Benferhat, S.; Dubois, D.; and Prade, H. 1998. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. InLogic at work : essays dedicated to the memory of Helena Rasiowa / Ewa Orow., 473-511. Physica-Verlag.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and indirectly by the Flemish Minister responsible for Science and Technology (contract BIL98 37) I am greatly indebted to Diderik Batens for several ideas in this paper. This situation is mentioned as an open problem in [1] Di#erent approaches relevant to this situation are presented in [2]. The aims of this paper are first to make the Rescher Manor mechanisms adaptive so that they link up better with human reasoning, second to extend these mechanisms in the hope that it brings a significant enrichment and third to look for other adaptive strategies that could be more e#cient for ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Ewa Or#lowska, editor, Logic at Work. 17 Essays Dedicated to the Memory of Helena Rasiowa, pages 473--511. Physica Verlag (Springer), Heidelberg, New York, 1999.

....closure in terms of some monotonic logic (usually CL) of # 0 plus as much of # 1 as may consistently be added to # 0 , plus as much of # 2 as may be consistently added to the union of # 0 with the retained subset of # 1 , etc. Several di#erent such constructions are possible see for example [20] for an extensive study. It is fairly simple to characterize consequence relations defined along these lines in terms of prioritized adaptive logics. Where # A abbreviates A preceded by i occurrences of #, a sequence of CL premise sets such as (1) is translated to the modal premise set ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Or#lowska [25], pages 473--511.

....in view of the premises, then the abnormality of level i is avoided if i j. The results are the nice adaptive logics T from [22] For more examples see [48] and [49] the latter containing adaptive logics that characterize all the prioritized Rescher Manor consequence relations from [25]. A di#erent way to characterize prioritized adaptive logics is by seeing them as the result of applying a sequence of flat adaptive logics, each of these logics having a (nearly) similar structure. This characterization of prioritized adaptive logics is a special case of a more general ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Or#lowska [44], pages 473--511.

....whenever the external dynamics (non monotonicity) is present, the reasoning necessarily displays the internal dynamics (defeasible conclusions even if the premises are stable) The converse, however, does not hold. The Weak consequence relation, of Rescher and Manor see, for example, 46] and [24] is monotonic. Nevertheless, it may be shown that the reasoning from premises to weak consequences requires an internal dynamics. Some consequence relations that are monotonic as well as decidable may even be characterized (in an enlightening and attractive way) by a form of reasoning that ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 1: The flat case. Studia Logica, 58:17--45, 1997.

....A constantly updated overview of the results can also be found at http: logica.rug.ac.be adlog albib.html. Consequence relations that proceed in terms of maximal consistent subsets were first proposed by Rescher and Manor in [62] and are today very popular in AI applications (see [23] and [24] for an overview) Reconstructing these consequence relations in terms of adaptive logics has the advantage that it thus becomes possible to design a proof theory for them. In [5] one finds an adaptive logic that handles all CL abnormalities What is meant with the ambiguous term part will ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Or#lowska [60], pages 473--511.

....for the inconsistencies. The only disadvantage of the present version is that the # i are supposed to be consistent themselves. Here, also, the two main strategies for adaptive logics are given. The semantics and the proof theory of the reliability The latter is what is usually done, as in [5] [3], 6] and [2] strategy for the modal version are presented in Section 7. In Section 8, the logical equivalence of the reliability strategy for prioritized compatibility and that for the modal version is proved (in the case of consistent # i ) That Section concludes with the qualitative and ....

....here is that the T models that verify p, q #r block the information flow from p # r . This di#erence between the two abnormality strategies illustrates the shortcoming of the modal version. 11 Conclusion We conclude that both approaches are useful, certainly when opposed to [5] [3], 6] and [2] The logics presented here are more appropriate in certain contexts, namely, when the implications of the premises are of major concern and the formulation of the premises is insignificant. Both approaches presented in this paper have their advantages. The interpretation of ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Or#lowska [4], pages 473--511.

....be finite. It will reveal what is derivable from the premises at that stage of the proof. But obviously we are interested in final derivability. Whence the question: what does a proof at a stage reveal about final derivability The Weak consequence relation from [19] and [20] see [14] and [15] for an extensive study of such consequence relations is monotonic. Nevertheless, its proof theory necessarily displays an internal dynamics because there is no positive test for it see [6] and [10] Some logics for which there is a positive test, may nevertheless be characterized in a nice ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Or#lowska [18], pages 473--511.

....proof will be finite. It will reveal what is derivable from the premises at that stage of the proof. But obviously we are interested in final derivability. Whence the question: what does a proof at a stage reveal about final derivability The Weak consequence relation from [19] and [20] see [14] and [15] for an extensive study of such consequence relations is monotonic. Nevertheless, its proof theory necessarily displays an internal dynamics because there is no positive test for it see [6] and [10] Some logics for which there is a positive test, may nevertheless be characterized in ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 1: The flat case. Studia Logica, 58:17--45, 1997.

