Nebel, B. (1991) Belief Revision and Default Reasoning: Syntax-Based Approaches, Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning, pp. 417-428.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....is that the syntactic form in which a knowledge base is expressed can be important. For example, some semantics for knowledge base revision depend on the syntax of knowledge bases. If a knowledge base is replaced with an equivalent one, even a single update can lead to a completely di erent result [6, 13]. Problem Complexity Checking irredundancy NP complete A set is an i.e.S. D complete Existence of an i.e.S. of size k A clause is in all i.e.S. s NP complete A clause is in an i.e.S. Uniqueness of i.e.S. s 2 [log n] complete Table 1. The complexity results proved in this ....

B. Nebel, `Belief revision and default reasoning: Syntax-based approaches', in Proc. of KR'91, pp. 417-428, (1991).

....first order language instead of adding some specific non classical rules. There is a disadvantage of Poole s approach, however, that it does not allow to rep resent priorities between defaults. Brewka s preferred sub theories developed in [2, 5] have efficiently overcome this shortage. Nebel [3] combined both approaches of Poole and Brewka, and developed a system for default reasoning, called ranked default theory (RDT) As a very important result, Nebel established a relation between RDT and revised belief revision (called prioritized base revision) which strengthened Makinson and ....

....a set S Sx U . U S, where for all k (1 k n) Sx U . U S is a maximal consistent subset of Tx U . U T. The deductive closure Cn(S) of S is called an extension of T. It is easy to see that Poole s system is a special case of Brewka s, where n 2. 1. 4 Nebel s Generalization Nebel [3] combined both approaches of Poole s and Brewka s, and obtained a common generalization. A ranked default theory (RDT) is a pair A (D, F) where D is a finite sequence (Dx, D, of finite sets of propositions treated as ranked defaults and F is a finite set of propositions interpreted as ....

Bernhard Nebel. Belief revision and default reasoning: Syntax-based approaches. In Principles of Knowledge Representation and Reasoning, Proceedings of the Second International Conference, Allen J Aet al. (eds.), Morgan Kaufmann, 1991, pp.417-428.

....operations obtained from a given infobase. Notwithstanding these advances, much still needs to be done. Two obvious extensions that still needs to be developed has already been hinted at by Meyer et al. 13] Both involve the introduction of orderings of epistemic relevance in the spirit of Nebel [16, 17, 18]. It also remains to be seen how baisc infobase change fits into a more general theory of base change. Bibliography [1] Carlos E. Alchourr6n, Peter G irdenfors, and David Makinson. On the logic of theory change: Partial meet functions for contraction and revision. Journal of Symbolic Logic, ....

Bernhard Nebel. Belief revision and default reasoning: Syntax-based approaches. In James Allen, Richard Fikes, and Erik Sandewall, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference KR '91, pages 417-428. Morgan Kaufmann, San Francisco, California, 1991.

....line, Goldszmidt and Pearl [16, 49] have shown that implementation and characterization issues in belief revision can be realized through default knowledge. We refer to [16, 49] for more details. On the complexity side, a number of different revision approaches have been characterized, see e.g. [71, 76, 72, 64, 73]. In particular, the following reasoning problem has been considered there: Given a knowledge base, consisting of a set T of classical formulas, and classical formulas and , is it the case that is true in T after revision by This is also known as the Ramsey Test for conditional statements of ....

B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In Proc. 2nd International Conference on Principles of Knowledge Representation and Reasoning (KR-91), Cambridge, MA, pp. 417--428. Morgan Kaufmann, 1991. 61

....all formulae in L. This rather idealistic modelling of epistemic states may best be viewed as the agent s doxastic commitment to full recognition of the truth of the deductive consequences of what it believes (see Levi [65] p. 8) A lot of attention has also been paid to the study of belief bases [30, 42, 80, 85]; sets of formulae that are not necessarily closed under the logical consequence operation. Given any consistent belief set K, there are three types of epistemic attitude toward a sentence ff: i) ff is accepted (or believed) if ff 2 K (ii) ff is rejected (or not believed) if :ff 2 K (iii) ff ....

.... even further, showing that, for a finite propositional language, a mathematical definition of a coherence revision operator based on Katsuno and Mendelzon s [58] version of the AGM and a definition of a foundational revision operator motivated by syntax based approaches to belief revision (see [70, 85], for example) lead to identical classes of revision operators. This result, however, only shows the equivalence of operators satisfying the definitions given and leaves open the connection between coherence and foundational theories in general. Moreover, one must keep in mind that these theories ....

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Bernhard Nebel. Belief revision and default reasoning: Syntax based approaches. In Peter G ardenfors, editor, Belief Revision, pages 52--88. Cambridge University Press, 1992.

.... 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 ....

B. Nebel. Belief Revision and Default Reasoning: Syntax-Based Approaches. In J.F. Allen, R. Fikes, and E. Sandewall, editors, Proc. Second International Conference on Principles of Knowledge Representation and Reasoning (KR'91), pages 417--428. Morgan Kaufmann, 1991.

....becomes crucial in choosing one formalism instead of another to represent the knowledge. Another important aspect of nonmonotonic reasoning is that we have to deal with uncertain and or incomplete information. Several criteria for updating and or revising a knowledge base have been proposed [1, 11, 12, 18, 21, 22, 24]. Suppose we have a knowledge base T and a new piece of information, represented by a formula P , is given. It might be the case that T and P are not consistent. In this case the revision of T with P , denoted as T ffi P , contains those models of P dened by means of a belief revision operator ....

