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Merrie Bergmann (2003). The Logic Book.

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  1.  31
    Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different.Allen P. Hazen & Francis Jeffry Pelletier - 2014 - Studia Logica 102 (6):1103-1142.
    Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...)
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  2.  79
    Wittgensteinian Tableaux, Identity, and Co-Denotation.Kai F. Wehmeier - 2008 - Erkenntnis 69 (3):363-376.
    Wittgensteinian predicate logic (W-logic) is characterized by the requirement that the objects mentioned within the scope of a quantifier be excluded from the range of the associated bound variable. I present a sound and complete tableaux calculus for this logic and discuss issues of translatability between Wittgensteinian and standard predicate logic in languages with and without individual constants. A metalinguistic co-denotation predicate, akin to Frege’s triple bar of the Begriffsschrift, is introduced and used to bestow the full expressive power of (...)
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  3.  47
    The Power and the Limits of Wittgenstein's N Operator.James W. McGray - 2006 - History and Philosophy of Logic 27 (2):143-169.
    The power of Wittgenstein's N operator described in the Tractatus is that every proposition which can be expressed in the Russellian variant of the predicate calculus familiar to him has an equivalent proposition in an extended variant of his N operator notation. This remains true if the bound variables are understood in the usual inclusive sense or in Wittgenstein's restrictive exclusive sense. The problematic limit of Wittgenstein's N operator comes from his claim that symbols alone reveal the logical status of (...)
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  4.  75
    A Brief History of Natural Deduction.Francis Jeffry Pelletier - 1999 - History and Philosophy of Logic 20 (1):1-31.
    Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Ja?kowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks?the standard conduits of (...)
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  5.  28
    PDP Networks Can Provide Models That Are Not Mere Implementations of Classical Theories.Michael R. W. Dawson, D. A. Medler & Istvan S. N. Berkeley - 1997 - Philosophical Psychology 10 (1):25-40.
    There is widespread belief that connectionist networks are dramatically different from classical or symbolic models. However, connectionists rarely test this belief by interpreting the internal structure of their nets. A new approach to interpreting networks was recently introduced by Berkeley et al. (1995). The current paper examines two implications of applying this method: (1) that the internal structure of a connectionist network can have a very classical appearance, and (2) that this interpretation can provide a cognitive theory that cannot be (...)
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  6.  47
    Sturgeon and Brink on Moral Explanations.Ken Yasenchuk - 1994 - Southern Journal of Philosophy 32 (4):483-502.
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  7.  40
    A New Semantics for First-Order Logic, Multivalent and Mostly Intensional.Hugues Leblanc - 1984 - Topoi 3 (1):55-62.