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This paper is an extended version of my talk in the Conference of Non-Classical Logics 2016. In this paper we will introduce a system that rejects the principle of identity "A is A", one of the third Aristotelian principles for thinking. The proposed system allows to deal with paradoxical sentences, like a Liar sentence "A is not A". We present both an axiomatic system and an adequate semantics for it.departmental bulletin pape
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