  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.
