Incoherent objects and fuzzy sets

In this paper we introduce the concept of the incoherent object with the use of the modal logic structure. The definition of the incoherent object is inside the meta-theory of uncertainty that represent the fuzzy set algebras by the definition of the world. We improve the traditional definition of the world by the conceptual space and the uncertainty by the nonlocality inside the conceptual space. Context is included as the geometric reference in a non Euclidean set of coordinates of quality dimension or features. Every logic expression can be written in a traditional way or by the action of semantic agents that change the logic value of the logic variables in a subset of the worlds. Fuzzy sets and fuzzy invariants are introduced by the conflicting set of evaluation in different worlds. We can rewrite the classical axiomatic structure in the classical logic in a new pseudo-axiomatic structure that represent any type of fuzzy reasoning.