Combinatory Logic, Semantics and Cognition
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Combinatory Logic (CL) of H. B. Curry is a formalism where any operators can be composed and transformed by abstract operators (called combinators), without using bound variables. The actions of combinators are presented by introduction and elimination rules in the Gentzen’s.natural deduction style. By explicit deductions using combinators, it is shown how linguistic expressions are analyzed and linked to their structured semantic and cognitive representations where different types of cognitive primitives (operators and relators) are composed together. CL is used in the theoretical model of GRACE (GRammar of Applicative, Cognitive and Enunciative operations) to explain how activity of language, expressed by natural languages, works with changes of metalinguistic representations between different levels of processing: from a linguistic level towards a semantic-cognitive interpretation, according to a bottom up processing and from cognitive schemes towards their linguistic expressions, according to a top down processing. Some illustrating examples of changes of representations are given; one example is about a semantic representation of the verbal unit ‘go out of’, other examples are about the semantic representations of aspects and tenses.
Abstract
Combinatory Logic (CL) of H. B. Curry is a formalism where any operators can be composed and transformed by abstract operators (called combinators), without using bound variables. The actions of combinators are presented by introduction and elimination rules in the Gentzen’s.natural deduction style. By explicit deductions using combinators, it is shown how linguistic expressions are analyzed and linked to their structured semantic and cognitive representations where different types of cognitive primitives (operators and relators) are composed together. CL is used in the theoretical model of GRACE (GRammar of Applicative, Cognitive and Enunciative operations) to explain how activity of language, expressed by natural languages, works with changes of metalinguistic representations between different levels of processing: from a linguistic level towards a semantic-cognitive interpretation, according to a bottom up processing and from cognitive schemes towards their linguistic expressions, according to a top down processing. Some illustrating examples of changes of representations are given; one example is about a semantic representation of the verbal unit ‘go out of’, other examples are about the semantic representations of aspects and tenses.