2025/02/15 by Lavinia Corina Ciungu, Ciungu, Lavinia Corina
Computer Science · Decision Sciences · #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Quantum Algebra (math.QA) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2503.00006
openalex publication_date 2025/02/15 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
We define various type of states on implicative involutive BE algebras (Jauch-Piron state, (P)-state, (B)-state, subadditive state, valuation), and we investigate the relationships between these states. Moreover, we introduce the unital, full and rich sets of states, and we prove certain properties involving these notions. In the case when an implicative involutive BE algebra possesses a rich or a full set of states, we prove that it is an implicative-orthomodular lattice. If an implicative involutive BE algebra possesses a rich set of (P)-states or a full set of valuations, then it is an implicative-Boolean algebra. Additionally, based on their deductive systems, we give characterizations of implicative-orthomodular lattices and implicative-Boolean algebras.