From Aspecto-Temporal Analysis of a Natural Language to Logical Modeling Using Combinatory Logic

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Hee-Jin RO, Jong-Seok Soh

Abstract

The logic of Haskell Curry is a relatively adequate formalism for linguistics and more generally, for behavioral science, cognitive science, computer science and philosophy. To machine-readable treatment of a natural language, this paper presents the logical formalism of operators using the combinatory logic and the applications of their representations. The combinatory logic — which, along with Alonzo Church's lambda calculus and functional programming languages is a part of the family of applicative languages — is provided with a basic applicative operation, where the first argument is an operator, the second an operand, and the result is an applicative expression that can function as an operator or operand. This study assumes that the basic units of natural language are operators and operands, respectively. To the treatment of tenses and aspects in the linguistic domain, especially in the aspecto-temporal theory and a topological approach, the application of an operator to an operand is necessary. This article treats the logical formalization of elementary aspecto-temporal operators, which is based on the applicative operation. Additionally, it demonstrates in using natural deduction how an utterance can be formalized logically as an applicative expression. Using these methodologies (combinatory logic and natural deduction), this study aims to show how natural language calculates and computerizes expressions involving semantic domains including tense and aspect beyond the morpho-syntactic side.


 

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