B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In Proc. of KR-91, pages 417428, 1991.

....of whether there is a counterpart contraction in nonmonotonic logic. Keywords: nonmonotonic logic, default reasoning, belief revision 1 Introduction Reiter s default logic ( 1] is one of the most well developed system of nonmonotonic reasoning. A number of variants of default logic ( 2][3][4] etc. have been developed in past several years. Poole s approach ( 4] is simple This work was supported by the National Natural Science Foundation of China (69785004) and the Science and Technology Funding for the Youth of Jiangsu Province. 1 and natural. In his system facts and ....

....rst order language instead of adding some speci c non classical rules. There is a disadvantage of Poole s approach, however, that it does not allow to represent priorities between defaults. Brewka s preferred sub theories, developed in( 2] 5] have eciently overcome this shortage. Nebel in [3] combined both approaches of Poole and Brewka, and developed a system for default reasoning, called ranked default theory(RDT) As a very important result, Nebel established a relation between RDT and revised belief revision (called prioritized base revision) which strengthened Makinson and ....

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Bernhard Nebel, Belief revision and default reasoning: syntax-based approaches, in: J. A. Allen, R. Fikes, and E. Shndewell (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the second International Conference, (Morgen Kaufmann, 1991), 417-428.

....of the theories, i.e. T #G P = Q i# for all T # # W (T, P ) T # # P = Q. In other words, Ginsberg considers all sets in W (T, P ) equally plausible and inference is defined skeptically, i.e. Q must be a consequence of each set. A more general framework has been defined by Nebel in [Neb91]. Here we do not analyze his definitions. WIDTIO. Since there may be exponentially many new theories in T # G P , a simpler (but somewhat drastical) approach is the so called WIDTIO (When In Doubt Throw It Out) which is defined as T # W id P . #W (T, P ) # P [Win89] Note that ....

B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In Proceedings of the Second International Conference on the Principles of Knowledge Representation and Reasoning (KR'91), pages 417--428, 1991.

....entailment, and then, conclude only the sentences which are in the intersection of all the closures. Many semantics use this cautious principle. This includes notably the framework of Rescher and Manor [26] which has been recommended in the areas of belief update [13] belief base revision [16,24], and combined knowledge [2,17] If all pieces of information in the environment are equally reliable, this principle can be specified by a mapping 4, which we call cautious scheme, from finite sets of sentences of LW to sentences of LW and defined as follows: 4(A) T max(fB A : B is ....

....as follows: A j= p OE iff 4 p (A) j= OE: 4.2 Approximate reasoning Now, we turn to the formalization of approximate reasoning. From this point of view, it is interesting to notice that cautious reasoning, possibly prioritized, corresponds neatly to revising a knowledge base, in the sence of [16,24], with the sentence true , which indeed eliminates inconsistency. However, it has been recently proved that deciding whether a sentence belongs to such a revised knowledge base is a Pi P 2 complete problem in the propositional case [11] In other words, it seems impossible to solve it by a ....

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B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In J. Allen, R. Fikes, and E. Sandewall, editors, Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning, pages 417--428, San Mateo (CA), 1991. Morgan Kaufmann.

....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) ....

B. Nebel. Belief Revision and Default Reasoning: Syntax-Based Approaches. In Proc. Second International Conference on Principles of Knowledge Representation and Reasoning (KR'91), pages 417--428, 1991.

....the ordering on single defaults defined in [12] one obtains the lexicographic closure presented in this paper. Its computational complexity has been studied in [2] and [9] it is in Delta p 2 and is NP hard and co NP hard. The lexicographic closure is a syntactic construction in the sense of [14], i.e. it is sensitive to the presentation of the default information. 3 Nonmonotonic Reasoning 3.1 The Rational Enterprise We shall briefly summarize [8] and [12] and set up the stage. This section was prepared in collaboration with David Makinson. Some nonmonotonic inference relations are ....

Bernhard Nebel. Belief revision and default reasoning: Syntax-based approaches. In J. Allen, R. Fikes, and E. Sandewall, editors, Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning, pages 417--428. Morgan Kaufmann, 1991.

....initial one. A redundant formula can be detected by checking if it can be deduced by the rest of the schema. A minimal equivalent schema of a given schema can be found by removing redundant formulas until no more redundant formulas are left. Syntax based approaches for updating logical theories [16, 15, 21] are very popular because of their conceptual simplicity. When updating a schema S with a schema formula f (update formula) with respect to these approaches, the maximal subsets of the schema that do not imply the update formula in the case of a deletion (or the negation of the update formula in ....

B. Nebel. Belief revision and default reasoning: syntax based approaches. In Proc. of the Second Intl. Conf. on Principles of Knowledge Representation and Reasoning, pages 417--428, 1991.

....line, Goldszmidt and Pearl [16, 49] have shown that implementation and characterization issues in belief revision can be realized through default knowledge. We refer to [16, 49] for more details. On the complexity side, a number of different revision approaches have been characterized, see e.g. [71, 76, 72, 64, 73]. In particular, the following reasoning problem has been considered there: Given a knowledge base, consisting of a set T of classical formulas, and classical formulas and , is it the case that is true in T after revision by This is also known as the Ramsey Test for conditional statements of ....

