Knowledge Extraction and Knowledge Integration governed by
  {\L}ukasiewicz Logics
  The development of machine learning in particular and artificial intelligent
in general has been strongly conditioned by the lack of an appropriate
interface layer between deduction, abduction and induction. In this work we
extend traditional algebraic specification methods in this direction. Here we
assume that such interface for AI emerges from an adequate Neural-Symbolic
integration. This integration is made for universe of discourse described on a
Topos governed by a many-valued {\L}ukasiewicz logic. Sentences are integrated
in a symbolic knowledge base describing the problem domain, codified using a
graphic-based language, wherein every logic connective is defined by a neuron
in an artificial network. This allows the integration of first-order formulas
into a network architecture as background knowledge, and simplifies symbolic
rule extraction from trained networks. For the train of such neural networks we
changed the Levenderg-Marquardt algorithm, restricting the knowledge
dissemination in the network structure using soft crystallization. This
procedure reduces neural network plasticity without drastically damaging the
learning performance, allowing the emergence of symbolic patterns. This makes
the descriptive power of produced neural networks similar to the descriptive
power of {\L}ukasiewicz logic language, reducing the information lost on
translation between symbolic and connectionist structures. We tested this
method on the extraction of knowledge from specified structures. For it, we
present the notion of fuzzy state automata, and we use automata behaviour to
infer its structure. We use this type of automata on the generation of models
for relations specified as symbolic background knowledge.
