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An emergence of formal logic induced by an internal agent
1 , * 2
1  Department of Earth & Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe 657-8501, Japan
2  The Senior High School, Japan Women’s University, Tama, Kawasaki 214-8565, Japan

Abstract: In this paper, we mainly address three issues: externality of an agent, purpose of an agent, and a kind of "softness" of components in a system. Agents are independent of a system in an ordinary multi-agent model, hence the behavior of a system is not autonomous but influenced by the agents. If a multi-agent model is considered as a completely autonomous one, agents in the model are inevitably deprived of their externality and independence from the model. In order to treat of the completely autonomous transition of a system, we introduce an agent which is a part of a system, and has a purpose which is independent from a system. The interaction between a system and an agent transforms a random graph corresponding to the system into the graph which represents formal logic adequately. In the emergent graph, there are many complete subgraphs, which can be regarded as conceptualized things. We modify the definition of a conceptualized thing into a subgraph which is a cycle of arrows, and regard the density of arrows of each conceptualized thing as validness. We define this object with the density as a soft object. A complete graph has maximum number of arrows, hence is the most reliable soft object. In a similar way, we call an arrow with the validness a soft arrow, and treat of the relation between soft objects and soft arrows. The argument of this paper is relevant to dynamical formal logic, and at the same time, is intended to serve as a basis for an agent model.
Keywords: Formal logic, Directed graph, Multi-agent model, Internal measurement