Abstract
The Formal Axiomatic Systems are used in Artificial Intelligence and Mathematics to indicate any set of axioms, from which some or all axioms can be in conjunction to provide theorems. In this paper, we tend to combine and analyze FAS (Formal Axiomatic Systems) and Agents of Artificial Intelligence to enhance their intelligence, by promoting a transition from mechanical to intelligent mode. In addition, we will apply typographic and arithmetic methods to define isomorphism and its importance. It would be very easy to program a computer to generate theorem after theorem of a given system, however, if a machine could transit from the so called mechanical mode and use the intelligence, it would jump out of the formal axiomatic system and think autonomously. The recursive algorithm will be used to specify a model that would use the prior step to find the next one in a case study. The mapping between self referenced systems and formal axiomatic systems would help researchers differentiate the performances of artificial agents in their perceptions and actions in a certain environment. Key words: Artificial Intelligence, FAS, MIU System, Isomorphism, Recursive algorithm, agents.
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