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  1.  39
    Eight Inference Rules for Implication.Michael Arndt - 2019 - Studia Logica 107 (4):781-808.
    Utilizing an idea that has its first appearance in Gerhard Gentzen’s unpublished manuscripts, we generate an exhaustive repertoire of all the possible inference rules that are related to the left implication inference rule of the sequent calculus from a ground sequent, that is, a logical axiom. We discuss the similarities and differences of these derived rules as well as their interaction with the implication right rule under cut and the structural axiom. We further consider the question of analyticity of cuts (...)
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  2.  35
    The Explosion Calculus.Michael Arndt - 2020 - Studia Logica 108 (3):509-547.
    A calculus for classical propositional sequents is introduced that consists of a restricted version of the cut rule and local variants of the logical rules. Employed in the style of proof search, this calculus explodes a given sequent into its elementary structural sequents—the topmost sequents in a derivation thus constructed—which do not contain any logical constants. Some of the properties exhibited by the collection of elementary structural sequents in relation to the sequent they are derived from, uniqueness and unique representation (...)
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  3.  32
    The Role of Structural Reasoning in the Genesis of Graph Theory.Michael Arndt - 2019 - History and Philosophy of Logic 40 (3):266-297.
    The seminal book on graph theory by Dénes Kőnig, published in the year 1936, collected notions and results from precursory works from the mid to late nineteenth century by Hamilton, Cayley, Sylvester and others. More importantly, Kőnig himself contributed many of his own results that he had obtained in the more than twenty years that he had been working on this subject matter. What is noteworthy is the fact that the fundamentals of what he calls directed graphs are taken almost (...)
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