....inconsistent base. A technique introduced and elaborated by N. Rescher and R. Manor appropriate to this context is reasoning from consistent parts of the inconsistent whole. I shall call these mechanisms Rescher Manor mechanisms. Di#erent approaches relevant to this situation are presented in [2]. The aims of this paper are first to make the Rescher Manor mechanisms adaptive so that # I am greatly indebted to Diderik Batens for several ideas in this paper This situation is mentioned as an open problem in [1] they link up better with human reasoning, second to extend these mechanisms ....

....one, then to extract from the consequences of the third last intervention what is compatible with the already collected statements and so on at each lower level to extract from its consequences what is compatible with the position constructed out of the higher levels. The approaches presented in [2] are shortcoming in that the compatibility criterion is only applied to the statements themselves and not to their consequences. For example q will never be selected from # = #p #. Nevertheless in a discussion people are inclined to stick to their positions even when they can no longer ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Ewa Or#lowska, editor, Logic at Work. Essays Dedicated to the Memory of Helena Rasiowa, pages 473--511. Physica Verlag (Springer), Heidelberg, New York, 1999.

....The underlying idea is to define consequence relations in terms of the CL consequences of maximal consistent subsets of a set of premises. A survey of the flat (non prioritized) Rescher Manor consequence relations is offered in [14] a survey of prioritized such consequence relations in [15]. All those consequence relations are characterized by inconsistency adaptive logics as well as by ampliative adaptive logics see [8] 13] 7] 24] and [25] All those consequence relations may be strongly enriched by relying on an idea from [18] that enriches Jaskowski s paraconsistent ....

....#ALEXP #. # #AL # EXP of maximal cardinality (for which there is no # # such that #(# # ) #(#) For reasons explained in Section 1, it is useful to generalize ALEXP and AL # EXP to make them apply to # = #. The natural place to look for such generalizations is [15], which contains a survey of prioritized inconsistencyhandling consequence relations that are based on consistent chunks. The most natural generalization of ALEXP is the SMC consequence relation. Out of the SMC consequence relation a generalization of AL # EXP can be forged. In some A major ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Or#lowska [19], pages 473--511.

....consequence relations to refer to such logical mechanisms. The underlying idea is to define consequence relations in terms of the CL consequences of maximal consistent subsets of a set of premises. A survey of the flat (non prioritized) Rescher Manor consequence relations is offered in [14]; a survey of prioritized such consequence relations in [15] All those consequence relations are characterized by inconsistency adaptive logics as well as by ampliative adaptive logics see [8] 13] 7] 24] and [25] All those consequence relations may be strongly enriched by relying on ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 1: The flat case. Studia Logica, 58:17--45, 1997.

....belief bases in terms of consistent subsets, into dynamic proof theories that are a more faithful representation of human reasoning processes. 1 Introduction To handle an inconsistent belief base in terms of consistent subsets, many consequence relations are available, for a survey see [4] for the flat case and [5] for the case non logical preferences play a part the prioritized case. They all are defined in terms of a selection of consistent subsets or in terms of the existence of certain consistent subsets. Because there is no positive test for the consistency of a set of ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 1: The flat case. Studia Logica, 58:17--45, 1997. 15 to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Orlowska [6], pages 473--511.

....resulting from data fusion of multiple sources is to fragment an inconsistent set into consistent subsets and then extract conclusions by applying classical inference to these subsets. This approach was first introduced by Rescher and Manor [18] and more recently extended by Benferhat et al. [5 7]. In this section we present similar but slightly more general inference mechanisms to extract conclusions from an inconsistent set based on ideas presented in [22] We take an inference to be a triple consisting of a premiss set # , a consistent constraint set # and a conclusion A. The main role ....

....is summarized in the following figure. Downward arrows indicate proper set inclusions. # Safe # Universal # Argued # Large # Existential figure 1 We note that by setting # = #, we recover the paraconsistent consequences defined in [7]. We also note that in our definitions # only provides side constraints on premises. We can in fact allow # to be used directly to derive conclusions. We have the following stronger notions of consequence: Definition 3. # universal consequence A # C # U# (# ) i# for each A # M# (# ) A## ....

S. Benferhat, D. Dubois, and H. Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study, part i: The flat case. Studia Logica, 58 (1):17--45, 1997.

