Adaptive Logics and Dynamic Proofs. Mastering the Dynamics by Diderik Batens

By Diderik Batens

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Extra info for Adaptive Logics and Dynamic Proofs. Mastering the Dynamics of Reasoning, with Special Attention to Handling Inconsistency

Example text

So all CLuNmodels of {A∨B, ¬A} that falsify A∧¬A verify B. 6 below. 3. e. {A ∈ WO | M A} = {A ∈ WO | M A}. This presupposes obviously that both semantic systems are defined with respect to the same language. 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.

10. 1 A line l that has ∆ as its fourth element is marked iff a member of ∆ has been derived. 16 Later, this expression will obtain a more general meaning. Its name abbreviates “disjunction of abnormalities”. At the present point, abnormalities are contradictions. We shall see later that the notion of abnormality has a much more general meaning. 50 CHAPTER 2. EXAMPLE: HANDLING INCONSISTENCY Let us consider a simple proof that illustrates the matter. I shall write the marks, if any, at the right of the lines as a check followed by the number of the stage at which the line is marked.

For some examples from the empirical sciences see [Bro90, Meh93, Meh99a, Meh02a, Ner02, 37 38 CHAPTER 2. EXAMPLE: HANDLING INCONSISTENCY Nor87, Nor93, Smi88]. Moreover, it appears from the history of the sciences that scientists do not simply give up inconsistent theories in order to start from scratch. Even if a theory T is inconsistent, and so according to consistentists cannot be a correct description of the structure of the world, it may still correctly describe a great deal of the structure of the world.

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