| Ajdukiewicz is famous polish philosopher and logician who is recognized as the founder of categorial grammars today.Roughly speaking the term categorial grammars refers to some approaches using logical sentences and deduction rules to study natural language.This logical approach employs methods from mathematical logic and situates categorial grammars in the context of logics,which is deeply associated with the work of Joachim Lambek.Today modern categorial grammars have developed different branches in which the type logical grammars followed the traditional of Ajdukiewicz and J.Lambek is one of the most activity and influential ones.Ajdukiewicz’s original philosopher ideas and thinking on language and logic leads to the basic categorial grammars,AB Grammars,later philosophers and logicians improved and expanded category grammars for different motives,and gradually developed into a variety of schools of modern type-logical grammars.Among them,Lambek grammars and Lambek calculus won a place for categorial grammars in logic.We discuss some most cited language problems in the study of categorial grammars and representative solutions.On the basis of a large number of language case studies,we try to give our solution.The solution developed in the present work is inspired by Ajdukiewicz’s original ideas on language and logic,and it is expected that our work will provide new possibilities for the study of categorial grammars.Focuses on Ajdukiewicz and modern type-logical grammars,this paper is organized as follows:In the first chapter,we review the development of categorial grammars,explain our work and movitation.In the second chapter,we discuss Ajdukiewicz’s concept of language,showing his thinking and research on language and logic.In the third chapter we recall the most basic categorial grammars,AB grammars.In the fourth chapter,we mention the basic of modern type-logical grammars(Lambek grammars)and the language problems often encountered in the study of type grammars.Further,we introduce known solutions to the currently used extended arithmetic type syntax.In the last chapter we present solutions to popular language problems based on Lambek calculus enriched with subtype hypothesis set. |
