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Sam Butchart [6]Samuel John Butchart [1]
  1. Sam Butchart & Susan Rogerson, Algebraizing A→.
    Abelian Logic is a paraconsistent logic discovered independently by Meyer and Slaney [10] and Casari [2]. This logic is also referred to as Abelian Group Logic (AGL) [12] since its set of theorems is sound and complete with respect to the class of Abelian groups. In this paper we investigate the pure implication fragment A→ of Abelian logic. This is an extension of the implication fragment of linear logic, BCI. A Hilbert style axiomatic system for A→ can obtained by adding (...)
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  2. Samuel John Butchart, Evidence and Explanation in Mathematics.
    .................................................................................................... ......................7 Chapter One: Foundational Epistemology...............................................................14..
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  3. Sam Butchart & Susan Rogerson (2014). On the Algebraizability of the Implicational Fragment of Abelian Logic. Studia Logica 102 (5):981-1001.
    In this paper we consider the implicational fragment of Abelian logic \({{{\sf A}_{\rightarrow}}}\) . We show that although the Abelian groups provide an semantics for the set of theorems of \({{{\sf A}_{\rightarrow}}}\) they do not for the associated consequence relation. We then show that the consequence relation is not algebraizable in the sense of Blok and Pigozzi (Mem Am Math Soc 77, 1989). In the second part of the paper, we investigate an extension of \({{{\sf A}_{\rightarrow}}}\) in the same language (...)
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  4. Sam Butchart (2010). An Introduction to Non-Classical Logic: From If to Is. Australasian Journal of Philosophy 88 (4):745-748.
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  5. Sam Butchart, Toby Handfield & Greg Restall (2009). Teaching Philosophy, Logic and Critical Thinking Using Peer Instruction. Teaching Philosophy (1):1-40.
    Peer Instruction (or PI for short) is a simple and effective technique you can use to make lectures more interactive, more engaging, and more effective learning experiences.
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  6. Tomasz Kowalski & Sam Butchart (2006). A Note on Monothetic BCI. Notre Dame Journal of Formal Logic 47 (4):541-544.
    In "Variations on a theme of Curry," Humberstone conjectured that a certain logic, intermediate between BCI and BCK, is none other than monothetic BCI—the smallest extension of BCI in which all theorems are provably equivalent. In this note, we present a proof of this conjecture.
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  7. Susan Rogerson & Sam Butchart (2002). Naïve Comprehension and Contracting Implications. Studia Logica 71 (1):119-132.
    In his paper [6], Greg Restall conjectured that a logic supports a naïve comprehension scheme if and only if it is robustly contraction free, that is, if and only if no contracting connective is definable in terms of the primitive connectives of the logic. In this paper, we present infinitely many counterexamples to Restall''s conjecture, in the form of purely implicational logics which are robustly contraction free, but which trivialize naïve comprehension.
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