The Logic of Here and There and its Applications
In this talk I will describe the nonclassical, superintuitionistic logic of here-and-there, first presented around 80 years ago by A Heyting. Stable inference in disjunctive DATALOG and the stable models for answer set programs are easily captured in this logic, which serves as a foundation for the paradigm of Answer Set Programming (ASP). The talk will focus on a few of the many applications this logic has in ASP, knowledge representation and non-monotonic reasoning. In particular I will mention program transformations and safety, as well as extensions of the language of ASP that deal with temporal reasoning and with the combination of rules and ontologies.