M. Dalal. Updates in Propositional Databases. Technical Report, DCSTR -222, Dept. of Computer Science, Rutgers Univ., 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the belief revision problem is due to Fagin, Ullman and Vardi [6] However, as proven in the same paper, their method forces us to completely abandon the old knowledge whenever we update the base with an inconsistent piece of information. This may be unacceptable in most applications. Dalal in [2, 3] proposed another, more promising method of revising beliefs. He provided a specific algorithm for updating propositional databases which was based on four basic principles, namely: 1) Irrelevance of Syntax: Logically equivalent databases (and updates) should give logically equivalent update ....

....keep the database consistent. 4) Fairness: All things being equal, when we have more than one choice for the result of the update, none of the choices should be arbitrarily chosen, in order to preserve determinism. Dalal also formalized the notion of minimal change (third principle) and proved ([3]) that his method generally retained more knowledge in cases of inconsistent updates than any of the up to then proposed algorithms. An alternative approach was presented by Alchourron, G irdenfors and Makinson in a series of papers ( 1, 8, 14] Their idea was to recede from the search of any ....

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Dalal M., "Updates in Propositional Databases", Technical Report, DCS-TR222, Department of Computer Science, Rutgers University, February 1988.

....and any rational belief revision algorithm should do the same operation, in a similar way. One of the fundamental properties of any updating scheme should be the retention of as many as possible of the old data. This property is also known as Dalal s principle of persistence of prior knowledge ([3]) This is a widely accepted property of belief revision algorithms, in contrast to other considerations, which are heavily debated. One such consideration deals with the representation of the KB. There are two general types of theories concerning this representation: foundational and coherence ....

....user defined parameter, representing a trade off between knowledge integrity and processing speed. 7 Comparison with Previous Work Many different propositions exist for the problem of belief revision. Most of them are based on different assumptions and placed on a different context. Dalal in [3] proposed a very promising method of revising beliefs. He provided an algorithm for updating propositional KBs and formalized the notion of minimal change. He proved in [3] that his method generally retained more knowledge than the up to then proposed algorithms. It can be shown ( 11] that his ....

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M. Dalal, "Updates in Propositional Databases", Technical Report, DCS-TR-222, Department of Computer Science, Rutgers University, February 1988.

....the result of the revision operation is also a belief set. One can perceive this as the requirement that the revised set be also closed under the consequence relation. 4 (K # 2) A # K# a A (K # 2) is known as the success postulate and corresponds to Dalal s principle of primacy of the update [4]. It basically says that the revision process should be successful in the sense that the new belief is e#ectively accepted in the revised belief state. K # 3) K# a A # Cn(K # A ) K # 4) If A ## K, then Cn(K # A ) # K# a A (K # 5) K# a A = K# only if A is unsatisfiable To understand ....

....di#erent, we need check only (K # 3,4 ) and (K # 5) K # 6) If A # B, then K# a A # K# a B (K # 6) specifies that the revision process should be independent of the syntactic form of the sentences involved. It is called the principle of irrelevance of syntax by many authors, see for instance, [4]. K # 7) K# a (A # B) # Cn( K# a A) # B ) K # 8) If B ## K# a A, then Cn(K# a A # B ) # K# a (A # B) To understand what postulates (K # 7) K # 8) are saying, we again have to make a case analysis. The postulates have to do with the relationship of inputing (A, B) as a sequence ....

M. Dalal. Updates in propositional databases. Technical report, Department of Computer Science, Rutgers University, February 1988. Technical Report DCS-TR-222.

....assignment that maps each epistemic state S to a total pre order S such that: Mod( S Delta ] min( S Delta] Hence the sole revision operator with memory that satisfies (H1 H9) and (C2) is the basic revision operator. 4. 2 Dalal memory operator We use in this section the Dalal s distance [Dal88], defined in the following way: Definition 9 Let I and J be two interpretations, the Dalal s distance dist(I ; J) is defined as the number of propositional letters the two interpretations differ. Let be a knowledge base, the Dalal s distance between this interpretation and the knowledge base ....

