The purpose of this book is to develop neural nets as astrong theory for both brains and machines. The theory isdeveloped in close correlation with the biology of theneuron and the properties of human reasoning. This approachimplies the following:- Updating the biology of the artificialneuron. Theneurosciences have experienced a tremendous development inthe last 50 years. One of the main purposes of the presentwork is toincorporate this knowledge into a strong model ofthe artificial neuron. Particular attention is devoted toformalizing the complex chemical processes at the synapticlevel. This formal language supports both symbolicreasoningand uncertainty processing.- Investigating the properties of expert reasoning. Thiskind of reasoning is approximate, partial and non-monotonic,and therefore requires special mathematical tools for itsformalization, such as fuzzy set theory and fuzzy logic.Three different intelligent systems developed with thistechnology are presented and discussed.