Deductive Parsing of Visual Languages

Abstract

Computational linguistics has largely focussed on written and spoken textual languages. However, humans use many other kinds of symbolic notations for communication, in particular, two-dimensional graphical notations such as mathematical notation, choreography notation, organizational charts and electrical circuit diagrams. We can term such multi-dimensional symbolic notations, visual languages. Like textual languages, many of these notations have a well defined syntax and semantics. The standard approach to computer interpretation of visual languages is to utilize parsing technologies based on multi-dimensional grammars. In this paper we investigate a new approach to parsing visual languages based on linear logic. The advantages of this logic-based approach are threefold: It provides a more adequate level for modelling the semantics of visual languages; it allows us to implement them based on automated deduction and it provides a good basis for the investigation of their formal properties. We show how attributed multiset grammars, one of the most widely used methods for multi-dimensional parsing, can be embedded into linear logic, demonstrate how parsing corresponds to linear proofs and prove the soundness and correctness of this embedding. Importantly, our embedding is into a subset of a linear logic programming language. Thus, we also demonstrate how multi-dimensional parsing can be implemented as a directly executable linear logic program.