Quasi-Matrix Deontic Logic. In: 7th International Workshop on Deontic Logic in Computer Science, Madeira, Portugal, 2004

We use non-relational semantics for the formalization of the systems S3d, S3dp and S3dq of deontic logic. The system S3d is weaker than the standard logic SDL. The semantics for S3dp represents combination of quasi-matrix semantics and the semantics of truth value gluts, which allows S3dp to avoid deontic explosion OA ∧ O¬A ⊃ OB. The system S3dq rejects both deontic explosion and the formula OA ∧ O¬A ⊃ OA ∧ ¬OA, thus it allows to consider deontic dilemmas without classical contradictions. The systems S5d, S5dp and S5dq in which the two types of deontic operators are used, namely, strong and weak obligation (permission), can be built as an extension of the correspondent systems S3d, S3dp and S3dq.