Simplification logic for the management of unknown information

This paper aims to contribute the extension of classical Formal Concept Analysis (FCA), allowing management unknown information. In a preliminary paper, we define new kind attribute implications represent knowledge from information currently available. The whole FCA framework has be appropriately extended manage introduces logic for reasoning with this implications, which belongs family logics an underlying Simplification paradigm. Specifically, introduce algebra, named weak dual Heyting Algebra, that allows us extend these implications. To provide solid framework, also prove its soundness and completeness show advantages Finally, allow further use in applications, algorithm automated reasoning, is directly built logic, defined.