Symmetric Generalized Galois Logics

Symmetric generalized Galois logics (i.e., symmetric gGls) are distributive gGls that include weak distributivity laws between some operations such as fusion and fission. Motivations for considering distribution between such operations include the provability of cut for binary consequence relations, abstract algebraic considerations and modeling linguistic phenomena in categorial grammars. We represent symmetric gGls by models on topological relational structures. On the other hand, topological relational structures are realized by structures of symmetric gGls. We generalize the weak distributivity laws between fusion and fission to interactions of certain monotone operations within distributive super gGls. We are able to prove appropriate generalizations of the previously obtained theorems—including a functorial duality result connecting classes of gGls and classes of structures for them. Mathematics Subject Classification (2000). Primary 03B47;