Bound-Founded Semantics for Answer Set Programming with Difference Constraints: Preliminary Report

While the integration of linear constraints has significantly expanded the reach of Answer Set Programming (ASP), existing hybrid solvers often rely on disparate semantic underpinnings that lack a unified logical foundation. We address this gap by introducing a many-sorted variant of the Bound-founded Logic of Here-and-There (HTb), providing a versatile framework capable of characterizing equilibrium models across a wide spectrum of alternative semantics for extensions of ASP with linear constraints. We apply this framework to the setting of difference constraints, focusing on the semantic characterization of clingo[DL]. Central to our approach is the formalization of foundedness for numeric variables. By investigating how different hybrid systems - such as clingo[DL], clingcon, and flingo - justify constraint atoms, we uncover the semantic roots of their varying behaviors. This investigation results in a single, consistent framework that not only formalizes the foundations of current systems like clingo[DL] but also facilitates the rigorous study of program simplifications and the future integration of diverse semantic principles.

Smart Expansion Techniques for ASP-based Interactive Configuration

Product configuration is a successful application of Answer Set Programming (ASP). However, challenges are still open for interactive systems to effectively guide users through the configuration process. The aim of our work is to provide an ASP-based solver for interactive configuration that can deal with large-scale industrial configuration problems and that supports intuitive user interfaces via an API. In this paper, we focus on improving the performance of automatically completing a partial configuration. Our main contribution enhances the classical incremental approach for multi-shot solving by four different smart expansion functions. The core idea is to determine and add specific objects or associations to the partial configuration by exploiting cautious and brave consequences before checking for the existence of a complete configuration with the current objects in each iteration. This approach limits the number of costly unsatisfiability checks and reduces the search space, thereby improving solving performance. In addition, we present a user interface that uses our API and is implemented in ASP.

Hybrid Answer Set Programming: Foundations and Applications

Answer Set Programming (ASP) is a powerful tool for solving real-world problems. However, many problems involve numeric values and complex constraints beyond the capabilities of standard ASP solvers. Hybrid solvers like CLINGCON and CLINGO[DL] address this by using specialized methods for specific constraints. However, these solvers lack a strong theoretical foundation. This issue has first been addressed by introducing the Logic of Here-and-There with constraints (HT_c) as an extension of the Logic of Here-and-There (HT) and its non-monotone extension Equilibrium Logic. Nowadays, HT serves as a logical foundation for ASP and has facilitated a broader understanding of this paradigm. The idea is that HTC (and other extensions) play an analogous role for hybrid ASP. There remain many open questions about these logics regarding their fundamental characteristics as well as their practical use in solvers, ie. how they can guide the implementation. Having a formal understanding of these hybrid logics is also needed to better understand the inherent structure of the (real-world) problems they are applied to and to improve their representations in ASP. As an example of an application of ASP we use product configuration.

plingo: A system for probabilistic reasoning in clingo based on lpmln

We present plingo, an extension of the ASP system clingo with various probabilistic reasoning modes. Plingo is centered upon LP^MLN, a probabilistic extension of ASP based on a weight scheme from Markov Logic. This choice is motivated by the fact that the core probabilistic reasoning modes can be mapped onto optimization problems and that LP^MLN may serve as a middle-ground formalism connecting to other probabilistic approaches. As a result, plingo offers three alternative frontends, for LP^MLN, P-log, and ProbLog. The corresponding input languages and reasoning modes are implemented by means of clingo's multi-shot and theory solving capabilities. The core of plingo amounts to a re-implementation of LP^MLN in terms of modern ASP technology, extended by an approximation technique based on a new method for answer set enumeration in the order of optimality. We evaluate plingo's performance empirically by comparing it to other probabilistic systems.