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A Simplified and Improved Free-Variable Framework for Hilbert's epsilon as an Operator of Indefinite Committed Choice

arXiv.org Artificial Intelligence

Free variables occur frequently in mathematics and computer science with ad hoc and altering semantics. We present the most recent version of our free-variable framework for two-valued logics with properly improved functionality, but only two kinds of free variables left (instead of three): implicitly universally and implicitly existentially quantified ones, now simply called "free atoms" and "free variables", respectively. The quantificational expressiveness and the problem-solving facilities of our framework exceed standard first-order and even higher-order modal logics, and directly support Fermat's descente infinie. With the improved version of our framework, we can now model also Henkin quantification, neither using quantifiers (binders) nor raising (Skolemization). We propose a new semantics for Hilbert's epsilon as a choice operator with the following features: We avoid overspecification (such as right-uniqueness), but admit indefinite choice, committed choice, and classical logics. Moreover, our semantics for the epsilon supports reductive proof search optimally.


From Python to Numpy

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We pick the cell size to be bounded by (r)/( (n)), so that each grid cell will contain at most one sample, and thus the grid can be implemented as a simple n-dimensional array of integers: the default 1 indicates no sample, a non-negative integer gives the index of the sample located in a cell. Step 1. Select the initial sample, x0, randomly chosen uniformly from the domain.


An Introduction to Machine Learning Theory and Its Applications

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The supply of able ML designers has yet to catch up to this demand. A major reason for this is that ML is just plain tricky. This tutorial introduces the basics of Machine Learning theory, laying down the common themes and concepts, making it easy to follow the logic and get comfortable with the topic. So what exactly is "machine learning" anyway? ML is actually a lot of things. The field is quite vast and is expanding rapidly, being continually partitioned and sub-partitioned ad nauseam into different sub-specialties and types of machine learning.


Women in Natural Language Processing

@machinelearnbot

The first WiNLP workshop will be co-located with ACL 2017 in Vancouver. The workshop aims at highlighting research done by women, providing a supportive venue for junior members, and offering opportunities for networking and career discussion.



Digital learning - Individual Adaptive Construction or Connected Sociโ€ฆ

#artificialintelligence

Attributes of Participatory Culture @TransformSoc (Henry Jenkins) โ€ข Affiliations: online communities โ€ข Expressions: new creative forms โ€ข Collaborations: Problem-solving in teams โ€ข Circulations: Shaping media flow Source: Confronting The Challenges Of Participatory Culture, by Henry Jenkins, MIT Press, 2009 31.


Deciphering the Neural Language Model

@machinelearnbot

Recently, I have been working on the Neural Networks for Machine Learning course offered by Coursera and taught by Geoffrey Hinton. Overall, it is a nice course and provides an introduction to some of the modern topics in deep learning. However, there are instances where the student has to do lots of extra work in order to understand the topics covered in full detail. One of the assignments in the course is to study the Neural Probabilistic Language Model (The related article can be downloaded from here). An example dataset, as well as a code written in Octave (equivalently Matlab) are provided for the assignment.


A computer program that learns how to save fuel

#artificialintelligence

FROM avoiding jaywalkers to emergency braking to eventually, perhaps, chauffeuring the vehicle itself, it is clear that artificial intelligence (AI) will be an important part of the cars of the future. But it is not only the driving of them that will benefit. AI will also permit such cars to use energy more sparingly. Cars have long had computerised engine-management that responds on the fly to changes in driving conditions. The introduction of electric power has, however, complicated matters.


Tutorial on Deep Learning Simons Institute for the Theory of Computing

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This series of talks is part of the Foundations of Machine Learning Boot Camp. Videos for each talk area will be available through the links above.


Artificial Intelligence: Reinforcement Learning in Python

#artificialintelligence

When people talk about artificial intelligence, they usually don't mean supervised and unsupervised machine learning. These tasks are pretty trivial compared to what we think of AIs doing - playing chess and Go, driving cars, and beating video games at a superhuman level. Reinforcement learning has recently become popular for doing all of that and more. Much like deep learning, a lot of the theory was discovered in the 70s and 80s but it hasn't been until recently that we've been able to observe first hand the amazing results that are possible. In 2016 we saw Google's AlphaGo beat the world Champion in Go. We saw AIs playing video games like Doom and Super Mario.