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  1. Andrew Schumann (2013). Logical Cornestones of Judaic Argumentation Theory. 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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  2. Andrew Schumann (2013). On Two Squares of Opposition: The Leśniewski's Style Formalization of Synthetic Propositions. [REVIEW] Acta Analytica 28 (1):71-93.
    In the paper we build up the ontology of Leśniewski’s type for formalizing synthetic propositions. We claim that for these propositions an unconventional square of opposition holds, where a, i are contrary, a, o (resp. e, i) are contradictory, e, o are subcontrary, a, e (resp. i, o) are said to stand in the subalternation. Further, we construct a non-Archimedean extension of Boolean algebra and show that in this algebra just two squares of opposition are formalized: conventional and the square (...)
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  3. Andrew Schumann (ed.) (2012). Logic in Central and Eastern Europe: History, Science, and Discourse. University Press of America.
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  4. Andrew Schumann (2011). Preface. History and Philosophy of Logic 32 (1):1-8.
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  5. Andrew Schumann (2011). Qal Wa- Omer and Theory of Massive-Parallel Proofs. 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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  6. Andrew Schumann (ed.) (2010). Judaic Logic. Gorgias Press.
     
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  7. Andrew Schumann (2010). Modal Calculus of Illocutionary Logic. In Piotr Stalmaszczyk (ed.), Philosophy of Language and Linguistics. Ontos Verlag. 261.
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  8. Andrew Schumann (2008). Non-Archimedean Fuzzy and Probability Logic. Journal of Applied Non-Classical Logics 18 (1):29-48.
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  9. Andrew Schumann (ed.) (2008). Philosophical Logic. University of Białystok.
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  10. Andrew Schumann (2007). Non-Archimedean Valued Predicate Logic. Bulletin of the Section of Logic 36 (1/2):67-78.
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  11. A. Yu Khrennikov & Andrew Schumann (2006). Logical Approach to P-Adic Probabilities. Bulletin of the Section of Logic 35 (1):49-57.
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  12. Andrew Schumann (2006). A Lattice for the Language of Aristotle's Syllogistic and a Lattice for the Language of Vasiľév's Syllogistic. Logic and Logical Philosophy 15 (1):17-37.
    In this paper an algebraic system of the new type is proposed (namely, a vectorial lattice). This algebraic system is a lattice for the language of Aristotle’s syllogistic and as well as a lattice for the language of Vasiľév’s syllogistic. A lattice for the language of Aristotle’s syllogistic is called a vectorial lattice on cap-semilattice and a lattice for the language of Vasiľév’s syllogistic is called a vectorial lattice on closure cap-semilattice. These constructions are introduced for the first time.
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