385 research outputs found
A Computable Measure of Algorithmic Probability by Finite Approximations with an Application to Integer Sequences
Given the widespread use of lossless compression algorithms to approximate
algorithmic (Kolmogorov-Chaitin) complexity, and that lossless compression
algorithms fall short at characterizing patterns other than statistical ones
not different to entropy estimations, here we explore an alternative and
complementary approach. We study formal properties of a Levin-inspired measure
calculated from the output distribution of small Turing machines. We
introduce and justify finite approximations that have been used in some
applications as an alternative to lossless compression algorithms for
approximating algorithmic (Kolmogorov-Chaitin) complexity. We provide proofs of
the relevant properties of both and and compare them to Levin's
Universal Distribution. We provide error estimations of with respect to
. Finally, we present an application to integer sequences from the Online
Encyclopedia of Integer Sequences which suggests that our AP-based measures may
characterize non-statistical patterns, and we report interesting correlations
with textual, function and program description lengths of the said sequences.Comment: As accepted by the journal Complexity (Wiley/Hindawi
Abduction for (non-ominiscient) agents
Among the non-monotonic reasoning processes, abduction is one of the most important. Usually described as the process of looking florexplantions, it has been recognized as one of the most commonly used in our daily activities. Still, the traditional definitions of an abductive problem and an abductive solution mention only theories and formulas, leaving agency out of the picture. Our work proposes a study of abductive reasoning from an epistemic and dynamic perspective, making special emphasis on non-ideal agents. We begin by exploring what an abductive problema is in terms of an agent’s information, and what an abductive solution is in terms of the actions that modify it. Then we explore the different kinds of abductive problems and abductive solutions that arise when we consider agents whose information is not closed under logical consequence, and agents whose reasoning abilities are not complete
Visualizing Abduction
info:eu-repo/semantics/publishedVersio
Natural scene statistics mediate the perception of image complexity
Humans are sensitive to complexity and regularity in patterns. The subjective
perception of pattern complexity is correlated to algorithmic
(Kolmogorov-Chaitin) complexity as defined in computer science, but also to the
frequency of naturally occurring patterns. However, the possible mediational
role of natural frequencies in the perception of algorithmic complexity remains
unclear. Here we reanalyze Hsu et al. (2010) through a mediational analysis,
and complement their results in a new experiment. We conclude that human
perception of complexity seems partly shaped by natural scenes statistics,
thereby establishing a link between the perception of complexity and the effect
of natural scene statistics
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