M. Dalal. Updates in propositional databases. Technical report, Rutgers University, 1988.

....arbitration is a medical treatment, we can t merge several therapies and so we have to use Liberatore and Schaerf operators. Liberatore and Schaerf s operators take, in a sense, the interpretation as unit of change, we propose to take the propositional variable as such a unit, as Dalal says in [Dal88]: Change in truth value of a single symbol can be considered as the smallest unit of change , we want to apply this to arbitration. Lin and Mendelzon proposed a theory merging by majority operator [LMa, Lin96] which solves conflicts between knowledge bases by taking the majority into account. ....

....by giving three examples of operators. The first one is not a merging operator but it illustrates an approach to arbitration operators. The second one is a majority merging operator and the last one is a true arbitration operator. For the following operators we will use the Dalal s distance [Dal88] to calculate the distance between two interpretations: let I ; J be interpretations, dist(I ; J) is the number of propositional letters the two interpretations differ. We also define the distance between an interpretation and a knowledge base as the minimum distance between this interpretation ....

M. Dalal. Updates in propositional databases. Technical report, Rutgers University, 1988.

....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: feiter,gottlobg vexpert.dbai.tuwien.ac. at 1 the WIDTIO approach [19, 21, 58] Dalal s revision [7], the approach by Forbus [14] Borgida s method [3] Winslett s Possible Models Approach [57] Satoh s method [53] and Weber s approach [56] Each of these methods is suited for particular application domains; most researchers agree that none of them can be considered as a general purpose ....

....retracted as a whole or left in the knowledge base. These approaches, referred to as formula based changes, heavily depend on the syntax of T . On the other hand, model based changes refer only to the extensions, i.e. models, of T . These methods respect Dalal s principle of Irrelevance of Syntax [7]. ffl Revision versus Update. Different change operators are appropriate according to whether the theory change consists of a revision, i.e. a correction to the actual state of beliefs due to new, more precise, or more reliable information for instance, or of an update reflecting a change in the ....

M. Dalal. Updates in Propositional Databases. Technical Report DCS-TR-222, Rutgers University, Dept. of Computer Science, Feb. 1988.

....Worlds approach [21] introduced by Fagin, Ullman, and Vardi [15, 14] and further studied by Nebel [41, 42] the This paper is an overview of [11] which contains detailed proofs of all complexity results. Cross Product approach [15] the WIDTIO approach [21, 47, 52] Dalal s revision [7, 8], the approach by Forbus [16] Borgida s method [4] Winslett s Possible Models approach [51] Satoh s method [49] and Weber s approach [50] All these methods adhere to the principle of Minimality of Change, which states that the knowledge base should change as small as possible if new ....

....T i ; 1 i mg, where fT1 ; Tmg = T G p WIDTIO T Wid p = T W2W (p;T ) W [ fpg Table 1: Formula based revision operators heavily depend on the syntax of T . In contrast to this, model based changes refer only to the models of T in respect of the principle of Irrelevance of Syntax [8]. Model based change is favored by many researchers, but formula base change also has its uses [30] Revision versus Update. Di erent change operators are appropriate if p consists of an update, which re ects a change in the world, or of a revision, that is a correction of the description of the ....

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M. Dalal. Updates in Propositional Databases. Technical Report DCS-TR-222, Rutgers University, Dept. of Computer Science, Feb. 1988.

....arbitration is a medical treatment, we can t merge several therapies and so we have to use Liberatore and Schaerf operators. Liberatore and Schaerf s operators take, in a sense, the interpretation as unit of change, we propose to take the propositional letter as such a unit, as Dalal says in [Dal88] Change in truth value of a single symbol can be considered as the smallest unit of change , we want to apply this to merging. Lin and Mendelzon proposed a theory merging by majority operator [LM, Lin96] which solves con icts between knowledge bases by taking the majority into account. Their ....

