Online research in philosophy

A geometrical interpretation of independence and exchangeability leads to understanding the failure of de Finetti's theorem for a finite exchangeable sequence. In particular an exchangeable sequence of length r which can be extended to an exchangeable sequence of length k is almost a mixture of independent experiments, the error going to zero like 1/k.

Generalisations of theory change involving arbitrary sets of wffs instead of belief sets have become known as base change. In one view, a base should be thought of as providing more structure to its generated belief set, and can be used to determine the theory change operation associated with a base change operation. In this paper we extend a proposal along these lines by Meyer et al. We take an infobase as a finite sequence of wffs, with each element in the sequence being seen as an independently obtained bit of information, and define appropriate infobase change operations. The associated theory change operations satisfy the AGM postulates for theory change. Since an infobase change operation produces a new infobase, it allows for iterated infobase change. We measure iterated infobase change against the postulates proposed by Darwiche et al. and Lehmann.

Recently Timothy Williamson asked ‘How probable is an infinite sequence of heads?’ In this paper, I suggest the probability of an infinite sequence of heads.

If artificial neural networks are ever to form the foundation for higher level cognitive behaviors in machines or to realize their full potential as explanatory devices for human cognition, they must show signs of autonomy, multifunction operation, and intersystem integration that are absent in most existing models. This model begins to address these issues by integrating predictive learning, sequence interleaving, and sequence creation components to simulate a spectrum of higher-order cognitive behaviors which have eluded the grasp of simpler systems. Its capabilities are described based on simulations calling for increasing levels of functionality and are used to show how the model can progress from fundamental sequence learning and recall tasks to sophisticated behaviors such as an ability to solve simple mathematical expressions and a creative capacity for the formation and application of inductive rules.

Assume T is a small superstable theory. We introduce the notion of a flat Morley sequence, which is a counterpart of the notion of an infinite Morley sequence in a type p, in case when p is a complete type over a finite set of parameters. We show that for any flat Morley sequence Q there is a model M of T which is τ-atomic over {Q}. When additionally T has few countable models and is 1-based, we prove that within M there is an infinite Morley sequence I, with I $\subset$ dcl(Q), such that M is prime over I.

• Intelligent Tasks: Finding the Next Term of a Sequence • Difference Analysis of Polynomial Sequences • Charles Babbage’s Difference Engine • Finding the Form of the Sequence. • Gaussian Elimination. • Example Application: the Pie Cutting Sequence • What has this to do with Intelligence? • What has it all to do with Consciousness (if anything)?

Sequential behavior is essential to intelligence, and it is a fundamental part of human activities ranging from reasoning to language, and from everyday skills to complex problem solving. In particular, sequence learning is an important component of learning in many task domains — planning, reasoning, robotics, natural language processing, speech recognition, adaptive control, time series prediction, financial engineering, DNA sequencing, and so on. Naturally, there are many different approaches towards sequence learning, resulting from different perspectives taken in different task domains. These approaches deal with somewhat differently formulated sequential learning problems (for example, some with actions and some without), and/ or different aspects of sequence learning (for example, sequence prediction vs. sequence recognition). Sequence learning is clearly a difiicult task. More powerful algorithms for sequence learning are needed in all of these afore-mentioned domains. It is our view that the right approach to develop better techniques, algorithms, models.

We define DNA sequence by a bottom-up approach, starting with a real sequence from an actual biological sample. By providing axioms for notions of string, substring and strand, we formally define a DNA sequence, and a DNA molecule as composed of two antiparallel strands. We note that a sequence is a kind of group in which each member stands a certain relation to every other. The spatial aspects of a DNA sequence are also described.

What Numbers Could Not Be’) that an adequate account of the numbers and our arithmetic practice must satisfy not only the conditions usually recognized to be necessary: (a) identify some w-sequence as the numbers, and (b) correctly characterize the cardinality relation that relates a set to a member of that sequence as its cardinal number—it must also satisfy a third condition: the ‘<’ of the sequence must be recursive. This paper argues that adding this further condition was a mistake—any w-sequence would do, no matter how undecidable its ‘<’ relation.