2022/01/12 by Alexander V. Grefenstejn, Grefenstejn, Alexander V.
Computer Science · #03B45 (Primary) 03B50 #03B53 (Secondary) #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2201.04707
openalex publication_date 2022/01/12 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
We consider a quantified version of the (propositional) modal logic BK, proposed earlier by S. P. Odintsov and H. Wansing; this version will be denoted by QBK. Using the canonical model method, we prove the strong completeness of QBK with respect to a suitable possible world semantics with expanding domains. Similar results are obtained for some natural QBK-extensions. In particular, it is proved that the extension of QBK with Barcan scheme is strongly complete with respect to a suitable possible world semantics with constant domains. Moreover, we define faithful embeddings (à la Gödel-McKinsey-Tarski) of the quantified versions of Nelson's constructive logics into appropriate QBK-extensions.