Logic Column 15: Coalgebras and Their Logics

of proposed research. A short bibliography is optional. Domain theory has been developed around 40 years since 1970s by D. Scott, and S. Abramsky revealed the "junction between semantics (spaces of points = denotations of computational processes) and logic (lattices of properties of processes)" via Stone duality[1] which also guarantees the consistence between semantics and its logic. Nowadays we have generalised Stone duality over coalgebras and the corresponding logic - the coalgebraic logic. As A. Kurz wrote in [2], we have a general framework to describe the relationship between systems and logic via coalgebras and algebras. The current study of Stone duality is, however, not completely satisfactory. As the domain theory has been extended over the stably compact space and the recent research revealed that the space could be embedded to bitopological spaces in an extension of Stone duality, we believe that it is also possible to transpose the notion of coalgebraic logic ov...

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Alexander Kurz
• Keywords: CORR 2006, Domain Theory, Education, Logic, Stone Duality