G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, Cambridge, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....results in demanding L i L L j L provided L j is later guessed than L i . Learning algorithms behaving thus are called monotonic. Weakening the strong monotonicity constraint in the same way as the monotonicity principle of classical logic is generalized to cumulativity (cf. e.g. Brewka [10]) yields weak monotonic learning, i.e. now the learner is required to behave strong monotonically as long as it does not receive data contradicting its actual guess (cf. Definition 2.3) All the models of monotonic learning share the common property that they model learning by generalization. ....

Brewka, G.: Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, Cambridge, (1991).

....work, default logic by Reiter [122] the family of circumscription type formalizations [92, 93] McDermott and Doyle style logics [96, 95] and autoepistemic logic [98] stand out as leading logical formalizations of nonmonotonic reasoning. The books of Etherington [26] Besnard [6] and Brewka [11] provide introductions to nonmonotonic reasoning. The aim of this work is to strengthen the theoretical foundations of symbolic nonmonotonic reasoning. For that purpose we strive for a framework where nonmonotonic reasoning can be analysed as sentences in some formal language with well defined ....

....set of premises are the sentences true in every minimal model of the original premises. There is obviously many different notions of a minimal model. Consequently, there is a large number of variants of circumscription starting from the work of McCarthy [92, 93] Etherington s [26] and Brewka s [11] books are good sources on circumscription. Statements of the type birds typically fly can be formalized using circumscription in terms of abnormality. A bird flies unless it is abnormal in some sense: 8x( b(x) ab(x) f (x) The idea is to minimize abnormality to only those objects which ....

G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, Cambridge, 1991.

....literature, yielding different classes of modal nonmonotonic logics. Although modal nonmonotonic logics have been extensively studied from a theoretical point of view (for a recent work discussing proof theoretical issues, cf. e.g. 1] besides some early attempts about implementational issues [4, 2, 21, 3], most of these approaches lack generally available solvers thus far. This despite the fact that recent years witnessed an increasing amount of successful implementations for various nonmonotonic formalisms, mostly for the answer set programming paradigm, as realised, This work was partially ....

G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, 1991.

.... is unsatisfiable only if P is unsatisfiable no (K6) U4) P P ) no (K7) U5) Bel( P; P [ P ) yes 5 (U6) Bel(P ) no implies Bel( P; P ) Bel( P; P is satisfiable, then no Bel(Bel( P; P ) P Table 1: Interpretation of Postulates (K1) K8) and (U1) U6) [10, 49, 8]. Revision with a new piece of information Q is accomplished by simply changing the epistemic state to P = P 1 ; P n ; Q) The change of the belief base is then automatically accomplished by the nonmonotonic semantics of a sequence of logic programs. Under this view, updating logic ....

G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge Tracts in Theoretical Computer Science, vol. 12. Cambridge Univ. Press, 1991.

....problems entailed here. 3.2 Advanced Logics Since we have mentioned the situation calculus and the frame problem, it is also worth noting that there is a group of logics that have been mainly developed to address this problem. These logics are referred to as nonmonotonic logics [Ginsberg, 1987, Brewka, 1991] Davis, 1990, section 3.1] The classic approaches here are Default Logic [Reiter, 1980] and Circumscription [McCarthy, 1980b, McCarthy, 1980a] However, as these approaches address the problem by changing the inference mechanism rather than fundamentally changing the representation, they are ....

Gerhard Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, Cambridge, UK, 1991.

....extensions. Many of these logics have been successfully implemented in artificial systems, such as the logic programming language PROLOG and a wide variety of expert systems (e.g. MYCIN for medical diagnosis, PROSPECTOR for geological prospection) Description of several systems and logics are in [BRE91, COR84, GIN87, LUK90, WAT86, WEB81]. Analogical, or similarity based reasoning can beneficially be used to complement deductive reasoning. In particular, when no rule exists that exactly matches a new situation, analogy may be used to attain a result. Analogical reasoning typically uses similarity with known situations to make ....

