Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Diderik Batens, Chris Mortensen, Graham Priest, and Jean Paul Van Bendegem, editors, Frontiers of Paraconsistent Logic, pages 189--201. Research Studies Press, Baldock, UK, 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are mutually inconsistent. In still other cases, progress in a discipline was realized by reasoning from a theory and a set of data that are mutually inconsistent. The reasoning that occurs in such situations is explicated by inconsistencyadaptive logics see, for example, 3] 2] 5] 23] [14], 25] 12] 7] 8] These logics isolate the involved inconsistencies and in this way provide an interpretation of the premises (theories and or data) that is as consistent as possible. Precisely this type of interpretation is needed in order to reason from the inconsistent premises and in ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Batens et al. [10], pages 189--201.

....a minimal Dab consequence of a premise set. If this is the case, the Reliability and Minimal Abnormality strategies lead to the same result and coincide with what is called the Simple strategy: a formula behaves abnormally just in case the abnormality is derivable from the premise set see [14] [24] and [ for examples. Several other strategies have been studied. Most of them were the result of characterizing an existing consequence relation by an adaptive logic. Examples may be found in [9] 12] 22] and [30] 3 Prioritized Adaptive Logics Let us start with combined adaptive logics. If ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Diderik Batens, Chris Mortensen, Graham Priest, and Jean Paul Van Bendegem, editors, Frontiers of Paraconsistent Logic, pages 189--201. Research Studies Press, Baldock, UK, 2000.

....example [42] 43] 47] 27] 39] 36] and [38] Not all of these authors side with me on the required approach. One way to implicitly apply Ex Falso Quodlibet proceeds by first applying Addition to obtain p q from p and next applying Disjunctive Syllogism to obtain q from q. See [37] for an exception: the paraconsistent logic AN validates Disjunctive Syllogism (and all analysing rules of CL) but invalidates Addition (and Irrelevance and similar rules) Explicating this type of kind reasoning was at the origin of the adaptive logic programme see [5] 8] and many other ....

....set is such that # is a singleton. In such cases, the Reliability and Minimal Abnormality strategies lead to the same result and coincide with what is called the Simple strategy: a formula behaves abnormally just in case the abnormality is derivable from the premise set. Examples may be found in [37] and [18] Several other strategies have been studied, but seem to have a less general import. Most of them were the result of characterizing an existing consequence relation by an adaptive logic. Examples may be found in [14] 17] 29] and [49] A di#erent way to characterize most flat ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Batens et al. [23], pages 189--201.

....both C#E and C#E. Dropping EFQ is clearly also a step in the direction of paraconsistent logics, and as not all paraconsistent logics are relevant one may hope to obtain one of them. But again, trouble arises. Most paraconsistent logics reject #E. The few that accept it logics such as AN from [12] and consequence relations defined by filters as in [14] reject C#E. Pc is not likely to become a popular logic. The obvious reason is that Pc derivability is not transitive. Indeed, p Pc p q and #p, Pc q, but p, # Pc q. This nicely illustrates the extent to which the ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Batens et al. [8], pages 189--201.

....premisses are analysed beforehand. The system presented in this paper has to be seen against the background of a recent development in the adaptive logic program. The first adaptive logics were corrective logics. Examples of this type of logics are ACLuN1, ACLuN2 (see [2] and [3] and ANA (see [15]) In corrective adaptive logics, the ULL determines the standard of reasoning and specific deviations from this standard are minimized. They adapt themselves to specific violations of presuppositions of CL such as inconsistencies. The system I present in this paper is an ampliative logic like ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Batens et al. [6], pages 189--201.

.... speaking, a derivation is conditional when the derivation rule is part of the upper limit logic (mostly CL) and not of the lower limit logic (one or other paraconsistent logic like CLuN) It should also be noted that not every paraconsistent logic lacks disjunctive syllogism, see for instance [4] and [2] for counterexamples. 3 if we would at a later stage learn that p :p, then our knowledge has changed, and we ought to revise earlier derivations. Also, inconsistency adaptive logics have a richer consequence set than ordinary paraconsistent logics. It should be noted that in ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. To appear.

....de ne the notion of clauses. Section 3 will then de ne the transformation procedure, with special attention towards negation, and its meaning Research for this paper was supported by the Fund for Scienti c Research Flanders. 1 The only exceptions, to my knowledge, being Joke Meheus AN, see [7], and QC, from [4] by Philippe Besnard and Anthony Hunter. 1 in a paraconsistent environment. Section 4 then adds some closing remarks and points out the importance of this paper for further research. 2 Some basics on CLuNs and clauses 2.1 Introducing CLuNs CLuNs is an extension of the basic ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. To appear.

No context found.

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Diderik Batens, Chris Mortensen, Graham Priest, and Jean Paul Van Bendegem, editors, Frontiers of Paraconsistent Logic, pages 189--201. Research Studies Press, Baldock, UK, 2000.

