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M. Abraham, Dov M. Gabbay & U. Schild (2009). Analysis of the Talmudic Argumentum A Fortiori Inference Rule Using Matrix Abduction.

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  1.  2
    Jacob’s Ladder: Logics of Magic, Metaphor and Metaphysics.Julio Michael Stern - forthcoming - Sophia:1-21.
    In this article, we discuss some issues concerning magical thinking—forms of thought and association mechanisms characteristic of early stages of mental development. We also examine good reasons for having an ambivalent attitude concerning the later permanence in life of these archaic forms of association, and the coexistence of such intuitive but informal thinking with logical and rigorous reasoning. At the one hand, magical thinking seems to serve the creative mind, working as a natural vehicle for new ideas and innovative insights, (...)
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    Logical Cornestones of Judaic Argumentation Theory.Andrew Schumann - 2013 - Argumentation 27 (3):305-326.
    In this paper, the four Judaic inference rules: qal wa- ḥ omer, gezerah š awah, heqe š, binyan ’av are considered from the logical point of view and the pragmatic limits of applying these rules are symbolic-logically explicated. According to the Talmudic sages, on the one hand, after applying some inference rules we cannot apply other inference rules. These rules are weak. On the other hand, there are rules after which we can apply any other. These rules are strong. This (...)
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    Logical Analysis of the Talmudic Rules of General and Specific (Klalim-U-Pratim).Michael Abraham, Dov M. Gabbay, Gabriel Hazut, Yosef E. Maruvka & Uri Schild - 2011 - History and Philosophy of Logic 32 (1):47-62.
    This article deals with a set-theoretic interpretation of the Talmudic rules of General and Specific, known as Klal and Prat (KP), Prat and Klal (PK), Klal and Prat and Klal (KPK) and Prat and Klal and Prat (PKP).
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    Preface.Andrew Schumann - 2011 - History and Philosophy of Logic 32 (1):1-8.
  5.  21
    Qal Wa- Omer and Theory of Massive-Parallel Proofs.Andrew Schumann - 2011 - History and Philosophy of Logic 32 (1):71-83.
    In this article, the author attempts to explicate the notion of the best known Talmudic inference rule called qal wa- omer. He claims that this rule assumes a massive-parallel deduction, and for formalizing it, he builds up a case of massive-parallel proof theory, the proof-theoretic cellular automata, where he draws conclusions without using axioms.
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