B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In Proc. 2nd International Conference on Principles of Knowledge Representation and Reasoning (KR-91), Cambridge, MA, pp. 417--428. Morgan Kaufmann, 1991. INFSYS RR 1843-00-06 61

....processes by offering a language and its semantics for representing information and axioms for characterizing the correct reasonings. And, in the context of beliefs modelling, many logical approaches have been proposed for reasoning with beliefs that one or several agents have about a situation [5], 6] 7] 8] 9] 10] 11] So, it is pertinent to point out the relations between, on the one hand, the numerical method for data fusion suggested by Dempster and, on the other hand, the logical methods suggested by logician people. We think that the first step is to reformulate the Theory ....

B. Nebel. Belief revision and default reasoning : syntax-based approaches. In Second conference on Principles of knowledge representation and reasoning, 1991.

....set of formulas (called belief base, whose deductive closure is called published in Proc. of AAAI 96, American National Conference on Artificial Intelligence, Portland, Oregon, August 4 8, 1996, pp. 550 555 belief set) and can be roughly classified into two types: the syntax based approach [9, 13] and the semanticsbased approach [4, 9] The syntax based approach to belief base revision selects set inclusion maximal subsets of a belief base that do not allow for the derivation of the negation of the new sentence. The semanticsbased approach to belief base revision operates on models of ....

Nebel, B., Belief revision and default reasoning: Syntax-based approaches, Proc. of KR'91, 1991

....to p. The second alternative causes s to be true in addition to p. In addition, both alternatives cause q to be true. It is not possible to come up with a belief revision semantics that would allow us to identify, in all situations, which of the two alternatives in the above example is better [AGM85, Dal88, EG92, FKUV86, Gar88, Gra91, KM91, Mar91, MS86, Neb91, RdK87, Win90]. So, normally we are forced to make a choice and almost all the update mechanisms proposed in the literature make a choice or leave it to the user to make a choice, where s he may have no way of knowing apriori which is the correct choice [BKSW91, Dec90, GL90, KM90, RB92, SI91, Tom88, TA91, ....

B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In Proc. KR'91, pages 417--428, 1991.

....and Kuper [11, 10] which is one of the most important methods for updating logical databases. This method was later used in AI by Ginsberg, who demonstrated the relevance of counterfactual reasoning to a number of AI and knowledge base applications in [14] The reader is referred to this and [10, 12, 19, 37, 23, 16] for a background. The complexity of evaluating counterfactuals over propositional knowledge bases, i.e. finite propositional theories, was considered in [23, 16, 9] For the method of Fagin, Ullman, and Vardi, evaluation was shown to be Pi P 2 complete [23, 9] In the present paper we deal ....

....counterfactual reasoning to a number of AI and knowledge base applications in [14] The reader is referred to this and [10, 12, 19, 37, 23, 16] for a background. The complexity of evaluating counterfactuals over propositional knowledge bases, i.e. finite propositional theories, was considered in [23, 16, 9]. For the method of Fagin, Ullman, and Vardi, evaluation was shown to be Pi P 2 complete [23, 9] In the present paper we deal with nested counterfactuals over propositional knowledge bases, i.e. counterfactuals where the premise or the conclusion can be a counterfactual itself instead of a ....

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B. Nebel. Belief Revision and Default Reasoning: Syntax-Based Approaches. In Proceedings KR-91, pages 417--428, 1991.

....12 on the extensional part of the KB. Both of these updates satisfy the integrity constraints. However, only the first update satisfies the integrity constraints if we are given the further update insert mother(Joan; Bob) The general problem of belief revision has been studied formally in [42, 91, 92, 21]. Gardenfors proposes a set of axioms for rational belief revision containing such constraints on the new theory as no change should occur to the theory when trying to delete a fact that is not already present and the result of revision should not depend on the syntactic form of the new data . ....

....be integrated with improvements of the abductive 63 proof procedure considered in isolation. We have seen that the process of belief revision also needs to be considered within a KA context. In particular, it could be useful to investigate relationships between the belief revision frameworks of [21, 42, 91, 92] and various integrity constraint checking and restoration procedures. The extension of logic programming to include integrity constraints is useful both for abductive logic programming and for deductive databases applications. We have seen, however, that for many applications the use of ....

Nebel, B., Belief revision and default reasoning: syntax-based approaches. Proc. 2nd International Conference on Principles of Knowledge Representation and Reasoning, Cambridge, Mass. (1991) 417--428

....Minimality of Change which states that the knowledge base should change as little as possible if new information is incorporated. In this paper we deal with the following methods of updating knowledge bases: Ginsberg s approach [19] also considered by Fagin, Ullman, and Vardi [13] and by Nebel [44, 45], An extended abstract of this paper appeared in the proceedings of the Eleventh ACM SIGACTSIGMOD SIGART Symposium on Principles of Database Systems, San Diego, CA, June 2 4, 1992. y Mailing address: Paniglgasse 16, A 1040 Wien, Austria. Internet e mail: ....

