VRule: Novel Pixel Rewriting System Formalisms

Abstract

This work presents novel formalisms for Pixel Rewriting Systems (PRSs) that expand PRS-based programming into new domains of end-user modeling and other forms of computation. A key aspect of this work is that it leverages a Pattern Directed Inference System (PDIS) architectural approach to develop the new formalisms presented herein, yet retains the core image-to-image computational framework of PRSs.

Diagrams have been used for heuristic and pedagogical tools, but have not generally been considered formal mechanisms for logical proof and inference. The ubiquity of graphical user interfaces and a continued focus upon non-keyboard based interfaces has led to a reexamination into both the computational and cognitive roles of diagrams, including the development of visual programming systems which are a subfield of diagrammatic reasoning.

With respect to deductive inference, pattern directed inference systems offer a programming paradigm that differs from the imperative, procedural, or object oriented paradigms familiar to practitioners of FORTRAN, C, C++, Java, or Python. BitPict was the first diagrammatic reasoning system to demonstrate a programming environment that bridges the two paradigms of diagrammatic reasoning and pattern directed inference systems, offering a computational environment where reasoning occurs from image to image through pixel rewriting without any sentential representation. A common critique of BitPict is that it is too simplistic for end user programming domains. SOAR+SVI utilized the pixel rewriting systems pioneered by BitPict to implement part of and end user programming environment in the domain of image manipulation for exploration of spatial and visual models in a cognitive architecture.

This work will explore the architectural aspects of pixel rewriting systems based upon the concepts of pattern directed inference systems, and will describe new formalisms for pixel rewriting systems that provide new formalisms for classes of problems which include some forms of emerging approaches to cellular automata and agent based modelling to be programmed and executed in an entirely visual image-to-image processing environment, and will demonstrate how recent models in the domains of epidemiology and climate change analysis programmed respectively in Python and C# could be similarly programmed in a pixel rewriting system using the newly developed formalisms.

An examination of Cellular Automata (CAs) furthers this goal as CAs have been used with modelling and simulation extensively, and includes an examination of the relationship between rule based pixel rewriting systems and cellular modelling systems. New formalisms are also demonstrated that leverage the diagrammatic nature of CA models enabling large classes of CA models to be implemented in a purely graphical rule based pixel rewriting environment, including numerous examples of CA model implementations. Representative examples of problem classes demonstrate the utility of these new formalisms and the wide variety of programming problems that can be addressed with purely image to image computation. Additionally, an examination of the natural alignment between pixel rewriting systems and the parallelized architecture of General-Purpose computing on Graphics Processing Units (GPGPU) environments such as OpenCL is briefly presented.