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The Taming of the Cut. Classical Refutations with Analytic Cut
No full textThe method of analytic tableaux is a direct descendant of Gentzen's cut-free sequent calculus and is regarded as a paradigm of the notion of analytic deduction in classical logic. However, cut-free systems are anomalous from the proof-theoretical, the semantical and the computational point of view. Firstly, they cannot represent the use of auxiliary lemmas in proofs. Secondly, they cannot express the bivalence of classical logic. Thirdly, they are extremely inefficient, as is emphasized by the ‘computational scandal’ that such systems cannot potynomially simulate the truth-tables. None of these anomalies occurs if the cut rule is allowed. This raises the problem of formulating a proof system which incorporates a cut rule and yet can provide a suitable model of classical analytic deduction. For this purpose we present an alternative refutation system for classical logic, that we call KE. This system, though being ‘close’ to Smullyan's tableau method, is not cut-free but includes a classical cut rule which is not eliminable. Analytic deductions are then obtained by restricting the cut rule to analytic applications, namely applications that do not violate the subformula principle. It turns out that this analytic restriction of the KE system shares all the interesting properties of Smullyan's tableau method and of cut-free systems—it obeys the subformula principle and admits systematic refutation procedures—but uniformly and essentially improves on them from the complexity viewpoint. In particular, we show that the analytic KE system linearly simulates the tableau method, but the tableau method cannot p-simulate the analytic KE system. Finally, we show that every proof system that can simulate the cut rule in a constant number of steps is strictly more powerful than cut-free systems, from the complexity viewpoint, even in the domain of analytic deduction. Hence, the speed-up of the analytic KE system does not depend on the form of the operational rules but only on the analytic cut rule
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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