Hierarchical Intelligent Simulation

Separating the different hierarchy types reveals their comprehensive constructive importance based on structural approach, symbolic meaning, object-oriented representation, their combination in looking for self-organization, self-control and conscience. Knowledge and construction hierarchies can cooperate to integrate design and verification into simulation; object-oriented concepts can be symbolized to handle data and operations formally; structural representation of behavior manages its realization. Hierarchy types open, or at least show, the way to simulate intelligence as adaptable consciousness. Artificial Intelligence means simulation of intelligence, either behavioral (functional or procedural) or structural (e.g., neural, genetic, cellular). Only hierarchical simulation, assisted mathematically to build theories and formalisms, can lead to understand the results, so to manage them truly. The hierarchical approach should concentrate on knowledge hierarchies, to enable metaknowledge simulation, for the system's adaptability, but also for looking for the way to simulate consciousness. Introduction Intelligence assumes, at least, consciousness and adaptability. Consciousness simulation demands transcending the present limits of computability, by an intensive as well as extensive research effort to integrate essential physical and mathematical knowledge and intuition guided by philosophical goals. An algorithm is a computer simulable entity, so it represents computability, bottom-up (construction, design, plan) or topdown (understanding, verification, learning). The algorithmic approach is equivalent to the formal one: If a sentence of a formal system is true, then an algorithm can confirm it. Reciprocally, for a verification algorithm of the mathematical sentences a formal system can be defined, that holds for true the sentences in the set closure of the algorithm's results towards the operations of the considered logic. Formal systems, partialrecursive functions, Turing machines, λ -calculus, are only the best-known formalisms for computation, i.e., for algorithm and computability. Hierarchy Types Multiple, coexistent and interdependent hierarchies structure the universe of models for complex systems. They belong to different hierarchy types, defined by abstraction levels, block structures, classes, symbolization and knowledge abstractions. Abstraction and hierarchy are semantic and syntactical aspects of a unique fundamental concept, the most powerful tool in systematic knowledge; hierarchy results formalizing abstraction. Hierarchy types correspond to the various abstraction ways (↑abstraction goal): Class hierarchy (↑ concepts) ↔ virtual framework to represent any kind of hierarchy, based on form-contents dichotomy, modularity, inheritance, polymorphism; an object is defined by identity, state and behavior, being instance of a class, that defines its structure and behavior (internal completing the structure, external for communication); to exist behaviorally, the object hides its structure, what helps it to integrate in a world of adaptable objects that intercommunicate, developing towards conscious and intelligent objects, i.e. subjects. Symbolization hierarchy (↑ mathematics) ↔ stepwise formalism for any kind of types, e.g., hierarchy types. Structure hierarchy (↑ problem-solving) ↔ stepwise managing of all (other hierarchy) types on different levels by recursive autonomous block decomposition, following the principle "Divide et Impera et Intellige". Construction hierarchy (↑ simulation) ↔ design/ verification (= simulation) framework of autonomous levels for different abstraction grades of description; time is explicit at highest (behavioral) levels, being integrated in the model, and exterior on lowest (structural) levels, being implicit for the system’s activity; artificial intelligence approaches try to configure the simulation hierarchies as reciprocal to knowledge hierarchies. Knowledge hierarchy (↑ theories) ← reflexive abstraction ("in a deeper sense"); each level should know of its inferior levels, itself included; recurrence of structures and operations enables self-knowledge (with improved precision on the higher levels of knowledge hierarchies); a continuous model for hierarchy levels, without loosing the hierarchy attributes, would offer a better model for conscience and intelligence. Understanding and construction have correspondent hierarchy types: their syntax relies on classes, their meaning on symbols, their use on modules (Figure 1). simbolization object-orientation structure knowledge construction Figure 1: H Diagram All hierarchy types have common structures as the following: (U, { Hi∈Sh}) universe, with different hierarchies Hi, Sh set of hierarchies, Sl set of hierarchy levels: H = (Rel_eq, {(Levelj,Structurej): j∈Sl}, Rel_ord, {Aj: j∈Sl}) generic hierarchy: Rel_eq equivalence relation, divides U in levels, Structurej structure defined of level j, Rel_ord order relation (total), defined on Sl, Aj∈{(x,y):x∈Levelj-1,y∈Levelj, j∈Sl} abstraction. Hierarchies are leveled structures, which represent different domains. A level is an autonomous mathematical structure, containing abstract/ concrete entities, linked by intralevel relations. Abstraction relates the levels: this induces an interlevel order relation, partial, concerning entities, and total, regarding the levels. Beyond the hierarchical point of view, the system can be formalized as an autonomous domain, structured by metahierarchical relations, building a level in a higher order hierarchical system. Hierarchical structures exhibit two complementary processing strategies: top-down and bottom-up. A sketch to formalize hierarchy types follows: • Knowledge ← structure, classes, symbolization (abstraction, recurrence → reaction) • Construction ← structure, classes, symbolization (recurrence, space ↔ time) • Classes ← existential abstract types (syntax of construction/ knowledge) • Symbolization ← universal abstract types (semantics construction/ knowledge) • Structure ← comprehensive concrete types (pragmatics construction/ knowledge) The different hierarchy types can be formalized by the theory of categories (Kasch and Pareigis 1986). Constructive type theory permits formal specification as well as formal verification by generating an object satisfying the specification. Example: The classical activities in complex systems simulation, that regard different levels of the construction or knowledge hierarchy, can be expressed symbolically then represented objectoriented and simulated structurally, as sketched in Figure 2: