## what is default reasoning in ai

Similarly, Streetwet implies in this sense both its only explanation Rained and a collateral effect Grasswet. Bayesian analysis should be consulted as a standard for abstracting more refined logical systems. Though there are various types of uncertaintyin various aspects of a reasoning system, the "reasoning with uncertainty" (or "reasoning under uncertainty") research in AI has been focused on the uncertainty of truth value, that is, to allow and process truth values other than "true" and "false". Theorist defined the notion of extension as a set of propositions generated by a maximal consistent scenario. Assume that an abductive system is determined by the set Δ of rules. The matching process is partly controlled by information associated with the frame (which includes information about how to deal with surprises) and partly by knowledge about the system's current goals. A second point is that human reasoning performance seems to improve, that is, to commit fewer fallacies, when the reasoning in question is set in a deontic-context (Cheng and Holyoak [1985]). Motivated primarily by the intractability of logic-based abduction, this representation allowed for incomplete deduction in connecting hypotheses to observations for which tractable abduction mechanisms can be developed. 3. Alexander Bochman, in Handbook of the History of Logic, 2007. If we are told that he cooked breakfast, we might imagine him in his kitchen. An event calculus domain description consists of an axiomatization, observations of world properties, and a narrative of known world events. The use of explicit negation (also called strong, or even classical negation) enables more natural knowledge representation, including the representation of rules and exceptions. The basic structure of the fallacy is the (invalid) argument form: On the standard analysis, ad ignoratiam arguments are not only deductively invalid, but wholly implausible as well. Arguably, the extension to disjunctive conclusions is more problematic, because it creates the need to decide between alternative representations, for example between the two representations: In the general case, different representations have different stable models. Moreover, it is quite feasible that the major computational benefits of causal reasoning could be tapped with just a rough quantification of rule strength. Under these assumptions we can establish the following theorem. In such cases it is necessary to make plausible assumptions, which in default reasoning are based on default rules. In general, given a normal logic program P: For example, given P = {q, p ← q ∧ not r}, and the Herbrand interpretation M = {p, q}, the condition not r is true in M, and therefore the set of Horn clauses reduct(P, M) = {q, p ← q} has the same meaning as P in the context of M. This meaning is the minimal model of reduct(P, M), which is identical to M. Therefore M is a stable model of P. Moreover, it is the only stable model of P. A program can have one, many or no stable models. With this renaming and the addition of clauses ← A ∧ A* for every pair of contrary atoms, the stable models of a program with explicit negation are isomorphic to the stable models of the same program without explicit negation. Now we turn to autoepistemic logic and show how the approach introduced for default reasoning leads to a decision procedure for autoepistemic reasoning. Thus some of the components we assume to be behaving normally must really be malfunctioning. When new information becomes available, the circumscriptions can be recomputed and reasoning again performed, which may lead to new conclusions. Robert Kowalski, in Handbook of the History of Logic, 2014. By retracting enough of the original assumptions about correctly behaving components, we can remove the inconsistency between the predicted and observed behavior. This suggests the following notion: The abductive semantics S of an abductive system is the set of theories {Cn(a) |a ⊆ A}. Default reasoning is concerned with making inferences in cases where the information at hand is incomplete. Soundness and completeness of the procedure can be guaranteed under similar assumptions as in the case of default logic. By continuing you agree to the use of cookies. 4. Given an observation of symptoms for a particular case, a diagnosis is a set of causes that covers all of the observed symptoms and contains no irrelevant causes. In fact, the study of abduction is one of the success stories of nonmonotonic reasoning, and it has a major impact on the development of an application area. For example, if a bird comes up in conversation, people typically picture a fist-sized animal that sings and flies. In the late 1980s, several other logical formalisms began to appear, including the features and fluents framework, action languages, and the fluent calculus. Jürgen Dix, ... Mirek Truszczyński, in Handbook of Automated Reasoning, 2001. 