Modern unmanned systems require the capability to make intelligent decisions in the face of uncertain information. Existing logical frameworks often fall short in addressing the inherent vagueness and randomness present in the available data. In this paper, we introduce an innovative reasoning system called Earthling Logic (EL), developed by emulating the mechanism of human reasoning. EL extends classical propositional and predicate logic to accommodate statements that exhibit varying degrees of vagueness and randomness. Within the framework of EL, we establish statemental algebras and truth measures. We introduce the notions of syntactical consequences and semantical consequences. Building on these ideas, we develop a general deduction principle that rigorously manages uncertainty when deriving statements from premises. We are able to establish the soundness and completeness of this deduction method. Additionally, we provide a general framework for decision-making based on EL, which can enhance the reasoning abilities of intelligent systems.
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