....of changing knowledge bases. Moreover, it is now widely believed that there is no general purpose, domain independent means of updating knowledge bases that will do the right thing under all circumstances [58] As pointed out by Katsuno and Mendelzon [30] as well as by various other authors [58, 45, 23], an important problem to explore is the computational complexity of the different approaches. Note that though all methods are clearly intractable in the general case for almost all of the cited methods a precise determination of the complexity was left as an open issue. Furthermore, it was ....

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B. Nebel. Belief Revision and Default Reasoning: Syntax-Based Approaches. In Proceedings KR-91, pages 417--428, 1991.

....have been proposed in the literature which handle inconsistent update knowledge appropriately. This makes those methods applicable for evaluating counterfactuals, which are conditional statements of the form if F , then G , where F is assumed to be false in the current knowledge base [30] Nebel [53] and Eiter and Gottlob [22] have shown that for almost all update operators ffi, deciding whether a knowledge base T updated, according to ffi, with formula F implies the formula G is Pi P 2 complete or mildly harder. Closed World Reasoning and Circumscription. Eiter and Gottlob [21] have ....

B. Nebel. Belief Revision and Default Reasoning: Syntax-Based Approaches. In Proceedings KR-91, pages 417--428, 1991.

....reasoning is nonmonotonic in the sense that by augmenting the knowledge base a previously valid counterfactual may become false. The relevance of counterfactual reasoning to a number of AI applications was first demonstrated in [ Ginsberg, 1986 ] to which (and to [ Gardenfors, 1988; Nebel, 1991; Grahne, 1991 ] the reader is referred for a background. In this paper we mainly deal with nested counterfactuals, i.e. counterfactuals where the conclusion can be a counterfactual itself instead of a plain propositional This is a short version containing only proof sketches. An extended ....

....results we will derive for nested counterfactuals are equally relevant to the problem of inferencing after iterated knowledge base revisions. The complexity of evaluating unnested counterfactuals over propositional knowledge bases, i.e. finite propositional theories, was considered in [ Nebel, 1991; Grahne, 1991; Eiter and Gottlob, 1992 ] In this paper, we deal with evaluating nested counterfactuals based on Ginsberg s approach [ Ginsberg, 1986 ] which uses the method by Fagin, Ullman and Vardi [ Fagin et al. 1983 ] for incorporating changes to a knowledge base. Such statements ....

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Bernhard Nebel. Belief Revision and Default Reasoning: Syntax-Based Approaches. In Proceedings KR-91, pages 417--428, 1991.

....Bob) on the extensional part of the KB. Both of these updates satisfy the integrity constraints. However, only the rst update satis es the integrity constraints if we are given the further update insert mother(Joan; Bob) The general problem of belief revision has been studied formally in [42, 91, 92, 21]. G ardenfors proposes a set of axioms for rational belief revision containing such constraints on the new theory as no change should occur to the theory when trying to delete a fact that is not already present and the result of revision should not depend on the syntactic form of the new data . ....

....to be integrated with improvements of the abductive proof procedure considered in isolation. We have seen that the process of belief revision also needs to be considered within a KA context. In particular, it could be useful to investigate relationships between the belief revision frameworks of [21, 42, 91, 92] and various integrity constraint checking and restoration procedures. The extension of logic programming to include integrity constraints is useful both for abductive logic programming and for deductive databases applications. We have seen, however, that for many applications the use of ....

Nebel, B., Belief revision and default reasoning: syntax-based approaches. Proc. 2nd International Conference on Principles of Knowledge Representation and Reasoning, Cambridge, Mass. (1991) 417-428

....update operations choose the one that retains as many of the high priority formulae as possible. Database updates are a simple special case of the problem of updating arbitrary sets of e.g. rst order formulae. This problem is considered in the research of belief revision [ G#rdenfors, 1988; Nebel, 1991 ] In diagnostic reasoning, for example in expert systems for medical diagnosis or diagnosing faults in electronic equipment, the possible causes of a fault can be ordered on the basis how likely they are. When such priority information is available, it is often sensible to compute only the ....

.... priorities reasoning with prerequisite free normal default rules and Horn clauses is NP complete [ Stillman, 1990 ] A class of belief revision problems very closely related to the above class of formulae (without the restriction to Horn clauses) is one of the special cases investigated by [ Nebel, 1991 ] in which his belief revision system satises all eight AGM postulates. 4 Prioritized autoepistemic logic and other nonmonotonic formalisms In this section we compare our prioritized autoepistemic logic to other approaches to nonmonotonic reasoning that either use some kind of preferences in ....

Nebel, B.: Belief revision and default reasoning: Syntax-based approaches. In J. Allen, R. Fikes, and E. Sandewall, editors, Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning, pages 417428, Cambridge, MA, 1991. Morgan Kaufmann Publishers.

....theory is always taken to be monotonic, and nonmonotonicity is introduced through the semantics of the revision and contraction operators. In our exposition of Elaboration Tolerance we explicitly allowed our base theory to be nonmonotonic. The work on syntactic forms of Belief Revision (e.g. Nebel, 1991 ] has mostly focused on Theory Base Change [ Fagin et al. 1983 ] and the information that can be elicited from the syntactic form of the theory. Some authors interested in syntactic Belief Revision and Inductive Logic Programming and especially Theory Revision Re nement (see [ Abiteboul, 1988 ....