....procedure that only invalidates Ex Falso Quodlibet (while validating all other inference rules of CL) The price to be paid, however, is that the resulting consequence relation is not transitive. An example of a standard paraconsistent logic that validates Disjunctive Syllogism can be found in [12]. The example will be explained in more detail in Section 6. For the moment, note only that MPL models that verify # #p) verify all members of # # , even if they falsify #q. terms of the intended application context, the fact that one of the participants in the debate is maintaining a ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Diderik Batens, Chris Mortensen, Graham Priest, and Jean Paul Van Bendegem, editors, Frontiers of Paraconsistent Logic, pages 189--201. Research Studies Press, Baldock, UK, 2000.

....in an appropriate manner, every inference rule of CL that, when applied to an inconsistent set of premises, is not truth preserving. In line with this, almost all (monotonic) paraconsistent logics invalidate Reductio ad Absurdum. The only exception known to me is the logic AN presented in [44]; motivations for this system can be found in [45] and [46] Thus, an adequate replacement for Reductio ad Absurdum seems to be: 1) If # B, # and # CL B then may be added to any proof of # in which both A occur. In the case of the other examples, it seems that the ....

....4 Adaptive Logics The first adaptive logic was designed around 1980 by Diderik Batens (see [2] and [4] and was meant to handle in a sensible and realistic way inconsistent sets of premises. This logic was followed by several other inconsistency adaptive systems (see, for instance, 61] [44], and [51] and several inconsistency handling mechanisms that proceed in terms of maximal consistent subsets were reconstructed in terms of adaptive logics (see [7] and [68] and even strengthened (see [15] Later the idea of an adaptive logic was generalized to other forms of logical ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Batens et al. [22], pages 189--201.

....can sensibly be drawn from the premises) If the lower limit logic is weaker than CL (for instance, some paraconsistent fragment of CL) the logic is classified as corrective. The best studied examples of corrective adaptive logics are inconsistency adaptive logics (see, for instance, 2] and [11]) These logics are suited for situations in which a the The only di#erence is that, in the case of Q, it does not make sense to consider all extensions of #. This, however, is related to the fact that I defined Q and Q in such a way that only declarative w#s can be included in the premise ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Batens et al. [8], pages 189--201.

....from the adaptive logic programme. The first adaptive logic was designed by Diderik Batens around 1980 (see [2] and was meant to handle in a sensible and realistic way inconsistent sets of premises. This logic was followed by other inconsistency adaptive systems (see, for instance, 19] and [14]) and the idea of an adaptive logic was generalized to other forms of logical abnormalities, such as negation completeness, and ambiguity (see [3] for an adaptive logic that can handle all CL abnomalities) An important new development concerns the design of ampliative adaptive logics (see [13] ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Diderik Batens, Chris Mortensen, Graham Priest, and Jean Paul Van Bendegem, editors, Frontiers of Paraconsistent Logic, pages 189--201. Research Studies Press, Baldock, UK, 2000.

....from the adaptive logic programme. The first adaptive logic was designed around 1980 by Diderik Batens (see [2] and was meant to handle in a sensible and realistic way inconsistent sets of premises. This logic was followed by several other inconsistency adaptive systems (see, for instance, 33] [20], and [22] Later the idea of an adaptive logic was generalized to other forms of logical abnormalities, such as negationincompleteness and ambiguity (see, for instance, 3] and several inconsistencyhandling mechanisms that proceed in terms of maximal consistent subsets were reconstructed in ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Diderik Batens, Chris Mortensen, Graham Priest, and Jean Paul Van Bendegem, editors, Frontiers of Paraconsistent Logic, pages 189--201. Research Studies Press, Baldock, UK, 2000.

....logic; specific deviations from this standard are minimized. All currently studied corrective adaptive logics have CL as their upper limit logic, and hence, adapt themselves to specific violations of CL presuppositions. Examples in this category are the inconsistency adaptive logics from [2] and [16]. In an ampliative adaptive logic, the standard of reasoning is determined by the lower limit logic; specific extensions of this standard (that are considered desirable within the application context at issue) are maximized. 14 Examples of ampliative adaptive logics are the logic of ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Batens et al. [10], pages 189--201.

....CL as their upper limit logic, and hence, adapt themselves to specific violations of CL presuppositions. Inconsistency adaptive logics, for instance, interpret inconsistent theories as consistently as possible . Examples in this category are ACLuN1 and ACLuN2 (see especially [3] and ANA (see [23]) In an ampliative adaptive logic, the standard of reasoning is determined by the lower limit logic; specific extensions of this standard (that are considered desirable within the application context at issue) are maximized. 4 Thus, Priest s LP m is best viewed as an ampliative logic. For ....

....connectives may be in axiomatizing D2, they do not seem to have an intuitively acceptable interpretation in the context of interpreting debates. 16 It is interesting to compare D2 r to other inconsistency adaptive logics, for instance, ACLuN1 and ACLuN2 from [3] LP m from [28] and ANA from [23]. An important di#erence between D2 r and other inconsistency adaptive logics available today is that the former does not allow for the derivation of contradictions. Another di#erence concerns the rules of CL that are turned into conditional rules. In nearly all inconsistency adaptive logics, ....

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Batens et al. [11], pages 189--201.

No context found.

Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Batens et al. [5], pages 189--201.

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