Polyadic modal logics with applications in normative reasoning

摘要: The study of modal logic often starts with that unary operators applied to sentences, denoting some notions necessity or possibility. However, we adopt a more general approach in this dissertation. We begin object languages possess multi-ary operators, and interpret them relational semantics, neighbourhood semantics algebraic semantics. Some topics on subject have been investigated by logicians for time, present survey their results. But there remain areas be explored, examine order gain knowledge our territory. More specifically, propose polyadic axioms correspond seriality, reflexivity, symmetry, transitivity euclideanness relations, prove soundness completeness normal systems based these axioms. also put forward classical determined classes frames finite types such as superset-closed frames, quasifiltroids filtroids. Equivalences between categories algebras are demonstrated. Furthermore the studied dissertation shown translationally equivalent. While first part is purely formal, take different route second part. previously interpreted mathematical structures, given meanings ordinary discourse. read modalities normative thinking, instance, “ought” when say “you ought visit your parents, at least call if you cannot them”. A series logics, called deontic residuation, proposed. They represent real-life situations involving, example, conflicts contrary-to-duty obligations better than traditional logics do.