The intention of the present study is to establish the mathematical
fundamentals for automated problem solving essentially targeted for robotics by
approaching the task universal algebraically introducing knowledge as
realizations of generalized free algebra based nets, graphs with gluing forms
connecting in- and out-edges to nodes. Nets are caused to undergo
transformations in conceptual level by type wise differentiated intervening net
rewriting systems dispersing problems to abstract parts, matching being
determined by substitution relations. Achieved sets of conceptual nets
constitute congruent classes. New results are obtained within construction of
problem solving systems where solution algorithms are derived parallel with
other candidates applied to the same net classes. By applying parallel
transducer paths consisting of net rewriting systems to net classes congruent
quotient algebras are established and the manifested class rewriting comprises
all solution candidates whenever produced nets are in anticipated languages
liable to acceptance of net automata. Furthermore new solutions will be added
to the set of already known ones thus expanding the solving power in the
forthcoming. Moreover special attention is set on universal abstraction,
thereof generation by net block homomorphism, consequently multiple order
solving systems and the overall decidability of the set of the solutions. By
overlapping presentation of nets new abstraction relation among nets is
formulated alongside with consequent alphabetical net block renetting system
proportional to normal forms of renetting systems regarding the operational
power. A new structure in self-evolving problem solving is established via
saturation by groups of equivalence relations and iterative closures of
generated quotient transducer algebras over the whole evolution.Comment: This article is a part of my thesis giving the unity for both
knowledge presentation and self-evolution in autonomous problem solving
mathematical systems and for that reason draws heavily from my previous work
arxiv:1305.563