6 found
  1.  98
    Routes to triviality.Susan Rogerson & Greg Restall - 2004 - Journal of Philosophical Logic 33 (4):421-436.
    It is known that a number of inference principles can be used to trivialise the axioms of naïve comprehension - the axioms underlying the naïve theory of sets. In this paper we systematise and extend these known results, to provide a number of general classes of axioms responsible for trivialising naïve comprehension.
    Direct download (5 more)  
    Export citation  
    Bookmark   16 citations  
  2.  95
    Naïve comprehension and contracting implications.Susan Rogerson & Sam Butchart - 2002 - 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.
    Direct download (5 more)  
    Export citation  
    Bookmark   12 citations  
  3. Natural deduction and Curry's paradox.Susan Rogerson - 2007 - Journal of Philosophical Logic 36 (2):155 - 179.
    Curry's paradox, sometimes described as a general version of the better known Russell's paradox, has intrigued logicians for some time. This paper examines the paradox in a natural deduction setting and critically examines some proposed restrictions to the logic by Fitch and Prawitz. We then offer a tentative counterexample to a conjecture by Tennant proposing a criterion for what is to count as a genuine paradox.
    Direct download (4 more)  
    Export citation  
    Bookmark   10 citations  
  4.  33
    On the Algebraizability of the Implicational Fragment of Abelian Logic.Sam Butchart & Susan Rogerson - 2014 - Studia Logica 102 (5):981-1001.
    In this paper we consider the implicational fragment of Abelian logic \ . We show that although the Abelian groups provide an semantics for the set of theorems of \ 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 . In the second part of the paper, we investigate an extension of \ in the same language and having the same set of theorems and (...)
    Direct download (4 more)  
    Export citation  
    Bookmark   2 citations  
  5. Algebraizing A→.Sam Butchart & Susan Rogerson - unknown
    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 (...)
    Export citation  
  6.  24
    Hirokawa on right weakening and right contraction.Susan Rogerson - 2007 - In Jean-Yves Béziau & Alexandre Costa-Leite (eds.), Perspectives on Universal Logic. pp. 237--263.
    In his paper, ìRight Weakening and Right Contraction in LK î, Hirokawa investigates the properties of the structural rules of contraction and weak- ening as they appear in a certain sequent calculus formulation of Örst order classical logic. In what follows we explore the notion of correspondence, in particular with reference to the structural rules in the succedent, and in doing so critically examine the sensitivity of Hirokawaís results to the formulation of the calculus, both with respect to the formulations (...)
    Direct download  
    Export citation  
    Bookmark   1 citation