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The Semantics of Entailment

In Hughes Leblanc (ed.), Truth, Syntax, and Modality: Proceedings Of The Temple University Conference On Alternative Semantlcs. Amsterdam: North-Holland Publishing Company. pp. 199-243 (1973)

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  1. Logics for Classes of Boolean Monoids.Gerard Allwein, Hilmi Demir & Lee Pike - 2004 - Journal of Logic, Language and Information 13 (3):241-266.
    This paper presents the algebraic and Kripke modelsoundness and completeness ofa logic over Boolean monoids. An additional axiom added to thelogic will cause the resulting monoid models to be representable as monoidsof relations. A star operator, interpreted as reflexive, transitiveclosure, is conservatively added to the logic. The star operator isa relative modal operator, i.e., one that is defined in terms ofanother modal operator. A further example, relative possibility,of this type of operator is given. A separate axiom,antilogism, added to the logic (...)
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  • Corrupting the Youth: A History of Philosophy in Australia.James Franklin - 2003 - Sydney, Australia: Macleay Press.
    A polemical account of Australian philosophy up to 2003, emphasising its unique aspects (such as commitment to realism) and the connections between philosophers' views and their lives. Topics include early idealism, the dominance of John Anderson in Sydney, the Orr case, Catholic scholasticism, Melbourne Wittgensteinianism, philosophy of science, the Sydney disturbances of the 1970s, Francofeminism, environmental philosophy, the philosophy of law and Mabo, ethics and Peter Singer. Realist theories especially praised are David Armstrong's on universals, David Stove's on logical probability (...)
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  • Richard (Routley) Sylvan: Writings on Logic and Metaphysics.Dominic Hyde - 2001 - History and Philosophy of Logic 22 (4):181-205.
    Richard Sylvan (né Routley) was one of Australasia's most prolific and systematic philosophers. Though known for his innovative work in logic and metaphysics, the astonishing breadth of his philosophical endeavours included almost all reaches of philosophy. Taking the view that very basic assumptions of mainstream philosophy were fundamentally mistaken, he sought radical change across a wide range of theories. However, his view of the centrality of logic and recognition of the possibilities opened up by logical innovation in the fundamental areas (...)
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  • Incompactness of the A1 Fragment of Basic Second Order Propositional Relevant Logic.Guillermo Badia - 2019 - Australasian Journal of Logic 16 (1):1-8.
    In this note we provide a simple proof of the incompactness over Routley-Meyer B-frames of the A1 fragment of the second order propositional relevant language.
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  • Lower Semilattice-Ordered Residuated Semigroups and Substructural Logics.Szabolcs Mikulás - 2015 - Studia Logica 103 (3):453-478.
    We look at lower semilattice-ordered residuated semigroups and, in particular, the representable ones, i.e., those that are isomorphic to algebras of binary relations. We will evaluate expressions in representable algebras and give finite axiomatizations for several notions of validity. These results will be applied in the context of substructural logics.
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  • Philosophy, Drama and Literature.Rick Benitez - 2010 - In Graham Oppy & Steve Gardner (eds.), Companion to Philosophy in Australia and New Zealand. Melbourne, Australia: Monash University Press. pp. 371-372.
    Philosophy and Literature is an internationally renowned refereed journal founded by Denis Dutton at the University of Canterbury, Christchurch. It is now published by the Johns Hopkins University Press. Since its inception in 1976, Philosophy and Literature has been concerned with the relation between literary and philosophical studies, publishing articles on the philosophical interpretation of literature as well as the literary treatment of philosophy. Philosophy and Literature has sometimes been regarded as iconoclastic, in the sense that it repudiates academic pretensions, (...)
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  • Relevance Logic and the Calculus of Relations.Roger D. Maddux - 2010 - Review of Symbolic Logic 3 (1):41-70.
    Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.
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  • Positive Fragments of Relevance Logic and Algebras of Binary Relations.Robin Hirsch & Szabolcs Mikulás - 2011 - Review of Symbolic Logic 4 (1):81-105.
    We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.
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  • Tr, Te-R, Tec-R.Eunsuk Yang - 2002 - Bulletin of the Section of Logic 31 (3):171-181.
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  • Propositional Logic Extended with a Pedagogically Useful Relevant Implication.Diderik Batens - 2014 - Logic and Logical Philosophy 23 (3).
    First and foremost, this paper concerns the combination of classical propositional logic with a relevant implication. The proposed combination is simple and transparent from a proof theoretic point of view and at the same time extremely useful for relating formal logic to natural language sentences. A specific system will be presented and studied, also from a semantic point of view. The last sections of the paper contain more general considerations on combining classical propositional logic with a relevant logic that has (...)
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