Abstract
The duality of proofs and counterexamples, or more generally, refutations, is ubiquitous in science, but involves distinctions often blurred by the rethoric of argumentation. More crisp distinctions between proofs and refutations are found in mathematics, especially in well defined formalized fragments.
Every working mathematician knows that finding a proof and looking for a counterexample are two very different activities that cannot be carried on simultaneusly. Usually the latter starts when the hope to find a proof is fading away, and the failed attempts will serve as an implicit guide to chart the territory in which to look for a counterexample. No general recipe is, however, gained from the failures, and a leap of creativity is required to find a counterxample, if such is at all obtained.
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Negri, S. (2013). On the Duality of Proofs and Countermodels in Labelled Sequent Calculi. In: Galmiche, D., Larchey-Wendling, D. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2013. Lecture Notes in Computer Science(), vol 8123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40537-2_2
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