Theoretical Computer Science
A logical framework for depiction and image interpretation
Artificial Intelligence
Extending definite clause grammars with scoping constructs
Logic programming
Building visual language parsers
CHI '91 Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
Definite-clause set grammars: a formalism for problem solving
Journal of Logic Programming
Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
Using spatial logic to describe visual languages
Artificial Intelligence Review - Special issue on integration of natural language and vision processing: recent advances
A survey of visual language specification and recognition
Visual language theory
A fully formalized theory for describing visual notations
Visual language theory
A Linear Logic Treatment of Phrase Structure Grammars for Unbounded Dependencies
LACL '97 Selected papers from the Second International Conference on Logical Aspects of Computational Linguistics
Linguistic, Philosophical, and Pragmatic Aspects of Type-Directed Natural Language
LACL '97 Selected papers from the Second International Conference on Logical Aspects of Computational Linguistics
Non-standard Logics for Diagram Interpretation
Diagrams '00 Proceedings of the First International Conference on Theory and Application of Diagrams
Programming in Lygon: An Overview
AMAST '96 Proceedings of the 5th International Conference on Algebraic Methodology and Software Technology
A declarative specification and semantics for visual languages
Journal of Visual Languages and Computing
Visual Multiset Rewriting: Applications to Diagram Parsing and Reasoning
WMP '00 Proceedings of the Workshop on Multiset Processing: Multiset Processing, Mathematical, Computer Science, and Molecular Computing Points of View
Theory and Practice of Logic Programming
Functional-Logic Graph Parser Combinators
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Journal of Visual Languages and Computing
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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.