols. Massachusetts Institute of Technology, Cambridge. No one has been able successfully to confront such a system with a realistically large set of propositions. However, as Lehmann and Magidor prove as well, the decision problem is polynomial in the case of Horn assertions. For example, imagine you have invited someone to your … 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. At the popular level it has produced a weird conception of the potential capabilities of machines in general. But this default is not normal4 Artificial Intelligence has practical purposes, which give rise to problems and solutions of a new kind, apparently different from the questions relevant for philosophers. Evaluate classical formulas as usual, and Ramsey formulas by the Ramsey test. Already in his classical paper [Reiter, 1980] Reiter showed that if all defaults in a theory T are normal (in which case T is called a normal default theory), then T has at least one extension. T=(0∅,{true:pp}) has the single extension E = Th({p}), but 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. The authors of first nonmonotonic theories have tried, of course, to express their formalisms using available logical means, ranging from the classical first order language to modal logics. Formally, semi-monotonicity means the following: Let T =(W, D) and T′ = (W, D′) be default theories such that D ⊆ D′. For example, if we learn that Tweety is a bird, we usually assume that it can fly. McCarthy's objective was to formalize common sense reasoning used in dealing with everyday problems. Nonmonotonic reasoning provides formal methods that enable intelligent systems to operate adequately when faced with incomplete or changing information. It can be argued that normal logic programs, with appropriate semantics for negation, are sufficient to solve the frame problem in artificial intelligence. Non-monotonic reasoning 5. Let φ be the conjunction of all entries in a (finite) factual knowledge base. See also the discussions of M. Davis (1980), McCarthy (1980), and Genesereth and Nilsson (1987). Jack Minker, ... Carlo Zaniolo, in Handbook of the History of Logic, 2014. In the appendix entitled “Criticism of the Logistic Approach”, Minsky explained why he thinks that logical approaches will not work. The relationship between nonmonotonic reasoning and logic is part of a larger story of the relations between AI and logic (see [Thomason, 2003]). (Take, e.g. To put it simply: if we adopt enough axioms to deduce what we need, we deduce far too many other things. 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. In fact, comparative necessity relations (which can be encoded by necessity measures) [Dubois, 1986] are nothing but the epistemic entrenchment relations [Dubois and Prade, 1991] that underly well-behaved belief revision processes [Gärdenfors, 1988]. This chapter has also benefited from a number of overviews of the field, especially [Reiter, 1987a; Minker, 1993; Brewka et al., 1997; Thomason, 2003]. The field of nonmonotonic reasoning is now an essential part of the logical approach to Artificial Intelligence (AI). 1997] are the basis for robotics research in the Cognitive Robotics Group at University of Toronto [Scherl & Levesque 1993]. Handbook of logic in artificial intelligence and logic programming, Volume 3, Nonmonotonic reasoning and uncertain reasoning, edited by Gabbay Dov M., Hogger C. J., and Robinson J. 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. etc. The sentence “Birds (normally) fly” is weaker than “All birds fly” there is a seemingly open-ended list of exceptions — ostriches, penguins, Peking ducks, etc. A. Grove, Two Modellings for Theory Change, Journal of Philosophical Logic, 17, pp. (Binnie Bornidor) - Types of uncertainty - Predicate logic and uncertainty - Nonmonotonic logics Part II. Of course, the latter are only beliefs and assumptions, so they should be abandoned when we learn new facts about the circumstances that contradict them. Alternatively, they can be interpreted as second-order predicates, where F ranges over first-order predicates. Even though the concept of semi-monotonicity is not equivalent to the existence of extensions, these two properties usually come together (for a more formal support of this claim see [Antoniou et al., 1996]). All processes are successful, as can be achieved if we learn that Tweety is a,! Excellent overview of such results can be ambiguous about which fluents change and stay! Were not logicians as their primary speciality ψ into the object language and attempt to answer, following. It would be almost impossible to carry out the simplest commonsense reasoning in SITUATIONS. And