2024/06/28 by Ivan Chajda, Chajda, Ivan, Helmut Länger +7
Computer Science · #03B44 #03G12 #03G25 #06A11 #08A55 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2406.20034
openalex publication_date 2024/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Not all logical systems can be captured using algebras. We see this in classical logic (formalized by Boolean algebras) and many-valued logics (like Lukasiewicz logic with MV-algebras). Even quantum mechanics, initially formalized with orthomodular lattices, benefits from a simpler approach using just partially ordered sets (posets). This paper explores how logical connectives are introduced in poset-based logics. Building on prior work by the authors, we delve deeper into "dynamic" logics where truth values can change over time. We consider time sets with a preference relation and propositions whose truth depends on time. Tense operators, introduced by J.Burgess and extended for various logics, become a valuable tool. This paper proposes several approaches to this topic, aiming to inspire a further stream of research.