Computational methods for Dynamic Answer Set Programming

TL;DR

Dynamic, time-sensitive decision problems in domains like scheduling and routing challenge static ASP modeling. The paper argues for extending ASP with dynamic, temporal, and metric logics and outlines concrete routes—automata-based translations of $LDL_f$ to ASP via $AFA$ and $2AFA$, MSO-based automata pipelines via $MONA$, and metric logic programming under $MEL$—to enable robust dynamic reasoning within the clingo ecosystem. The key contributions include implementing automata- and linear-constraint translations in ASP, developing a finite-horizon $MLP$ framework, and integrating with interactive, industrially relevant workflows. These developments broaden ASP's applicability to dynamic domains, enabling efficient planning, scheduling, and reactive decision-making in practice. The work lays groundwork for combining non-monotonic reasoning with time and metrics, offering a modular, transparent approach via meta-programming and incremental solving.

Abstract

In our daily lives and industrial settings, we often encounter dynamic problems that require reasoning over time and metric constraints. These include tasks such as scheduling, routing, and production sequencing. Dynamic logics have traditionally addressed these needs but often lack the flexibility and integration required for comprehensive problem modeling. This research aims to extend Answer Set Programming (ASP), a powerful declarative problem-solving approach, to handle dynamic domains effectively. By integrating concepts from dynamic, temporal, and metric logics into ASP, we seek to develop robust systems capable of modeling complex dynamic problems and performing efficient reasoning tasks, thereby enhancing ASPs applicability in industrial contexts.