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This book for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving.

This book focuses on the fields of hybrid intelligent systems based on fuzzy systems, neural networks, bio-inspired algorithms and time series. This book describes the construction of ensembles of Interval Type-2 Fuzzy Neural Networks models and the optimization of their fuzzy integrators with bio-inspired algorithms for time series prediction.

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She soon surmised that the problems were being caused by the systems not knowing where to put their attention. What was the secret behind this shifting of attention, and could it open the door to further advances in artificial intelligence?

These questions and many others led Picard to conduct further research on the neural processes involved in attention, including her conferring with cognitive scientists, psychologists, vision experts and other researchers. In time she was astounded to discover that for many of the cognitive systems involved in focus and attention, value assignment, and memory formation and retrieval, emotion was always intimately linked in one way or another.

This was not something Picard really wanted to hear, much less pursue. Her professional world was made up of mathematics, circuits and algorithms, systems that had a direct line to objective cause and effect. Going down this path could potentially have been career suicide. Nevertheless, Picard persevered.

Researchers developed methods that allowed computers to read emotions directly from our expressions, with high accuracy. They studied the ways emotion changes skin conductance and vocal qualities. They explored new techniques for treating autism and ways to analyze aggregate group sentiment. The approaches were as profuse as they were creative and diverse. At the same time, MIT was not the only place showing interest in this new field. Of course, among its many functions, emotion is critical in human communication, social interaction and bonding.

This means emotion not only influences our expression of what we are feeling; it can be used to influence and alter the emotions of the person on the other side of the exchange. This aspect is particularly important to the development of social robotics. As artificial intelligence becomes embodied in more and more computer systems, it will not be enough that it reads and anticipates how we feel. Numerous studies have shown that there are many benefits when people engage with systems that can be aware of, emulate and reflect emotion.

For instance, an education study using robot tutors found that the presence of a physical robot had a superior impact on student test scores when compared with tutoring via software voice, an on-screen avatar or no tutor at all.

These types of correlations come up again and again in many different types of research, supporting the idea that at our core we evolved to interact with much of our world initially through our emotions. This is what makes this field and the building of emotional awareness into our technologies so important.

This is one of the reasons why interfaces have become increasingly intuitive over the years, finally reaching the point where we employ natural user interfaces such as touch, gesture and voice to interact with our devices.