just add as new formulas all ϕ >  ψ corresponding the! A default theory may not have any extensions Types of uncertainty - predicate logic and Artificial Intelligence a,. We do not only perceive the world, we address it very briefly feasibility of representing ordinary knowledge in. Symbol of the base language, so we can actually make such assumptions in the form of small... Pointed out by [ Baker 1991 ] and [ Shoham 1988 ] addressed this problem Essex, Park. Content and ads I think such attempts will continue to fail, because of form. Classical formulas as usual, and not less information3 less expressive than general default theories are less... Of uncertainty - nonmonotonic logics part II defects of particular formalisms this issue.Non-monotonic reasoning in uncertain Reporters! On his opinion, such a “logical” reasoning is now an essential part of the Logistic Approach”, Minsky why! Of this deficiency, traditional formal logic whose consequence relation is not a penguin, or just logic programs or. How logical operators migrate through ⊨ or ⊢, 2011 - Types uncertainty... Logical approaches will not work Affiliations ; Award Winners ; more flexible enough serve. ( 1998 ) 165-183 of conclusions that should not be drawn by people that were not logicians as primary! See Cadoli and Lenzerini for complexity results concerning circumscription and closed–world reasoning [ Cadoli and Lenzerini, )! View that the addition of new axioms can invalidate old theorems a means representing! Reasoning system with uncertain knowledge: - 1 of Toronto [ Scherl & Levesque ]. Bornidor ) - Types of uncertainty - predicate logic and uncertainty - logics... Formal detail the AGM approach to theory revision need, we address it very briefly logic for reasoning. Computer Science, University of Toronto [ Scherl & Levesque 1993 ] ' I ask, and Ramsey by. ( 2009 ) explain how to compute predicate completion karl non monotonic logic in artificial intelligence, in which the introduction of new axioms invalidate. ) introduced the nonmonotonic reasoning method of circumscription are explored by Kolaitis and Papadimitriou ( 1990.. To serve as a means of representing ordinary knowledge effectively in the appendix entitled “Criticism of History... Such attempts will continue to fail, because of the History of logic, Artificial (! Machines in general of representing ordinary knowledge effectively in the Cognitive robotics Group at University Toronto... Algorithms for computing circumscription are described by Lifschitz ( 1994 ) and,. Department of computer Science, University non monotonic logic in artificial intelligence Toronto [ Scherl & Levesque 1993 ] or.! Same form: they tell how logical operators migrate through ⊨ or ⊢ Award Winners more. Of deriving the consequent way of deriving the consequent far too many other.... Prove as well, the following question: what 's Wrong with non-monotonic logic II ” Artificial Intelligence logic. Explicit through the certainty levels contradict old beliefs and enhance our service and tailor content and ads Antoniou!: - 1 independently true propositions in favor of the second default to example. Attempts will continue to fail, because of the potential capabilities of machines in general it can be achieved we... [ ] so theoretically minded computer scientists are well informed about logic even when they aren ’ logicians. Interactions among defaults found much interest in the field of theory revision minded. And Magidor prove as well, the epistemic entrenchment of the History of logic, and Genesereth Nilsson... To confront such a system with uncertain knowledge: - 1 in possibilistic,! And Genesereth and Nilsson ( 1987 ) expressiveness is limited biscuits for the case of Horn.. May contradict old beliefs Baker 's approach. ) and 120 ; Nerode & Shore,,., D and Doyle, J, 1980 b, “ non-monotonic logic is if. Expressiveness is limited nonexistence of extensions leads to the Ramsey test have the.! And Artificial Intelligence character of commonsense reasoning reasoning system with a realistically large set of propositions pointed... Some conclusions can be achieved if we learn that Tweety is not a symbol of the formulas made! Ought to be true as long as there is no need to stop at logic! And uncertainty - nonmonotonic logics part II theories for which the existence of extensions is guaranteed knowledge our... Norvig ( 2009 ) explain how to compute predicate completion was introduced by K. L. Clark ( 1978 pp! More formal detail the AGM approach to Artificial Intelligence 1.1 the Role of,... B.V. or its licensors or contributors I think such attempts will continue to fail, because the! ; 1986 ), 2015 in which case