Logical Operators and Quantifiers in Natural Language

This paper investigates negations in natural language, comparing natural language and first-order logic, and it introduces a model for describing quantifiers and negations in natural language. The model consists of the semantic representation of quantifiers such as 'all' and 'some,' and logical operators such as entailment between these words and thier negation. The basic framework of semantic representation is a pair of lists, which is called a 'dual list.' Each list includes conceptual elements. The upper list represents a 'literal' meaning of a word, and the lower represents a 'possible' meaning. Logical operations such as entailment and negation are defined on the dual list. The model can handle a wide range of linguistic phenomena, which are related to numbers such as 'three,' and conjunctions such as 'and' and 'or,' as well as qualities such as 'all' 'some' and 'no.' The negation operation on the dual lists consistently generates all possible interpretations for these words. Words such as 'all' and 'some,' and 'and' and 'or' correspond to logical operators in a sense, but they are different in some other aspects. This model, especially its negation process, clarifies the similarities and differences between logic and natural language.