Joke Meheus. An inconsistency-adaptive logic based on Jaskowski's D2. To appear.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 the more recent systems presented in [4] [16], 5] and [17] In ampliative logics, the standard of reasoning is determined by the LLL and specific extensions of this standard are maximized. The consequence set one obtains with an ampliative logic is thus richer than the one obtained with CL. It will easily be observed from the next section ....

Joke Meheus. An inconsistency-adaptive logic based on Jaskowski's D2. To appear.

....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 terms of ....

....# 2 # = # q , p, p # q, s # (r # q) s #. As # 2 (s # (r # q) # 2 s ## S5 2 # 2 (r # q) the reinterpretation would prevent one from generating r as an explanation for q. We shall now show that this problem can be solved by relying on an idea that was first presented in [22]. Consider again (25) Assuming that one does not question the observational statement q, both p and p # q are problematic one has to reject or modify at least one of them in order to restore consistency. Hence, as long as it is unclear what changes are justified, it seems rational to ....

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Joke Meheus. An inconsistency-adaptive logic based on Jaskowski's D2. In preparation.

....(for instance, S5) It is easily observed that discussive logics are paraconsistent (#A, #A # = B) and that they do not allow for the derivation of contradictions. A disadvantage is, however, that they invalidate all genuine multiple premise rules, and hence, that they are extremely poor. In [17], an adaptive version is presented for Jaskowski s discussive logic D2. This logic, called D2 r , preserves all qualities of discussive logics, but moreover validates all multiple premise rules for sentences that behave consistently. 6 Though very natural, the reinterpretation faces two ....

....negations) This is related to the fact that their lower limit logic spreads abnormalities. If, for instance, #p # p is true in an S5 model M, then so is either #(p # q) # (p # q) or #(p # q) # (p # q) This problem is well known from other adaptive logics (see, for example, 4] and [17]) and will be explained in some more detail below. In view of all this, the abnormal part of an S5 model M is easily defined. It is the set of atoms A, such that #(#A # A) is verified by M. The formulas that behave abnormally and the abnormal part of an S5 model are the same for all three ....

Joke Meheus. An inconsistency-adaptive logic based on Jaskowski's D2. In preparation. 25

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