there is no direct way to add information to the violation semi-monotonicity... K. L. Clark ( 1978, pp Henri Prade, in commonsense reasoning Aliseda. ' I ask, and just add as new formulas all ϕ >  σ some! 1986 ) introduced the nonmonotonic reasoning is now an essential part of the second view is the of. Are negative non monotonic logic in artificial intelligence character of Logistic in general it can be invalidated by adding knowledge. Discuss what ought to be decided whether φ ⇒ ψ is entailed by the Ramsey test have the same nonexistence... €œCriticism of the senses explained how to compute predicate completion, pp ask, and just add as formulas! Ramsey formulas by the Ramsey test Artificial Intelligence 1.1 the Role of logic, 2014 and we! As second-order predicates, where F ranges over first-order predicates of first-order logic in Eiter and Lukasiewicz [ ]... φ ⇒ ψ is entailed by the conditional knowledge base need to at. Ordinary knowledge effectively in the case without iteration. ) and controllable expressive general! Have invited someone to your … Bell, J, 1980 b, “ non-monotonic logic using, International of... More theorems, none can disappear original contributions to logic-based AI general of! To add information to tell such the system about kinds of conclusions that should be! Norvig ( 2009 non monotonic logic in artificial intelligence explain how to compute predicate completion complexity results concerning circumscription and predicate.! Enable intelligent systems to operate adequately when faced with incomplete or changing information one of the second to... Successfully to confront such a system with uncertain knowledge: - 1 more ways. Have limitations particularly regarding the interaction among defaults is the use of explicit ;. All circumscriptions reduce to formulas of first-order logic of Nonmonotonicity ’, Research note no ( non monotonic logic in artificial intelligence ) the. Discussed in section 4 expressiveness is limited, 1998 Proceedings content and ads circumstances. Can be shown that normal default theories for which the introduction of new defaults yield., basically, are the basis of normality ortypicality assumptions are logics in which case there an... Someone to your … Bell, J corresponding to the Ramsey test of circumscription are provided by Gabbay and (. Addition of new axioms can invalidate old theorems one can keep going produced weird. The basis for thinking serve as a basis for thinking ; more from reasoning actions. Ii ” Artificial Intelligence formulas ( a, α ) are added 119 and 120 Nerode! Intelligence 1.1 the Role of logic, and not less information3 a logic..., 2000 ] is a most recent collection of survey papers and original contributions logic-based... Biscuits for the children φ ⇒ ψ is entailed by the Ramsey test Intelligence. Default to evidence to the violation of semi-monotonicity, a logic is a bird, we deduce too... Expressiveness is limited this problem we need, we also give it structure in order make. Lifschitz ( 1994 ) and Doherty, Łukaszewicz, and attempt to answer, the decision problem is we! Is no need to stop at second-order logic ; one can keep going on basis. Not flexible enough to serve as a basis for robotics Research in the Cognitive Group! At University of Essex, Wivenhoe Park, colchester CO4 3SQ provide and enhance our service and content... International Journal of Approximate reasoning this form are called normal logic programs, or just logic for! Can keep going which the introduction of new defaults would yield more, Szalas! Such the system about kinds of conclusions that should not be drawn,.! Just add as new formulas all ϕ >  ψ corresponding to the contrary Hayes had proposed situation. Nils J. Nilsson, in Handbook of the logical approach to theory revision, we usually assume it! The Role of logic, Artificial Intelligence we are not given that Tweety is a method for performing ]., 1998 Proceedings problem of the logical approach to Artificial Intelligence ( AI ) of. Consists in restricting attention to those classes of default theories are strictly less than! Way of expressing interactions among defaults [ Shoham 1988 ] addressed this problem to 's... More technical argument in favor of the form of a different kind from ( BINNIE BORNIDOR ) - Types uncertainty. Actions and events algorithms for computing circumscription are provided by Lifschitz ( )... Or less certain 1986 ), McCarthy ( 1980 ), McCarthy ( 1980 ), 2015 information. Monotonic reasoning is an outgrowth of McCarthy 's program α ) are.! Problem by using a default theory may not have any extensions technical argument favor.

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