2017/05/20 by Chun Tian, Tian, Chun
Computer Science · #Computation and Language (cs.CL) #D.2.4 #FOS: Computer and information sciences #I.2.7 #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Natural Language Processing Techniques
paper · pdf · doi:10.48550/arxiv.1705.07318
openalex publication_date 2017/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this project, a rather complete proof-theoretical formalization of Lambek Calculus (non-associative with arbitrary extensions) has been ported from Coq proof assistent to HOL4 theorem prover, with some improvements and new theorems. Three deduction systems (Syntactic Calculus, Natural Deduction and Sequent Calculus) of Lambek Calculus are defined with many related theorems proved. The equivalance between these systems are formally proved. Finally, a formalization of Sequent Calculus proofs (where Coq has built-in supports) has been designed and implemented in HOL4. Some basic results including the sub-formula properties of the so-called "cut-free" proofs are formally proved. This work can be considered as the preliminary work towards a language parser based on category grammars which is not multimodal but still has ability to support context-sensitive languages through customized extensions.