....this interpretation and the knowledge bases of the knowledge set. And the result of 4 operators can be considered as the election of the most popular possible choices among the integrity constraints. Lin and Mendelzon give a 4 operator (when the distance chosen is the Dalal distance [Dal88] as an example of what they called operators of theory merging by majority in [LM] And independently, Revesz gives the same operator as an example of weighted model tting in [Rev93] This operator is indeed a majority merging operator as stated in the theorem below. First of all notice the ....

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M. Dalal. Updates in propositional databases. Technical report, Rutgers University, 1988.

....new knowledge modification. The modification problem is to define and compute the modified KB. Many approaches have been proposed for defining changes to KBs in the AI and DB literature [10, 2, 25, 5, 24, 27, 11, a.o. All these approaches respect the principle of persistence of prior knowledge [5] or minimality of change [10] This principle states that when replacing an old KB by a new one the change must be minimal (the new KB must be as close as possible to the initial one) We can classify these methods according to various criteria: The primacy of the update: This criterion as a ....

....a plethora of proposals for semantics for modifying KBs, it is not clear how to translate a semantic definition into a procedure suitable for implementation. Algorithms have been provided 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 ....

M. Dalal. Updates in propositional databases. Technical Report DCS-TR222, Department of Computer Science, Rutgers Univ., Feb. 1988.

....Then I; R; is a universal order model. Now [ OE ] 6= since for instance fp 1 ; p 2 g 2 [ OE ] Likewise, we have that [ OE ] 6= and [ OE ] 6= It now follows from the soundness theorem that VCU 2 is non trivial: 2 18 In fact, this order is proposed by M. Dalal [9, 10] for updating propositional theories. 9 Conclusions Consider a counterfactual If A, then B . The Gardenfors Triviality Theorem shows that the antecedent cannot be read as If I knew, possibly contrary to my previous beliefs, that A were the case . On the other hand, our results show that the ....

Mukesh Dalal. Updates in propositional databases. Technical Report DCS-TR-222, Department of Computer Science, Rutgers University, Feb. 1988.

....states of the world its models. The revision is presented as a formula in L. Let ffi denote the revised knowledge obtained by revising the old knowledge by the new information , i.e. ffi = Revise( The problem of knowledge revision is: given and , define ffi . In [Dalal, 1988] we motivate certain principles that should be followed when characterizing the revised knowledge ffi . These are: 1. Adequacy of Representation: The revised knowledge should have the same representation as the old knowledge. Especially in a functional view of knowledge bases, this is ....

.... ffi = G k ( f g, where k is the least value of i for which G i ( f g is consistent. At first sight it might appear that we are doing an overkill by generalizing with respect to all the ground atoms in it, since the cause of inconsistency might be located in only a few of them. In [Dalal, 1988] we show that revised knowledge is the same (modulo logical equivalence) even if is generalized with respect to only the conflicting atoms. Thus, if it is easier to find the set of conflicting atoms, then it would be advantageous to generalize with respect to the conflicting atoms only. ....

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M. Dalal. Updates in propositional databases. Technical Report DCS-TR-222, Department of Computer Science, Rutgers University, February 1988.

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M. Dalal. Updates in Propositional Databases. Technical Report, DCSTR -222, Dept. of Computer Science, Rutgers Univ., 1988.

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M. Dalal. Updates in Propositional Databases. Technical Report, DCSTR -222, Dept. of Computer Science, Rutgers Univ., 1988.

No context found.

M. Dalal. Updates in propositional databases. Technical Report DCS-TR222, Department of Computer Science, Rutgers Univ., Feb. 1988.

No context found.

Mukesh Dalal. Updates in propositional databases. Technical Report DCS-TR-222, Computer Science Department, Rutgers University, February 1988.

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