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Simple Consequence Relations

Simple Consequence Relations,10.1016/0890-5401(91)90023-U,Information and Computation/information and Control,Arnon Avron

Simple Consequence Relations   (Citations: 93)
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We provide a general investigation of Logic in which the notion ofa simple consequence relation is taken to be fundamental. Our notionis more general than the usual one since we give up monotonicityand use multisets rather than sets. We use our notion for characterizingseveral known logics (including Linear Logic and non-monotoniclogics) and for a general, semantics-independent classification of standardconnectives via equations on consequence relations (these includeGirard's...
Journal: Information and Computation/information and Control - IANDC , vol. 92, no. 1, pp. 105-140, 1991
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    • ...The rule should also be pure in the sense of [1] (i.e...

    Arnon Avronet al. Strict Canonical Constructive Systems

    • ...notion of (abstract) consequence relation has been formalised by Gentzen, Tarski and Scott [2,22,45]...
    • ...A generalisation by Avron [2] also allows for inclusion of substructural (e.g., non-monotonic) logics...
    • ...1 More general notions work with multisets instead of sets of premises [2]...
    • ...Note that our definition of negation also covers intuitionistic negation (unlike the treatment in [2], which assumes ¬¬-elimination)...
    • ...A theory Γ ⊆ S is satisfiable ,i f it has am odelM (i.e., a model M ∈M such that M |= ϕ for ϕ ∈ Γ). Semantic entailment in a room is defined as usual: for Γ ⊆ S and ϕ ∈ S, we write Γ |= ϕ, if all models satisfying all sentences in Γ also satisfy ϕ. The following result is folklore [2]:...
    • ...What happens then when we change the set of propositional symbols? For example [2,3] mention the property of an entailment relation to be stable under mappings of the propositional variables...

    Till Mossakowskiet al. What is a Logic Translation?

    • ...The rule should also be pure in the sense of [1] (i.e., there should be no side conditions limiting its application), and its active formulas should be immediate subformulas of its principal formula...

    Arnon Avronet al. Canonical Constructive Systems

    • ...However, it rules out from the class of “logics in L” just two trivial logics (see [7]), and it is technically convenient to include it. 5 See [1] for the differences between the “truth” and “validity” consequence relations of...

    Arnon Avron. Multi-valued Semantics: Why and How

    • ...All rule systems representable in LF satisfy the structural properties of a hypothetical judgement (weakening, exchange, contraction, and substitution) because all LF rules are pure [4]—they place no constraints on the context in which they can be applied...

    Daniel R. LicataNoamet al. Focusing on Binding and Computation

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