Annotated Logic with Rough Double Stone Algebraic Interpretation

In this study, we present rough annotated logic R-tau which adopts rough double stone algebra (RDSA) as semantics interpretation for an annotation. Furthermore, we propose natural deduction system for NR tau, and we show R-tau is non-alethic since it is both paracomplete and paraconsistent. To incorporate an annotation of RDSA into annotated logic P-tau, we apply logical features of rough logic based on RDSA and its semantic structure represented with a lattice tau which is an annotation of NR tau. In addition, we present some features of R-tau and show a sketch of proof for soundness and completeness proof for NR tau.