B. Nebel. Belief revision and default reasoning: syntax-based approaches. In kr91, pages 417-428. MK, SF, 1991.

....the generalized framework. 3 Nebel (1992) also give a similar result. He give a relationship between RDT with constraints and prioritized removal operation. See [10] page 77 78 for the detail) 10 5 Related Work and Conclusion As mentioned above, there are several literatures ( 2] 4] 5] 8] [9] [13] discussing about the relationships between nonmonotonic reasoning and belief revision. In [8] Makinson and Gardenfors investigated the relations between belief revision and nonmonotonic logic. They tried to translate the membership in belief revision,y 2 K x, into the inference relation ....

Bernhard Nebel, Belief revision and default reasoning: syntax-based approaches, in: J. A. Allen, R. Fikes, and E. Shndewell (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the second International Conference, (Morgen Kaufmann, 1991), 417-428.

....rules (such as those introduced by [15, 12] Results are discussed in the conclusion. 2 Syntax Based Consequence Relations Throughout the paper, E denotes a non empty finite set of propositional formulae and is referred to as the belief base. The belief base is considered syntactically, as in [17]: each belief is a distinct piece of information and only beliefs which are explicitely present in the base are taken into account. It departs from the logical point of view where a base is identified with the set of its models. Due to the belief status of its elements, E is not assumed to be ....

....study, m belongs to fT, INCL, LEX, BOg and p belongs to fUNI, EXI, ARGg. More generally, we will consider non monotonic consequence relations of the form Phi is inferred from Psi with respect to E . Followingprevious works on the relationship between non monotonicinference and belief revision [17, 12], we define: Definition 4 Psi j p;m E Phi iff Psi Phi E j p;m Phi, where Psi Phi E denotes the prioritized belief base obtained from E by adding f Psi g as first stratum. More precisely, if E is stratified into (E 1 ; En ) then Psi Phi E = E 0 = f Psi g; E 1 ; En ) ....

Bernhard Nebel. Belief revision and default reasoning: Syntax-based approaches. In Proc. of the 2 nd KR, pages 417--428, Cambridge, MA, 1991. Morgan-Kaufmann.

....letters a, b, represent formulas. Let be a multiset of formulas (the same formula may be present several times) possibly inconsistent but not deductively closed. Cn( denotes the deductive closure of . When the multiset is not deductively closed, we call it a belief base , following Nebel (1991). A formula in is called a belief . Each piece of information, or belief can be seen as supplied by some expert and is self justifying. Beliefs are distinguished from plausible conclusions which are derived from beliefs. Definition 1: A sub base A of is said to be minimal inconsistent ....

Nebel B. (1991) Belief revision and default reasoning: Syntax-based approaches. Proc. of the 2nd Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR'91) (J.

....in this paper are flat, which means that all formulas in have the same reliability. In the following, sub(multi)sets of are denoted by capital letters A,B,C, They will be called subbases of . When the knowledge base is not deductively closed, we call it a belief base , following Nebel (1991), while bases which are deductively closed are called belief sets after G rdenfors (1988) Our view of a belief base is syntactic in the sense that, for instance, f is not the same as = f, f . A formula in is called a belief because it represents a proposition taken for granted, ....

B. Nebel (1991) Belief revision and default reasoning: syntax-based approaches. Proc. of the 2nd Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR'91) (J. Allen, R. Fikes, E Sandewall, eds.), April 22, Morgan & Kaufmann, Cambridge, MA, pp. 417-428.

....results. In the literature some other belief revision update operators have also been proposed. Most of them work on a finite set of formulas, called belief base, instead of infinite belief set 1 , and can be roughly classified into two types 2 : syntax based approach , e.g. Gin 86, Nebel 91] and semantics based approach , e.g. Dalal 88, Win 88] The essential idea of syntax based approaches to belief base revision is similar to the partial meet revision of [AGM 85] It selects set inclusion maximal subsets of a belief base that do not allow for the derivation of the negation of ....

....work with the possible worlds approach PWA, and the possible models approach PMA. 5.1 The possible worlds approach The possible worlds approach (PWA) Gin 86] is a representative of syntaxbased approaches to belief base revision updates. Other similar approaches can be found in, e.g. FUV 83, Nebel 91] Its basic idea is as follows: The belief base of a belief set is taken as the representation of an epistemic state, and incorporation of new belief is done at the syntax level of the belief base by taking the union of the new belief and a selected subset of the belief base which does not ....

Nebel, B., Belief revision and default reasoning: Syntax-based approaches, in: Allen. J., Fikes, R., and Sandewall, E. (eds.), Proc. of the 2nd Internat. Conf. on Principles of Knowledge Representation and Reasoning, 1991

....preferred sub theories. In order to discriminate between the consistent subsets of KB, the selection criterion generally makes use of uncertainty considerations by using explicitly uncertainty measures [Wilson93, Benferhat al95] or by using measures expressing priorities [Rescher64, Brewka89, Nebel91, Benferhat al93, Lehmann92] for a more detailed description of this kind of approach see [Cayrol Lagasquie95] These approaches consist in ranking the KB into priority levels (these levels are often supposed given by an expert (except in Pearl s system Z [Pearl90] where an automatic technique ....

B. Nebel. Belief revision and default reasoning: syntax-based approaches. In Proc. of the 2nd KR, p. 417-428. Cambridge, MA, 1991.

