Abstract
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.
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Goble, L. Combinator Logics. Studia Logica 76, 17–66 (2004). https://doi.org/10.1023/B:STUD.0000027466.68014.52
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DOI: https://doi.org/10.1023/B:STUD.0000027466.68014.52