.... bottleneck in the AI community [LEN90, MCC84, SUN92] Much work has been expended in characterizing common sense [FOR89, LER92, LIF88, SUN92, WOL94] formalizing its representation [DAV90, HOB85, LIF90, ZLA90] constructing logics (or implementations thereof) powerful enough to handle it [BRE91, GOL93, 13 LUK90, REI80], and developing models dealing with it, or at least some meaningful subset of it [HOR90, YOU93, SUN92, SUN93] One of the challenges of commonsense reasoning is its non monotonicity. Informally, a reasoning protocol is non monotonic if the acquisition of new information causes the retraction or ....

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Brewka, G. (1991). Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press.

....quite independently of its logical (or connective dependent) rules. By tinkering with the structural rules we may obtain formal systems that are useful for different purposes. To mention two recent developments, computer scientists have studied formal systems that are deductively non monotonic ([7], 8] 10] 14] 20] 22] and [27] There, the motivation is to provide a formal representation of a certain pattern of common sense reasoning. Since ordinary reasoners may revise their views in light of new information, the conclusion an agent draws at a given time need not always increase ....

G. Brewka. Nonmonotonic Reasoning: Logical Foundations Of Commonsense. Cambridge University Press, 1991.

....again to all birds. In both situations, further experience must be allowed to alter the the truth of previously accepted facts, if a solution consistent with the real world is to be found. Humans use commonsense reasoning to deal with their partial representation of the open world (e.g. see [4, 19]) The need for an open world assumption is clearly a consequence of incrementality. If all the data relevant to the problem at hand is indeed available a priori, then the world may be assumed closed. Otherwise, there is a need for special learning mechanisms that invalidate portions of ....

G. Brewka, Nonmonotonic Reasoning: Logical Foundations of Commonsense, Cambridge University Press, 1991.

....logics. In this section we present a brief description of three of the original nonmonotonic formalisms and some of their descendents. There are many other varieties of nonmonotonic logic. Some are covered in the collection edited by Ginsberg [55] others may be found in the books by Brewka [14] and Besnard [13] or the recent special issue of the Journal of Applied Non Classical Logics [22] One of the rst nonmonotonic systems to be proposed was Reiter s default logic. This augments standard rst order logic with a set of default rules which explicitly state what assumptions may be ....

Brewka, G. (1991) Nonmonotonic reasoning: logical foundations of commonsense, Cambridge Trends in Computer Science 12, Cambridge University Press. IEEE Transactions on Knowledge and Data Engineering, 8(3):353|372. 35

....in general, it holds if P 0 contains a single rule. Thus, all of the above postulates except (C4) fail, and, with the exception of (C3) each change is given by a single rule. We can view the epistemic state P = P 1 ; P n ) of an agent as a prioritized belief base in the spirit of [10, 46, 8]. Revision with a new piece of information Q is accomplished by simply changing the epistemic INFSYS RR 1843 00 08 15 POSTULATE INTERPRETATION POSTULATE HOLDS (K1) P; P ) represents a belief set yes (K2) U1) P Bel( P; P ) yes (U2) Bel(P ) Bel(P) implies Bel( P; P ) Bel(P) no (K3) ....

G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge Tracts in Theoretical Computer Science, vol. 12. Cambridge Univ. Press, 1991. INFSYS RR 1843-00-08 57

....In the logical paradigm, McCarthy s Circumscription [McC80] is one of the first major nonmonotonic reasoning tools. Since its debut, the nonmonotonic reasoning line of work has expanded and several textbooks now exist that give a fair view of nonmonotonic reasoning and its uses (e.g. [Bre91], Ant97] BDK97] DG94] San94] Sha97] The motivations for nonmonotonic reasoning vary from formalizing Common Sense reasoning through Elaboration Tolerance and representation of uncertainty to Belief Revision. We do not expand on these motivations further here, and the reader may look at ....

Gerhard Brewka. Nonmonotonic Reasoning: Logical Foundations of Common Sense. Cambridge University Press, 1991.

....that, even if one starts with normal defaults (as in our example) one ends up with semi normal defaults when realizing priorities this way. But this means that one has to face the undesirable properties of non normal defaults, such as non existence of extensions. As an additional problem, Brewka [6] points out that whenever additional knowledge requires blocking of a default, the default has to be rewritten. 8 3.2 Prioritized default theories In order to avoid the introduction of semi normal defaults, Brewka [6] takes the ideas underlying prioritized circumscription [10] and defines an ....