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. The stable model semantics is non-monotonic, because adding clauses to a program can non-monotonically decrease the consequences of the program. Knowledge Representation in AI describes the representation of knowledge. If it is known only that a patient has a fever, the most reasonable explanation is that he has the flu. Default reasoning and TMS PS must make conclusions based on incomplete information. The expressive power of a query language over a disjunctive ground database is studied in [Bonatti and Eiter, 1996]; they show there exist simple queries that cannot be expressed by any preferential semantics (including minimal model semantics and various forms of circumscription), while they can be expressed in default and autoepistemic logic. : for any sets b, c of propositions. To end this section on abduction, we will provide below a brief description of an abstract abductive system that is sufficient for the main applications of abduction in AI. The restriction of this kind is not essential, however. is inconsistent with) the observed system behavior. Default reasoning and the qualification problem Many of the things people know take the form of "working assumptions". Putting your intelligence into … Judea Pearl, in Probabilistic Reasoning in Intelligent Systems, 1988. In absorbing the dialogical approach to practical reasoning, we are free to engage — to appropriate or adapt — a large research literature. . Similar to the case of default logic the lower bound can safely include the logical consequences of the premises and the assumptions, i.e., AE-Cn(T ∪FS). Obtaining a tight upper bound for autoepistemic expansions is not straightforward. Postdiction consists of determining the initial state given events and a final state. Somehow human beings are rigged for what classically would be seen as hasty generalization fallacies in precisely these cases in which the reasoner is not generalizing to a universally quantified conditional (which is as brittle as a generic generalization is elastic), but rather to a generalization certain negative instances of which happen not to matter. The first, ‘procedural’ formalization of this reasoning was the set-covering model, proposed in [Reggia et al., 1985]. None of these things are true about all birds. The development is based on the work in [Niemelä 1995a] where an overview of decision methods for autoepistemic logic can be found. Theorist assumed the typical abductive machinery: a set of hypotheses, a first-order background theory, and the concept of explanation. The earliest attempts to formalise default reasoning in artificial intelligence employed non-logical, object-oriented representations, such as semantic networks and frames [Minsky, 1975]. Suppose, however, the system behavior predicted by this assumption conflicts with (i.e. In other words, it does not explain observations, but only excuses them. They also seem triggered by very small samples, as we have seen. The philosophical history of thesubject goes back to Aristotle, while the field of artificialintelligence has greatly intensified interest in it over the lastforty years. Default reasoning is very useful in modelling human reasoning as we can draw conclusions even in the absence of information by defaulting to the default rule. It is entirely possible that some of this difference lies in the fact that one and the same strategy might be a reasoning error in a non-practical context of reasoning, and yet be an error-free strategy deontically. However, since only ¬Grassswet is an abducible, non-wet grass does not require explanation, but wet grass does. As a related development from linguistics, generic inference discloses its thinking to default reasoning. It has been shown in [Inoue and Sakama, 1998] that abductive logic programs under the generalized stable semantics are reducible to general disjunctive logic programs under the stable semantics. We then present the theory and practice of answer set programming for event calculus reasoning. Taking their inspiration from the situation calculus, Robert Kowalski and Marek Sergot introduced the event calculus in 1986. Defaults of Poole's abductive system corresponded to a simplest kind of Reiter's default rules, namely normal defaults of the form : A/A. But as studies of autoepistemic reasoning show (e.g.,) there are non-deductive exceptions to so harsh a verdict, as witness: If there were a Department meeting today, I would know about it. It contained papers by John McCarthy [1980] on circumscription, Ray Reiter [1980] on default logic, and Drew McDermott and Jon Doyle [1980] on non-monotonic modal logic. 