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

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The trouble is what we should do next. e. contains all sentences as theorems. We have seen that this is not a viable choice. Another alternative is that we replace CL, the second element of the theory, by a paraconsistent logic. This means that we move to a theory which has the same non-logical axioms as T , but has a considerably weaker logical basis. 2. I do not only mean that the theory is not trivial, 1 In general, where T = Γ, L , A is a theorem of T iff A ∈ Cn CL (Γ). 2. A REGULAR PARACONSISTENT LOGIC 39 but, more importantly, that it is much weaker than ‘what T was intended to be’, much weaker than ‘T except for the pernicious consequences of its inconsistency’.

Prem If A ∈ Γ: RU If A1 , . . , An CLuN RC If A1 , . . , An CLuN ... A ... ∅ B: A1 ... An B ∆1 ... ∆n ∆1 ∪ . . ∪ ∆n B ∨ Dab(Θ): A1 ... An B ∆1 ... ∆n ∆1 ∪ . . ∪ ∆n ∪ Θ I still need to specify marking. Note that this cannot be governed by a rule. A rule is an instruction that comes with a universal permission and marking is not a matter to be decided by the person who constructs the proof. So it should be governed by a definition. I shall, however, change the convention underlying (∗ ) and implicitly also underlying (∗∗ ) in the previous section.

If they are not, one might still call both models L-equivalent iff they verify the same members of W. 11 The set of consistent CLuN-models form a semantics for CL in view of the following lemma. 1 Every consistent CLuN-model is equivalent to a CL-model and, for every CL-model M , there is an equivalent CLuN-model. Proof outline. Given a consistent CLuN-model M = D, v , consider the CLmodel M = D , v with D = D and v = v and verify that M and M are equivalent. The only crucial case concerns the clause for negation, C¬.

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Adaptive Logics and Dynamic Proofs. Mastering the Dynamics of Reasoning, with Special Attention to Handling Inconsistency by Diderik Batens


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