....8 Knowledge Assimilation In addition to physical actions by its effectors, our SICLE agent can assimilate new knowledge which is acquired by its sensors. There have been many proposals for knowledge assimilation or belief revision and update, e.g. the AGM theory [1] syntax based approaches [6, 13], and semantics based approaches [21] In SICLE, our situated agents adopt a divide and conquer strategy to knowledge assimilation. First, all predicates and fluents are classified into following categories: i) Fluents that can be changed only by the agent itself; ii) Fluents that can be changed ....

Nebel, B., Belief revision and default reasoning: Syntax-based approaches, Proc. of KR'91, 1991

....operators satisfying the AGM postulates give intuitively undesirable results. In the literature, some other belief revision update operators have been proposed to solve practical problems. These belief revision update operators can be roughly classified into two types: the syntax based approach [6, 10] and the semantics based approach [3, 11] The syntax based approach selects set inclusion maximal subsets of K that do not allow for the derivation of the negation of the new sentence. The semantics based approach selects those models satisfying the new sentence and differing minimally from the ....

Nebel, B., Belief revision and default reasoning: Syntax-based approaches, Proc. of KR'91, 1991

....for computing the modified theory in the context of different methods and in restricted cases of the problem [14, 5, 26, 28, 4, 6] The computational complexity of every approach is an important problem. All methods are clearly intractable [13] in the general case even for propositional languages [28, 23, 8]. In the framework presented above, it seems important to investigate under which restrictions tractability can be obtained for the various approaches proposed and which are the frontiers between tractability and intractability. Relaxing the initial problem with restrictions in order to achieve ....

....revision is a set of theories. The second approach satisfies the principle of the uniqueness of the resulting theory and it was first introduced as an approximation solution to the set of theories approach providing a lower bound to the formulas deduced by the modified KB. Syntax based approaches [10, 9, 14, 22, 23] have been very popular because of their conceptual simplicity. The complexity of the implication problem of the modified KB, given KB and a modification, in the propositional case is addressed, in [8] It is shown that tractability can be obtained in model based methods, if combined restrictions ....

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B. Nebel. Belief revision and default reasoning: syntax based approaches. In Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning, pages 417--428, 1991.

....of consequence relations, called ranked consequence operators. Each member of this class generates a rational ordering, and conversely, hence the class of ranked consequence relations coincides with that of rational inference. Also, we show how previous default logic systems in the literature ([18], 19] reduce to our framework. The above results pave the way towards a study of nonmonotonicity through orderings of formulas, allow us to translate previous work in belief revision into the context of nonmonotonic reasoning, and provide a framework for designing default systems obeying ....

....to conjunctions, disjunctions, and conjunctions, respectively. A study of the above default systems under the assumption of finite language, has been carried already in the context of belief revision (therefore, assuming consistency preservation, in addition to finite language) by Nebel ([18], 19] Our strict and liberal extensions are called prioritized and linear base revision, respectively. Also, Nebel showed in [19] that deciding if a certain formula is contained in the strict or in a liberal extension (that is, deciding ff fi) is P NP[O(log c n) and P NP[O(n) ....

B. Nebel. Belief revision and default reasoning: Syntax based approaches. In J. A. Allen, R. Fikes, J. R. Levesque, and R. Reiter, editors, Proceedings of The Second International Conference on Principles of Knowledge Representation and Reasoning (KR 91), pages 301--

....This research is partially supported by the NSERC grants OGP42193 and OGP9225. This paper appears in the Proceedings of the Third International Conference on Deductive and Object Oriented Databases, LNCS vol. 760, papers 444 458, 1993. 2 Li Yan Yuan and Jia Huai You sentences (see, for example, [13, 7]) where both the representation and the semantics of knowledge systems are defined by the same set of logic sentences. It has been noticed that this approach, though provides a unified point of view on knowledge systems, lacks retrospective power 1 , the main reason for its not being able to ....

....the FUV semantics) which takes the disjunction of all such candidate theories. As indicated in [7] the FUV semantics is syntax dependent and therefore fails to satisfy the AGM postulates. The revision problem over a theory in its syntactic form other than its closure is discussed by Nebel [13], where it is called base revision. Nebel discovered that base revision with epistemic relevance does not satisfy all of the AGM postulates and identified the cases where they are satisfied. Belief revision in its essence is a meta level concept and operation. Therefore, it is natural to use some ....

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B. Nebel. Belief revision and default reasoning: Syntax-based approaches. KR'91, pages 417--428, 1991.

....The symbol ; represents the classical consequence relation, Greek letters a,b,d, represent formulas. Let be a multiset of propositional formulas, possibly inconsistent but not deductively closed. When the knowledge base is not deductively closed, we call it a belief base , following Nebel (1991). In presence of inconsistency, the approaches developed in this paper must be syntactic in nature, since they explicitly use formulas that appear in the knowledge base originally, while two inconsistent knowledge bases over the same language are semantically equivalent (in a trivial way) This ....

....sources of information. 5.3 Syntax Sensitivity Baral et al. 1992) noticed that Incl preferred consequence relation depends upon the syntax of the belief base. It means that even if f y is logically equivalent to f,y , this equivalence does not matter when treating inconsistency. Following Nebel (1991), a syntactic consequence relation is a consequence relation which refers explicitly to the syntactic representation of the belief base. It is clear that all the consequence relations described in this paper are syntactic since they explicitly use formulas that appear in the belief base. However, ....