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. Let T be a set of autoepistemic formulae and FS a set ofBχ subformulae of T and their complements. The event calculus uses the default assumptions that (1) the only events that occur are those known to occur and (2) the only effects of events are those that are known. It was shown in [Reiter and de Kleer, 1987] that the label in ATMS is exactly the set of such explanations, so the ATMS can be used to compute parsimonious explanations for propositional Horn-clause theories. Erik T. Mueller, in Commonsense Reasoning (Second Edition), 2015. It is easy to see how default reasoning and generic inference touch on the classical fallacy of hasty generalization, and necessitate a substantial reconsideration of its traditional analysis. Non-Monotonic Reasoning 2. By default, reasoning is presumed to be fairly rigorous — strong reasoning, but in practice tends to be somewhat weaker than rigorous logic. Important formalisms for default reasoning such as circumscription and default logic appeared around 1980. So, it can reasonably be supposed that there’ll be no meeting. In other words, by taking defaults as possible hypotheses. Abductive logic programs are defined as pairs (Π, A), where Π is a logic program, and A a set abducible atoms. Commonsense reasoning evidently involves two types of default rules: expectation-evoking and explanation-evoking. Default reasoning requires two facilities, one that forces conclusions to be retracted in light of new refuting evidence and another that protects conclusions from retraction in light of new but irrelevant evidence. Categorization reveals a lot about the field of study. But if we learn that he also has jaundice, then it becomes more likely that he has a disease of the liver. These remain essentially same as in the case of default logic. The distinction between causal and evidential defaults allows to distinguish properly rules that should be invoked from rules that should not be invoked. Levesque [1989] suggested a knowledge level analysis of abduction in which the domain theory is represented as the beliefs of an agent. For papers on the null value problem both in relational and DDBs see [Grant and Minker, 1986; Reiter, 1986; Zaniolo, 1984]. Then extensions(T, Ø, φ) returns Yes if and only if there exists an expansion of T not containing φ (i.e.,extensions(T,θ,∅) returns No if and only if φ is contained in every expansion of T). Reasoning − It is the set of processes that enables us to provide basis for judgement, making decisions, and prediction. All these kinds of inference can be captured formally by considering only theories of Cn that are generated by the abducibles. In addition, Poole employed the mechanism of naming defaults (closely related to McCarthy's abnormality predicates) that has allowed him to say, in particular, when a default is inapplicable. We denote the closure of a set of autoepistemic formulae T under the classical consequence ⊢ and the necessitation rule by AE-CnN(T). In the spirit of David Israel, Poole argued that there is nothing wrong with classical logic; instead, nonmonotonicity is a problem of how the logic is used. Anyone who has seen the unforgettable horse's head scene in The Godfatherimmediately realizes what is going on. Reasoning Deriving information that is implied by the information already present is a form of reasoning. We discuss atemporal default reasoning and then temporal default reasoning. Default reasoningc can express facts like “by default, something is true” by contrast, standard logic can only express that something is true or that something is false. A classical abductive system can be safely equated with a pair (∑, A), where ∑ is a set of classical propositions (the domain theory). In other words, by taking defaults as possible hypotheses, default reasoning has been reduced to a process of theory formation. McDermott [1987] levied a similar criticism about the absence of a firm theoretical basis behind diagnostic and other programs dealing with abduction: This state of affairs does not stop us from writing medical diagnosis programs. It should exploit the fact that human reasoning is non-monotonic and that non-monotonic structures have been investigated by Al researchers (e.g., Geffner [1992] and Pereira [2002]). The relevant transformation of abductive programs can be obtained simply by adding to Π the program rules p, not p ←, for any abducible atom p from A. “Closed-World Assumption” (CWA) X is true unless there is an evidence to the contrary. Which of the following is/are true about default reasoning? The main inference mechanism in the ATMS is the computation of a label at each node. The stable model semantics has been extended to programs of the form: where l ≥ 0, n ≥ 0 and m ≥ 0. Let test(T, FS, φ) return Yes for all T, FS, and φ. Thenextensions(T,θ,∅) returns Yes if and only if T has an expansion. Copyright © 1988-2020, IGI Global - All Rights Reserved, Additionally, Enjoy an Additional 5% Pre-Publication Discount on all Forthcoming Reference Books, Learn more in: Managing Uncertainties in Interactive Systems. (Gabbay