Studia Logica 76 (1):17 - 66 (2004)

Combinator logics are a broad family of substructual logics that are formed by extending the basic relevant logic B with axioms that correspond closely to the reduction rules of proper combinators in combinatory logic. In the Routley-Meyer relational semantics for relevant logic each such combinator logic is characterized by the class of frames that meet a first-order condition that also directly corresponds to the same combinator's reduction rule. A second family of logics is also introduced that extends B with the addition of propositional constants that correspond to combinators. These are characterized by relational frames that meet first-order conditions that reflect the structures of the combinators themselves.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/B:STUD.0000027466.68014.52
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References found in this work BETA

The Semantics of Entailment — III.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (2):192 - 208.
The Semantics of Entailment Omega.Yoko Motohama, Robert K. Meyer & Mariangiola Dezani-Ciancaglini - 2002 - Notre Dame Journal of Formal Logic 43 (3):129-145.
Relevant Logics.Edwin D. Mares & Robert K. Meyer - 2001 - In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell. pp. 280--308.

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