....such as non existence of extensions. As an additional problem, Brewka [6] points out that whenever additional knowledge requires blocking of a default, the default has to be rewritten. 8 3. 2 Prioritized default theories In order to avoid the introduction of semi normal defaults, Brewka [6] takes the ideas underlying prioritized circumscription [10] and defines an iterated version of default logic, which he calls prioritized default logic (PDL) Instead of one set of defaults he takes a finite number of sets D 1 ; D n of closed defaults, with the intended meaning that ....

G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, Cambridge, 1991.

.... different researchers have put forward different proposals, with different applications in mind, including database dynamics [1] reason maintenance systems [6, 7] reasoning about actions [14, 39] belief change in a static world [9] belief change in a dynamic world [23] and nonmonotonic logics [5, 24], to mention only a few. An approach to rational belief change that has influenced much of this discussion is the AGM model [2] In the AGM model, a belief state (epistemic state) is represented as a belief set (i.e. as a set of sentences K closed under the consequence operation of a suitable ....

Brewka, G, Nonmonotonic Reasoning: Logical Foundations of Commonsense, CUP, 1991.

....by priority. A default with more important priority overrides a conflicting default of less important priority: from the point of view of the later the more important default is evidence to the contrary . Axioms are formulas that cannot be overridden. Prioritized defaults have been introduced in [10] and further studied in [5, 4, 26, 27] Their impact in specification is stated in [7, 9] This structure of axioms and prioritized defaults (and the corresponding semantics) has been used to model di#erent database completions (see [6, 3] the frame rule (see [10, 8] and the taxonomic ....

.... have been introduced in [10] and further studied in [5, 4, 26, 27] Their impact in specification is stated in [7, 9] This structure of axioms and prioritized defaults (and the corresponding semantics) has been used to model di#erent database completions (see [6, 3] the frame rule (see [10, 8]) and the taxonomic structure of classes and subclasses (see [26, 27, 28] The operation of adding new information at a new most important priority level (recall the specification of reserved books) is a belief revision ( 18, 17] operator (see [26] Axioms and prioritized defaults are the ....

G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, 1991.

....of a set of premises to those premises should not change the derivable formula. Default logic has been shown not to exhibit this logically desirable property (Makinson, 1989) Default logic also cannot handle arbitrary new information in a way that guarantees that a belief set remains consistent (Brewka, 1991): we must know in advance where the exceptions are going to arise and code these in the logic, i.e. we cannot, as in the path based approach, add new exceptions as they come along. A third problem, and perhaps the most damning in the eyes of AI researchers, 2 is that DL cannot by itself signify ....

Brewka, G. (1991). Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press.

....own purposes. Users of the stand alone version should have general experiences with computers and programming. Knowledge about predicate logic, rule based systems, and principles of represenation may be helpful. Introductions to these topics are [Genesereth and Nilsson, 1987] and [Richter, 1989] [Brewka, 1990] and [Schaub, 1990] are surveys of default reasoning. If Except is used as a submodule of own programs then Lisp experiences are required. 1.3 About this Report This report describes the features of Except II, how it works, and how to use it. We have tried to keep the report simple and ....

G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Common Sense. Cambridge University Press, Cambridge, UK, 1990.

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G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, Cambridge, 1991.

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Gerhard Brewka. Nonmonotonic Reasoning: Logical Foundations of Common Sense. Cambridge University Press, 1991.

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G. Brewka. Non-monotonic Reasoning: Logical Foundations of Commonsense. Cambridge Tracts in Computer Science. Cambridge University Press, 1991.

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G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, Cambridge, 1991.

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G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, 1991.

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G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, Cambridge, 1991.

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G Brewka. Non-monotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, 1991.

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G. Brewka, Nonmonotonic Reasoning: Logical Foundations of Commonsense, (Cambridge University Press, Cambridge, 1991).

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G. Brewka. Nonmonotonic reasoning: logical foundations of commonsense. Cambridge University Press, Cambridge, UK, 1991.

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