and Woods [1999], [2004a].). Table 1.1. Finally, we discuss two useful tools for answer set programming: the F2LP program and the E language. Then extensions(T, FS, φ) returns Yes if and only if there exists an expansion of T agreeing with FS such that test(T, FS′, φ) returns Yes where the FS′ is the corresponding full set. Abduction is the process of finding explanations for observations. Let T be a set of autoepistemic formulae and φ an autoepistemic formula. To Support Customers in Easily and Affordably Obtaining the Latest Peer-Reviewed Research, A non-monotonic logic proposed by Raymond Reiter to formalize. and the set of abducibles Rained, ¬Rained, Sprinkler, ¬Sprinkler, ¬Grassswet. This consequence relation describes not only forward explanatory relations, but also abductive inferences from propositions to their explanations. However, Artificial Intelligence field has so diverse approaches to achieve its goals, presenting one nice and neat taxonomy of current existing diverse approaches is difficult. In the 1960s, he and Patrick J. Hayes introduced the situation calculus, a logical formalism for commonsense reasoning. On the face of it, consistency-based and abductive diagnosis appear very different. In medical diagnosis, the type of reasoning involved is abductive in nature and consists in explaining observations or the symptoms of a patient. The resulting system has been shown to capture many of the representative capabilities of Reiter's default logic in an almost classical logical framework. man “default reasoning” or “plausible inference” through their infer- ence mechanisms just as modus ponena provides a model for deduc- tive reasoning. An example of the former is, “Fred must be in either the museum or the café. For example the program {p ← not p} has no stable models, but {p ← not q, q ← not p} has two stable models, {p} and {q}. A comprehensive survey of the extension of logic programming to perform abductive reasoning (referred to as abductive logic programming) can be found in [Kakas et al., 1992] together with an extensive bibliography on abductive reasoning. Wikipedia states, following : “Commonsense reasoning is one of the branches of artificial intelligence (AI) that is concerned with simulating the human ability to make presumptions about the type and essence of ordinary situations they encounter every day. Basically, it is a study of how the beliefs, intentions, and judgments of an intelligent agent can be expressed suitably for automated reasoning. Given a domain description, various types of commonsense reasoning can be performed. expand: expand(T, FS) returns a set FS′ of Bψ formulae and their complements which extends FS and with which every expansion of T agreeing with FS agrees. Thenextensions(T,θ,∅) returns Yes if and only if there exists an expansion of T containing ψ. It is characterized by a set of axioms and definitions: 17 in EC and 12 in DEC. Knowledge is represented as answer set programs, and reasoning is performed by answer set solvers. Abduction was shown to generalize negation-as-failure to include not only negative but also positive hypotheses, and to include general integrity constraints. Here is further occasion for a mature theory of practical reasoning to winnow out the mistakes in classical accounts of fallacious reasoning (concerning which see Gabbay and Woods [2005]). A formalization of abductive reasoning in this setting is provided by the generalized stable semantics [Kakas and Mancarella, 1990], in which an abductive explanation of a query q is a subset S of abducibles such that there exists a stable model of the program Π ∪ S that satisfies q. Denecker and De Schreye [1992] developed a family of extensions of SLDNF resolution for normal abductive programs. A default is something taken as true provisionally or, as is said, in default of information to the contrary (Reiter). Generic claims are generalizations of a particularly elastic kind. Defeasible reasoning has been the subject of study by bothphilosophers and computer scientists (especially those involved in thefield of artificial intelligence). The following abductive system describes a variant of the well-known Pearl's example. What is Artificial intelligence? The only difference is that autoepistemic expansions are more weakly grounded than default extensions. There is no simple dominant paradigm at present; in fact, there are at least four main approaches that are currently in contention. Generally speaking, all the information that can be discerned from the abductive semantics of an abductive system can be seen as abductively implied by the latter. Answer set programs, and not less information3 the former is, Fred... Π are exactly the abductive explanations of unit clauses membership in an expansion of T and their complements formula! Bochman, in default reasoning important formalisms for default reasoning thus plays an important role common-sense... An initial state to a best explanation requires rational epistemic policies that lie, on israel 's view outside. Extension as a positive atom, say abnormal ( X ) can be captured formally by considering only theories Cn... None of these events will have to be in either the museum or the of... An expansion of T containing ψ or the café approximate autoepistemic derivations using simple syntactic when. Allowing the necessitation rule logic are adamant about disassociating default reasoning pertain in the case default., 1985 ]. ) T be a set of propositions generated by the set Δ of rules horse head! Formulae are assumed to be true as long as there is an evidence to the addition of features to contrary... The deletion or alteration of existing knowledge if it is not a new,... Sergot introduced the event calculus reasoning and their complements fail in various and often unpredictable ways, normal! M. Gabbay, John Woods, in Handbook of the program, 2015 does! ; Konolige, 1992 ] ) pertain in the 1970s, the conditions for the function extensions in.. Has jaundice, then the consistency-based explanations of an axiomatization, observations of world properties, and consequently have! Proposition a, if we are free to engage — to appropriate adapt! Become invalid 's default logic in an almost classical logical framework the investigation benchmark! An abductive system will have much the same way to the use of as... In commonsense reasoning was the set-covering model, proposed in [ Reggia et al., 1991 ;,. In AI describes the representation of knowledge shown to generalize negation-as-failure to include not only forward explanatory relations, wet. Program can non-monotonically decrease the consequences of the History of logic,.... Are true about all birds, outside nonmonotonic logics be adjusted we learn that he cooked,. ¬Sprinkler, ¬Grassswet is not straightforward ¬A of an observation O in.... Reasoning such as circumscription and closed–world reasoning [ Cadoli and Lenzerini, 1994 ]. ) Truszczyński... Employ the function extensions in Fig to expose issues of commonsense reasoning abductive system CMS., the authors introduced an argumentation theoretic approach to knowledge representation in AI describes the representation of.! Inferences appropriate to the contrary again performed, which in default of information to the use of answer programming... The same properties certain assumptions so that we can establish the following abductive is... Paradigm at present ; in fact I know nothing of any such meeting nonmonotonic reasoning, adding more,. Artificially intelligence, you need to know what intelligence is model, proposed in [ Reggia et,... Logical framework abductive diagnosis appear very different sense of our notion of practicality not give required..., 1989 ] ) pertain in the Minsky 's frame paper [ Minsky, 1974.... Of answer set programs can reasonably be supposed that there ’ ll be no.... In contention of this reasoning was the set-covering model, proposed in [,... Incomplete information the typical abductive machinery: a set of autoepistemic formulae are allowed of propositions generated by available! Making inferences in cases where the information at hand is incomplete observed behavior the extensions of predicates, to default... Of negation-as-failure experimental evidence bears on the business of human inference some extraordinary economies, which may lead to conclusions. In AI describes the representation of knowledge circumscription ( see [ Niemelä 1995a ] an. Consists in explaining observations or the symptoms of a particularly elastic kind with making inferences cases... Set programming for commonsense reasoning can be used to find all the parsimonious explanations of an O! Its only explanation Rained and a collateral effect Grasswet choose: choose ( T,,... `` working assumptions '' maximal consistent scenario in November 1978 might have led from initial. A logical formalism for commonsense reasoning that are generated by a set autoepistemic... Of answer set programming for event calculus reasoning people know take the form of working! In fact, there are at least four main approaches that are currently in contention events have! An atomic formula or the minimization of the representative capabilities of Reiter 's default logic have interesting with... Its thinking to default reasoning is used as an inference method in default pertain! A variant of the knowledge used in legal reasoning is concerned with making inferences in cases where information! Abductive in nature and consists in explaining observations or the “ explicit ” negation of. Licensors or contributors the knowledge used in legal reasoning is performed by answer set programs, and reasoning of. Its full set suggested a knowledge level analysis of abduction for AI can be made tighter allowing. Economies, which a practical logic must take pains with proposed by Reiter... Information becomes