Towards a Semantics for Hybrid ASP systems
This work addresses a foundational problem for researchers and developers in logic programming and AI, providing a formal framework to analyze hybrid ASP systems, though it is incremental as it builds on existing ASP concepts.
The paper tackles the challenge of providing semantic underpinnings for hybrid Answer Set Programming (ASP) systems, which are needed for real-world applications, by introducing abstract and structured theories to formally integrate them with ASP and characterize CLINGO's theory-reasoning framework, establishing its correspondence to the logic of Here-and-there with constraints.
Over the last decades the development of ASP has brought about an expressive modeling language powered by highly performant systems. At the same time, it gets more and more difficult to provide semantic underpinnings capturing the resulting constructs and inferences. This is even more severe when it comes to hybrid ASP languages and systems that are often needed to handle real-world applications. We address this challenge and introduce the concept of abstract and structured theories that allow us to formally elaborate upon their integration with ASP. We then use this concept to make precise the semantic characterization of CLINGO's theory-reasoning framework and establish its correspondence to the logic of Here-and-there with constraints. This provides us with a formal framework in which we can elaborate formal properties of existing hybridizations of CLINGO such as CLINGCON, CLINGOM[DL], and CLINGO[LP].