....in [15] 16] and elsewhere. Later, further consequence relations were defined within the same approach. Some of these are called prioritized because they depend on non logical preferences. The nonprioritized ones are called flat . A survey and comparative study is presented in [10] and [11]. In the present section I concentrate on the flat consequence relations. That these consequence relations are characterized in terms of adaptive logics was first shown in [4] There, they are characterized in terms of inconsistencyadaptive logics. Direct dynamic proofs (that proceed directly in ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Ewa Or#lowska, editor, Logic at Work. Essays Dedicated to the Memory of Helena Rasiowa, pages 473--511. Physica Verlag (Springer), Heidelberg, New York, 1999.

....appeared in [15] 16] and elsewhere. Later, further consequence relations were defined within the same approach. Some of these are called prioritized because they depend on non logical preferences. The nonprioritized ones are called flat . A survey and comparative study is presented in [10] and [11] In the present section I concentrate on the flat consequence relations. That these consequence relations are characterized in terms of adaptive logics was first shown in [4] There, they are characterized in terms of inconsistencyadaptive logics. Direct dynamic proofs (that proceed ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 1: The flat case. Studia Logica, 58:17--45, 1997.

....of premises this is illustrated in [18] and [24] with some examples from nineteenth century thermodynamics. 3 Consequence relations that proceed in terms of maximal consistent subsets were first proposed by Rescher and Manor in [34] and are today very popular in AI applications (see [10] and [11] for an overview) Reconstructing these consequence relations in terms of adaptive logics has the advantage that it thus becomes possible to design a proof theory for them. 4 An inference pattern is called ampliative if it leads to conclusions that go beyond the information contained in the ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Ewa Or#lowska, editor, Logic at Work. Essays Dedicated to the Memory of Helena Rasiowa, pages 473--511. Physica Verlag (Springer), Heidelberg, New York, 1999.

....sets of premises this is illustrated in [18] and [24] with some examples from nineteenth century thermodynamics. 3 Consequence relations that proceed in terms of maximal consistent subsets were first proposed by Rescher and Manor in [34] and are today very popular in AI applications (see [10] and [11] for an overview) Reconstructing these consequence relations in terms of adaptive logics has the advantage that it thus becomes possible to design a proof theory for them. 4 An inference pattern is called ampliative if it leads to conclusions that go beyond the information contained ....

Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 1: The flat case. Studia Logica, 58:17--45, 1997.

....relations which honour the distinctions between 1 3. In particular, our inference relations should tolerate inconsistency at least in the sense of 3. Our starting point will be Rescher s work in this area ( 23] 24] and [25] We ll also examine recent works of Benferhat, Dubois and Prade ([5]) Eventually we will venture into the theoretical terrain explored by Jennings and Schotch ( 18] 28] 29] Rescher, Benferhat, Dubois and Parade, like Jennings and Schotch, approach the issue of paraconsistency by retaining substantial classical procedures and notions. But unlike Jennings and ....

....Definition 2.3 Inevitable and weak consequences are defined as follows: 4 Inevitable Consequence Gamma i A iff A A, for each A 2 U Gamma . Weak Consequence Gamma w A iff A A, for some A 2 U Gamma . We let Cn i ( Gamma) fA: Gamma i Ag and Cnw ( Gamma) fA: Gamma w Ag. In [5], Benferhat, Dubois and Prade propose 3 additional paraconsistent inference relations. Their ideas are similar to that of Rescher s an inconsistent set is first fragmented into various consistent subsets and then inference relations are defined in terms of these subsets. First, we state some ....

S. Benferhat, D. Dubois, and H. Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study, part i: The flat case. Studia Logica, 58 (1):17--45, 1997.

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Benferhat, S.; Dubois, D.; and Prade, H. 1998. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. InLogic at work : essays dedicated to the memory of Helena Rasiowa / Ewa Orow., 473-511. Physica-Verlag.

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Benferhat, S.; Dubois, D.; and Prade, H. 1997b. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 1: The flat case. Studia Logica 58(1):17-45.

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Benferhat, S., Dubois, D., Prade, H.: Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Logic at work : essays dedicated to the memory of Helena Rasiowa / Ewa Orow. - New York : Physica-Verlag, pp. 473-511, 1998.

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Benferhat S., Dubois D., Prade H. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. Logic at work : essays dedicated to the memory of Helena Rasiowa / Ewa Orlowska. - New York : Physica-Verlag, 473-511, 1998.

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S. Benferhat, D. Dubois, and H. Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. part ii: The prioritized case. In Ewa Orlowska, editor, Logic at work, volume 24, pages 473--511. Physica-Verlag , Heidelberg, 1998.

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Benferhat, S., Dubois, D., Prade, H.: Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. part ii: The prioritized case. In Orlowska, E., ed.: Logic at work. Volume 24. Physica-Verlag , Heidelberg (1998) 473--511

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Salem Benferhat, Didier Dubois, and Henri Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case. In Or#lowska [4], pages 473--511.

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