## GENERAL DYNAMIC LOGIC

The General Dynamic Logic (GDL) is an innovative multi-valued logic that allows the representation of complex dynamic and natural processes in the model.

The GDL is used in the formation of calculi that represent natural models of dynamic natural conditions by means of causal chains and with the aid of the category theory. This approach theoretically enables the modelling of complex conditions and dynamic processes towards strong AI applications.

The category theory can be understood as a hierarchical structure in which several levels exist. The top level is the meta-category, which is referred to as the macro system in GDL. The main level is formed by the categories. In GDL, these correspond to the information and micro systems. The structure of a category is defined by objects. In GDL, these correspond to the parameters that represent the model.

The crucial point in the category theory as well as in GDL is the mapping between the categories and the objects. The category theory allows for manifold mapping rules in the form of functors, including matrices. In GDL, this concept of matrices is extended by that of a calculus, which is comparable in structure.

The axioms contained in a calculus correspond to the rows of a matrix. These are formed by parameters, the objects, with fuzzy set extensions. As is usual in the formation of axioms, junctors are used here. The GDL extends these with new classes of junctors: an element of “Time” and “Priority”, respectively. In addition, there is another junction class called “Quarks”. These make it possible to limit the fuzzy set in the ordinate axis in its membership value.

These extensions enable the dynamic description of complex processes. The axioms are formal structures consisting of causal chains. These causal chains are descriptions of the model formulated in plain text. In practice (software application), the readability of the chains formulated by the experts, which form the model, ensures that the model description is always comprehensible, even in the case of high complexity. Software that works based on GDL, such as Dylogos, therefore represents a White-AI.

In contrast to a matrix, a calculus in GDL is a self-learning unit. The lines in a calculus are all equal at a start time t=0. Through a continuous application of the calculus, experience is gathered as to whether causal chains have been successfully applied. This experience value is used to assign a weight to the causal chains within a calculus.

Calculi are used in two places in the GDL. Firstly, as functors between the categories and secondly, between the objects. These objects are found as a definition structure in both micro systems and information systems. The two types of systems differ in their different tasks. Micro systems serve to process numerical values. Information systems serve to process and evaluate texts.

Macro systems, for their part, represent supersets whose elements consist of micro systems as well as information systems. A special feature of GDL is that a macro system can also have other macro systems as elements. Important at this point, to prevent paradoxes (Russell Antinomy), is that a macro system must not contain itself. This structural design is fractal, self-similar and therefore universal.

General Dynamic Logic is an innovative approach to advancement in mathematical logic developed by the Private Institute for Dynamic Logic (PIFDL), Bernhard Stoinski. The software Dylogos, also developed by Bernhard Stoinski based on GDL, is distributed under license by Dylogos GmbH.