B. Nebel (1991) Belief revision and default reasoning: Syntaxbased approaches. Proc. KR'91, 417-428.

....about a changing scenario. For this purpose, they introduce a new set of postulates (KM postulates) to model the process of updating a knowledge base. While the AGM and KM postulates define general properties, actual belief revision and update operators have been proposed by several authors [2, 3, 5, 9, 11, 12]. Both update and revision deal with the problem of accommodating new, and completely reliable, information into an existing body of knowledge. A basic assumption of update and revision is that the new piece of information must be in the revised (or updated) knowledge base. Suppose that we are in ....

....NP and CoNP hard. Proof: The formula a is a theorem iff 4 j= a, where is the set of all models. The formula a is contradictory if and only if 4A j= a For a detailed analysis of the computational complexity of belief revision and update, we refer to the paper [4] by Eiter and Gottlob and [9] by Nebel. 4 Arbitration as Commutative Revision In this section, we study the properties of arbitration satisfying 1 8. Since these postulates are natural extensions of the AGM ones, we also refer to this form of arbitration as commutative revision. All arbitrations satisfying 1 8 can be ....

B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In Proceedings of the Second International Conference on the Principles of Knowledge Representation and Reasoning (KR-91), pages 417--428, 1991.

....each of the theories, i.e. T GP j= Q iff for all T 0 2 W (T; P ) T 0 [fPg j= Q. In other words, Ginsberg considers all sets in W (T; P ) equally plausible and inference is defined skeptically, i.e. Q must be a consequence of each set. A more general framework has been defined by Nebel in (Nebel 1991). We do not analyze its definitions. WIDTIO. Since there may be exponentially many new theories in T G P , a simpler (but somewhat drastical) approach is the so called WIDTIO (When In Doubt Throw It Out) which is defined as T Wid P : W (T; P ) fPg: see (Winslett 1989) Note that ....

Nebel, B. 1991. Belief revision and default reasoning: Syntax-based approaches. In Proc. of KR-91, 417-- 428.

.... we have In other words, what are the logical consequences of theory T when it is revised by formula P In symbols, what is the set of formulae Q such that T P j= Q Proposed formalizations of belief revision can be very different in spirit, rely on different assumptions and have different goals [Bor85, Dal88, FHV83, For89, Gin86, Neb91, Sat88, Web86, Win90]. Other researchers [EG92, Neb91, Win90] focused on computational properties of belief revision. As an example, they addressed questions such as: Given formulae T; P; Q and a suitable semantics for , what is the time complexity of deciding T P j= Q In which cases polynomial algorithms exist ....

.... revised by formula P In symbols, what is the set of formulae Q such that T P j= Q Proposed formalizations of belief revision can be very different in spirit, rely on different assumptions and have different goals [Bor85, Dal88, FHV83, For89, Gin86, Neb91, Sat88, Web86, Win90] Other researchers [EG92, Neb91, Win90] focused on computational properties of belief revision. As an example, they addressed questions such as: Given formulae T; P; Q and a suitable semantics for , what is the time complexity of deciding T P j= Q In which cases polynomial algorithms exist Both aspects of belief revision (semantic ....

[Article contains additional citation context not shown here]

B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In Proc. of the 2nd Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-91), pages 417--428, 1991.

....conveys all the necessary information to uniquely determine the outcome of revising K by any sentence [5] While the AGM framework provides a useful abstraction for the belief change process, it does not lend itself to implementation in a straightforward way. Several studies (such as [13]) have therefore focussed on belief bases, which are finite sets of sentences, instead of logically closed theories, as representations of beiief states. Belief base approaches consider priority relations on the belief base, instead of entrenchment relations defined on the entire language, in ....

....of requirements engineering. ffl The explicit representation of contractions in the set of THEORIST constraints C ensures that revisions and contractions are treated in a symmetric manner. In the AGM framework, as well in approaches inspired by it (including Nebel s operators for belief bases [13]) contractions are never represented explicitly, while revisions are. Consequently, the effects of a contraction operation are not guaranteed to persist beyond a single step. Requirements evolution operations such as the Telos UNTELL operation must persist over iterated evolution steps, which is ....

Bernhard Nebel. Belief revision and default reasoning: Syntax-based approaches. In Proc. of the Second International Conference on Principles of Knowledge Representation and Reasoning, pages 417--428, 1991.

....Keywords: knowledge bases, inconsistency handling, non monotonic reasoning, preferred sub theories, preferential models, penalties, discrete optimisation. 1 Introduction Les approches syntaxiques du raisonnement non monotone et de la r evision des connaissances (voir par exemple (Nebel 91[17]) consistent a consid erer chaque formule d une base de connaissances BC comme un granule de connaissance indivisible (qui doit etre soit enti erement accept e soit rejet e) On est alors amen e a calculer les sous bases maximales consistantes, ou encore sous th eories maximales de BC ; une ....

.... est effectu ee par un ordre de priorit e ; une base de connaissances avec priorit es etant une collection finie BC = BC 1 ; BC n ) d ensembles de formules (la strate de rang 1 contenant les formules les plus prioritaires) la m ethode la plus couramment etudi ee Brewka 89 [3] Nebel 91 [17], et Cayrol 92 [4] est fond ee sur l inclusion ; plus pr ecis ement elle consiste a pr ef erer (strictement) une sous th eorie A de BC a une sousth eorie B ssi il existe un rang i tel que pour tout j i, A BC j = B BC j , et A BC i contient strictement B BC i . Une autre d efinition a ....

