This paper presents Non-Axiomatic Term Logic (NATL) as a theoretical computational framework of humanlike symbolic reasoning in artificial intelligence. NATL unites a discrete syntactic system inspired from Aristotle's term logic and a continuous semantic system based on the modern idea of distributed representations, or embeddings. This paper positions the proposed approach in the phylogeny and the literature of logic, and explains the framework. As it is yet no more than a theory and it requires much further elaboration to implement it, no quantitative evaluation is presented. Instead, qualitative analyses of arguments using NATL, some applications to possible cognitive science/robotics-related research, and remaining issues towards a machinery implementation are discussed.
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