By Diderik Batens
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Additional resources for Adaptive Logics and Dynamic Proofs. Mastering the Dynamics of Reasoning, with Special Attention to Handling Inconsistency
All this shows that the historically documented behaviour of scientists is sensible: they reason from inconsistent theories in order to locate the inconsistencies and to find consistent replacements for the theory. The situation for dialetheists is pretty much the same. They claim that some inconsistencies are true, but consider most inconsistencies as false (and repeatedly stressed this). So when a dialetheist comes across an inconsistency and there is no serious justification for holding it true, the dialetheist will try to eliminate it, locally restoring consistency.
Several valuations 2 Note that A, ¬A L B does not exclude that A, ¬A L B holds for some A and B. Thus some logics L are paraconsistent because p, ¬p L q, even if (p ∧ r), ¬(p ∧ r) L q—see [Bat80]. 3 The logic CLuN is like CL, except that it allows for gluts with respect to N egation. 2. A REGULAR PARACONSISTENT LOGIC 41 may be associated with the same model if the semantics is indeterministic. 4 I refer to [Avr05, ABNK07, AK05] for some interesting technical studies of indeterministic semantics.
An CLuN B ∨ ((C1 ∧ ¬C1 ) ∨ . . ∨ (Cn ∧ ¬Cn )) and, for each Ci , either Ci or ¬Ci is not derivable from the premise set under consideration, to infer B from A1 , . . , An . Although († ) is intuitively appealing, it does not tell us how to define an inconsistency-adaptive logic from CLuN. It is actually a circular statement. It states that a sentence E is derivable if another sentence, D, is not derivable. But this comes to: D is derivable if E is not. In order to define an inconsistencyadaptive logic we need a way to circumvent this circularity.