B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In J.A. Allen, R. Fikes, and E. Sandewall, editors, Proc. of the 2 nd KR, pages 417--428, Cambridge, MA, 1991. Morgan-Kaufmann.

.... variants of possibilistic logic namely, leximin and discrimin [2] As for complexity, recall (Proposition 13) that nonmonotonic possibilistic entailment is in Delta P 2 (O(logn) then the leximin variant is in Delta P 2 (O(n) 9] and the discrimin variant is Pi P 2 complete [48] [9] This means that escaping the drowning effect generates an increase of complexity; as to practical computation, drowning free variants basically require computing some of the maximal consistent subsets of the knowledge base, which SPL does not. There are also some generalizations of ....

Bernhard Nebel. Belief revision and default reasoning: syntax-based approaches. Proceedings of KR'91, 417-428.

....only with regard to the formulae explicitly mentioned in the belief base. This line of research has been pursued by many researchers [ Alchourr on and Makinson, 1982; Dubois and Prade, 1991; Fagin et al. 1983; Fuhrmann, 1991; Hansson, 1996; Hannson, 1991; Hansson, 1994b; Nayak, 1994; Nebel, 1989; Nebel, 1991; Nebel, 1992; Rott, 1993 ] Further, similar approaches have been studied in the context of evaluating conditionals [ Ginsberg, 1986; Kratzer, 1981; Pollock, 1976; Veltman, 1976 ] hypothetical reasoning [ Rescher, 1964 ] and default reasoning [ Benferhat et al. 1995; Brewka, 1989; Poole, ....

....to that, other approaches are possible, which are also analyzed below. 5. 1 Full Meet Base Revision Applying the definition of remainder sets to belief bases, the full meet base revision scheme, written as A flF , could be defined as follows [ Fagin et al. 1983; Ginsberg, 1986; Nebel, 1989; Nebel, 1991 ] A flF def = i fCn(B)j B 2 (A : g j : 29) As shown in [ Nebel, 1991 ] the belief revision operations generated by the full meet base revision scheme are partial meet revisions. Further, it is easy to verify that the marking off relation is the complement of (a restricted) ....

[Article contains additional citation context not shown here]

Bernhard Nebel. Belief revision and default reasoning: Syntaxbased approaches. In J. A. Allen, R. Fikes, and E. Sandewall, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the 2nd International Conference (KR-91), pages 417--428, Cambridge, MA, April 1991. Morgan Kaufmann.

....a relation over the set of all sentences in a deductively closed theory, which is representationally infeasible. One way to address the two problems is to consider revision operations on belief bases (so called base revisions) i.e. operations that modify a belief base instead of a belief set [7, 8, 15, 18, 20, 24]. Such an approach often also matches certain characteristics of an application setting very well. If, for instance, a code of norms or a scientific or naive theory of the world is represented by a set of explicitly stated sentences, one may want to express preferences between these sentences. ....

....revision schemes that use preference information that has a size polynomial in the size of a belief base. In particular, we focus on schemes where the preference information is encoded by a complete preorder over the set of sentences in a belief base, also called epistemic relevance ordering [19, 20], with the intuitive meaning that if OE , then is at least as relevant, important, or reliable than OE (see also, e.g. 2, 7, 14] Equivalently, we can view a base A as partitioned into n priority classes or ranks A1 ; An as follows (using to denote the strict part of ) OE 2 A1 ....

[Article contains additional citation context not shown here]

B. Nebel, `Belief revision and default reasoning: Syntax-based approaches', in Proc. KR-91, eds., J. A. Allen, R. Fikes, and E. Sandewall, pp. 417--428, Cambridge, MA, (1991). Morgan Kaufmann.

....This requirement makes plan modification very similar to the belief revision problem, i.e. the problem of changing a logical theory minimally in order to accommodate a new information. As is well known, most revision schemata (but not all) turn out to be computationally harder than deduction [12,31]. 4 A similar result 4 More precisely, revision is in most cases Pi p 2 complete. Assuming, as is customary, that the polynomial hierarchy does not collapse (see, e.g. 16,22] this implies that revising a propositional theory is harder than deduction, which is Pi p 1 or co NP7 ....

B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In J. A. Allen, R. Fikes, and E. Sandewall, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the 2nd International Conference, pages 417--428, Cambridge, MA, Apr. 1991. Morgan Kaufmann.

No context found.

Nebel, B. (1991) Belief Revision and Default Reasoning: Syntax-Based Approaches, Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning, pp. 417-428.

No context found.

Bernhard Nebel. Belief revision and default reasoning: Syntax-based approaches. In James Allen, Richard Fikes, and Erik Sandewall, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference KR '91, pages 417--428. Morgan Kaufmann, San Francisco, California, 1991.

No context found.

Nebel, B. (1991). Belief revision and default reasoning: Syntax-based approaches. In Proceedings of the Second Conference on Knowledge Representation, 417-428, San Mateo, CA: Morgan Kaufmann.

No context found.

B. Nebel, Belief revision and default reasoning: syntax-based approaches, Proc. KR '91, Morgan Kaufmann, 1991 21

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