In the past, many knowledge representation systems failed because they were too monolithic and didn't scale well, whereas other systems failed to have an impact because they were small and isolated. Along with this trade-off in size, there is also a constant tension between the cost involved in building a larger community that can interoperate through common terms and the cost of the lack of interoperability. Its main contribution is in recognizing and supporting the fractal patterns of scalable web systems. In this article we discuss why fractal patterns are an appropriate model for web systems and how semantic web technologies can be used to design scalable and interoperable systems.
We present a fractal technique for addressing geometric analogy problems from the Raven's Standard Progressive Matrices test of general intelligence. In this method, an image is represented fractally, capturing its inherent self-similarity. We apply these fractal representations to problems from the Raven's test, and show how these representations afford a new method for solving complex geometric analogy problems. We present results using the fractal algorithm on all 60 problems from the Standard Progressive Matrices version of the Raven's test.
In one way, Jackson Pollock's mathematics was ahead of its time. When the reclusive artist poured paint from cans onto vast canvases laid out across the floor of his barn in the late 1940s and early 1950s, he created splatters of paint that seemed completely random. Some interpretations saw them as a statement about the futility of World War II, others as a commentary on art as experience rather than representation. As Pollock refined his technique over the years, critics became increasingly receptive to his work, launching him into the public eye. "We have a deliberate disorder of hypothetical hidden orders," one critic wrote, "or'multiple labyrinths.' " In 1999, Richard Taylor, a physicist at the University of Oregon, expressed the "hidden orders" of Pollock's work in a very different way.
We report a novel approach to addressing the Raven’s Progressive Matrices (RPM) tests, one based upon purely visual representations. Our technique introduces the calculation of confidence in an answer and the automatic adjustment of level of resolution if that confidence is insufficient. We first describe the nature of the visual analogies found on the RPM. We then exhibit our algorithm and work through a detailed example. Finally, we present the performance of our algorithm on the four major variants of the RPM tests, illustrating the impact of confidence. This is the first such account of any computational model against the entirety of the Raven’s.
Model-Based Diagnosis (MBD) approaches often yield a large number of diagnoses, severely limiting their practical utility. This paper presents a novel active testing approach based on MBD techniques, called FRACTAL (FRamework for ACtive Testing ALgorithms), which, given a system description, computes a sequence of control settings for reducing the number of diagnoses. The approach complements probing, sequential diagnosis, and ATPG, and applies to systems where additional tests are restricted to setting a subset of the existing system inputs while observing the existing outputs. This paper evaluates the optimality of FRACTAL, both theoretically and empirically. FRACTAL generates test vectors using a greedy, next-best strategy and a low-cost approximation of diagnostic information entropy. Further, the approximate sequence computed by FRACTAL's greedy approach is optimal over all poly-time approximation algorithms, a fact which we confirm empirically. Extensive experimentation with ISCAS85 combinational circuits shows that FRACTAL reduces the number of remaining diagnoses according to a steep geometric decay function, even when only a fraction of inputs are available for active testing.