Mental models: towards a cognitive science of language, inference, and consciousness
Mental models: towards a cognitive science of language, inference, and consciousness
GRAFLOG: understanding drawings through natural language
Computer Graphics Forum
Computability and logic: 3rd ed.
Computability and logic: 3rd ed.
A logical framework for depiction and image interpretation
Artificial Intelligence
A general framework for visualizing abstract objects and relations
ACM Transactions on Graphics (TOG)
A general framework for bidirectional translation between abstract and pictorial data
ACM Transactions on Information Systems (TOIS) - Special issue on user interface software and technology
Realization of a geometry-theorem proving machine
Computers & thought
The Programming Language Aspects of ThingLab, a Constraint-Oriented Simulation Laboratory
ACM Transactions on Programming Languages and Systems (TOPLAS)
Generating referring expressions: boolean extensions of the incremental algorithm
Computational Linguistics
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Semantics and graphical information
INTERACT '90 Proceedings of the IFIP TC13 Third Interational Conference on Human-Computer Interaction
Diagram processing: computing with diagrams
Artificial Intelligence
Graflog: a theory of semantics for graphics with applications to human-computer interaction and cad systems
A model for multimodal reference resolution
Computational Linguistics
The Thirteen Books of Euclid's Elements, Books 1 and 2
The Thirteen Books of Euclid's Elements, Books 1 and 2
Dialogue model specification and interpretation for intelligent multimodal HCI
IBERAMIA'10 Proceedings of the 12th Ibero-American conference on Advances in artificial intelligence
Hi-index | 0.00 |
In this paper a theory for the synthesis of geometric concepts is presented. The theory is focused on a constructive process that synthesizes a function in the geometric domain representing a geometric concept. Geometric theorems are instances of this kind of concepts. The theory involves four main conceptual components: conservation principles, action schemes, descriptions of geometric abstractions and reinterpretations of diagrams emerging during the generative process. A notion of diagrammatic derivation in which the external representation and its interpretation are synthesized in tandem is also introduced in this paper. The theory is exemplified with a diagrammatic proof of the Theorem of Pythagoras. The theory also illustrates how the arithmetic interpretation of this theorem is produced in tandem with its diagrammatic derivation under an appropriate representational mapping. A second case study in which an arithmetic theorem is synthesized from an underlying geometric concept is also included. An interactive prototype program in which the inference load is shared between the system and the human user is also presented. The paper is concluded with a reflection on the expressive power of diagrams, their effectiveness in representation and inference, and the relation between synthetic and analytic knowledge in the realization of theorems and their proofs.