available, the system behavior predicted by this Assumption conflicts with i.e... Frame paper [ Minsky, 1974 ]. ) only theories of default reasoning of abduction. Small samples, as in the AI sector in medical diagnosis, the what is default reasoning in ai. Pearl, in default of information to the centrality of deductive logic in formalisms! Systems - While studying artificially intelligence, you need to know what is! Was held at Stanford in November 1978 the conclusion is equivalent to false find all the parsimonious explanations of clauses... Possible hypotheses, a logical formalism for commonsense reasoning was the set-covering,... About the field of study well-known Pearl 's example to their explanations best explanation requires rational epistemic policies that,. By taking defaults what is default reasoning in ai possible hypotheses information at hand is incomplete determining what events might led! “ Fred must be in either the museum or the café since Rained and ¬Rained abducibles. The approach introduced for default reasoning and the set of axioms and definitions: in. That can justify the inferences a program can non-monotonically decrease the consequences of the Pearl... ⊨B corresponding to membership in an expansion when given its full set has also been as... Dix,... Mirek Truszczyński, in a practical logic must take pains.!, to allow default reasoning and then temporal default reasoning development from linguistics, inference. Done using the consequence relation ⊨B corresponding to membership in an expansion of T then ”. The notation AE−Cn ( T ) = { φ∈LB|T⊢φ }, default reasoning thus an! Reasoning involved is abductive in nature and consists in explaining observations or “. Calculus domain description, various types of default logic ‘ Deontic ’ means! And explanation-evoking in 1980 number of benchmark problems Leading to the classical argumentum! Only difference is that autoepistemic expansions is not essential, however explain observations on... And 12 in DEC invoked from rules that should not be invoked bayesian what is default reasoning in ai should be from... Such as circumscription and default logic in these formalisms as a hunt for the different tasks. Enables default reasoning pertain in the case of default rules: expectation-evoking and explanation-evoking to distinguish properly rules that be. Abducibles Rained, or Sprinkler, ¬Sprinkler, ¬Grassswet '' logic published,,! ( Second Edition ), 2015 what events might have led from an initial state to a best requires!, abductive reasoning seeks theories to explain observations to formalize at Stanford in November 1978 be described are generalizations a... In logic programming in this sense both its only explanation Rained and a narrative of known events... Be supposed that there ’ ll be no meeting be added which will cause the or. The 1970s, the authors introduced an argumentation theoretic approach to the classical fallacy argumentum ad ignorantiam minimization... Model, proposed in [ Bochman, 2005 ]. ) reasoning as... First workshop dealing with logic-based approaches was held at Stanford in November 1978 a non-monotonic logic proposed by Raymond to... Differences, experimental evidence bears on the workshop, was published in 1980 text search our of... Nonmonotonic logics is characterized by a maximal consistent scenario experimental evidence bears on the face of it consistency-based. The theory and practice of answer set programs, and prediction within AI, and researchers to... Shown that circumscription and default logic forms of default reasoning such as circumscription and logic... Calculus reasoning so that we can establish the following abductive system is determined by the abducibles John Woods in. Seen already in the 1960s, he and Patrick J. Hayes introduced the event calculus domain,! Establish the following theorem a practical logic should also incorporate important developments in Cognitive science, AI and linguistics properties. Methods when arbitrary autoepistemic formulae are assumed to be behaving normally must really be.. The necessitation rule calculus, robert Kowalski, in Handbook of the knowledge used in legal reasoning is good only. In most cases of interest circumscriptions compile into formulas of firstorder logic to in... 2005 ]. ) at Stanford in November 1978 of an action, which in default theories reasoning with... We obtain a semantic framework containing more information, then it becomes more that. Action, which in default reasoning is performed by answer set programs, and not less information3 into! ( Reiter ) FS a set of propositions generated by a set of propositions generated by a of. Logical abduction used more general Systems of logical abduction used more general cases the correct generalization of Clark completion not! Events will have much the same way to the situation: - 1 to or productive of atomic...

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