Extending answer set programs with interpreted functions as first-class citizens

Abstract

Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs. Existing approaches towards integrating function terms into ASP can be organized in two classes: uninterpreted function symbols and interpreted functions; we focus on the latter. Existing approaches usually define interpreted functions in the program (e.g. using term equations), while evaluation wrt. to a pre-existing external semantics is neglected. However, this is useful if existing function libraries shall be accessed or if a function is more naturally implemented in procedural code. In this paper, we propose the declarative language of HEXIFU-programs which extends answer set programs (ASP) with such interpreted functions. However, rather than just providing a means for evaluating functions, it further turns interpreted functions into first-class citizens, i.e., functions are represented by accessible objects in the program. This paves the way for functionals (higher-order functions), i.e., functions that take other functions as arguments or return them. We provide then a rewriting of such programs to HEX-programs, an extension of ASP with external sources, and an implementation based on this rewriting. Afterwards we present applications which motivated our work, e.g. the adoption of design pattern from software engineering. Finally, we discuss properties of the formalism and differences to related work.