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Go Mapping Theory and Factor Space Theory Part I: An Outline

Abstract : Inspired by Professor Wang, Peizhuang’s Factor Space Theory (FST), we propose a new scheme, called GO Mapping Theory, or GMT in short, to formalize the concept formation knowledge representation of AI. This scheme can be viewed as an extension of Willie’s Formal Concept Analysis (FCA), PZ Wang’s Factor Space Theory, and it naturally includes Gouguen’s L-Fuzzy Sets therefore it sounds a unified soft computing scheme. Potentially, GMT can be used for human-like knowledge representation and computation by modern computers. By deploying Grothendieck’s topos theory (this is the origin for the name GO mapping), we developed a unified mathematical language understandable by robots which can represent human language: concepts and logic, which also unified the current learning techniques at a more abstract level, therefore can be used as a basis for AGI or Super AI.By restating FST under category language, one can have a much more general setup for classical reductionist’s view about multiple sensory system, we call it a cognitive frame. Then under the assumption of uncertainty of any measurement, we can naturally, in fact ontologically, obtain an L-fuzzy set by FST, then we can construct from this L-fuzzy set a L-presheaf by standard procedure, we call it the GO mapping, which by Barr’s Embedding Theorem, can be viewed as the natural replacement for classical fuzzy sets. In fact, in topos theory, FST and GMT pairs a geometric morphism in Grothendieck’s topos theory, which shows the amazing power of pure math in real life applications.
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He Ouyang. Go Mapping Theory and Factor Space Theory Part I: An Outline. 2nd International Conference on Intelligence Science (ICIS), Oct 2017, Shanghai, China. pp.37-41, ⟨10.1007/978-3-319-68121-4_4⟩. ⟨hal-01820908⟩

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