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A Systemic Approach to Music Performance Learning with Multimodal Technology
Probabilities on Sentences in an Expressive Logic
Automated reasoning about uncertain knowledge has many applications. One
difficulty when developing such systems is the lack of a completely
satisfactory integration of logic and probability. We address this problem
directly. Expressive languages like higher-order logic are ideally suited for
representing and reasoning about structured knowledge. Uncertain knowledge can
be modeled by using graded probabilities rather than binary truth-values. The
main technical problem studied in this paper is the following: Given a set of
sentences, each having some probability of being true, what probability should
be ascribed to other (query) sentences? A natural wish-list, among others, is
that the probability distribution (i) is consistent with the knowledge base,
(ii) allows for a consistent inference procedure and in particular (iii)
reduces to deductive logic in the limit of probabilities being 0 and 1, (iv)
allows (Bayesian) inductive reasoning and (v) learning in the limit and in
particular (vi) allows confirmation of universally quantified
hypotheses/sentences. We translate this wish-list into technical requirements
for a prior probability and show that probabilities satisfying all our criteria
exist. We also give explicit constructions and several general
characterizations of probabilities that satisfy some or all of the criteria and
various (counter) examples. We also derive necessary and sufficient conditions
for extending beliefs about finitely many sentences to suitable probabilities
over all sentences, and in particular least dogmatic or least biased ones. We
conclude with a brief outlook on how the developed theory might be used and
approximated in autonomous reasoning agents. Our theory is a step towards a
globally consistent and empirically satisfactory unification of probability and
logic.Comment: 52 LaTeX pages, 64 definiton/theorems/etc, presented at conference
Progic 2011 in New Yor
A Chemical Survey of the Batang Belungkung River and the Gombak River
A chemical survey of water quality in the Batang Belungkung River and the Gombak River was conducted
to assess the degree of pollution due to the continuing discharge of rubber and domestic wastes.
Levels of dissolved oxygen (DO), biochemical oxygen demand (BOD), chemical oxygen demand (COD),
nutrients (phosphorus and nitrogen), solid and trace elements (sodium, potassium, calcium and magnesium)
were monitored sequentially downriver. The Batang Belungkung River was found to be severely polluted
with anaerobic conditions existing downriver. The upper region of the Gombak River was relatively unpolluted
while the lower region of the Gombak River was found to be severely polluted. An increase of
approximately fourteen-fold was found in the oxygen demand in the lower region of the Gombak River
over the ten year period from 1968/69 to 1978/79
Topological spin excitations of Heisenberg antiferromagnets in two dimensions
In this paper we discuss the construction and the dynamics of vortex-like
topological spin excitations in the Schwinger-boson description of Heisenberg
antiferromagnets in two dimensions. The topological spin excitations are Dirac
fermions (with gap) when spin value is a half-integer. Experimental and
theoretical implications of these excitations are being investigated.Comment: Latex file, no figur
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