DeepAI AI Chat
Log In Sign Up

Formalized Lambek Calculus in Higher Order Logic (HOL4)

by   Chun Tian, et al.

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.


page 1

page 2

page 3

page 4


The Logic for a Mildly Context-Sensitive Fragment of the Lambek-Grishin Calculus

While context-free grammars are characterized by a simple proof-theoreti...

Focus-style proof systems and interpolation for the alternation-free μ-calculus

In this paper we introduce a cut-free sequent calculus for the alternati...

Gentzen-Mints-Zucker duality

The Curry-Howard correspondence is often described as relating proofs (i...

Factorize Factorization

We present a new technique for proving factorization theorems for compou...

Divergence and unique solution of equations

We study proof techniques for bisimilarity based on unique solution of e...

h: A Plank for Higher-order Attribute Contraction Schemes

We present and formalize h, a core (or "plank") calculus that can serve ...

Encodability and Separation for a Reflective Higher-Order Calculus

The ρ-calculus (Reflective Higher-Order Calculus) of Meredith and Radest...