Philipp Obermeier

Ricochet Robots Reloaded: A Case-Study in Multi-shot ASP Solving

Nonmonotonic reasoning is about drawing conclusions in the absence of complete information. Hence, whenever new information arrives, one may have to withdraw previously drawn conclusions. In fact, Answer Set Programming is nowadays regarded as the computational embodiment of nonmonotonic reasoning. However, traditional answer set solvers do not account for changing information. Rather they are designed as one-shot solvers that take a logic program and compute its stable models, basta! When new information arrives the program is extended and the solving process is started from scratch once more. Hence the dynamics giving rise to nonmonotonicity is not reflected by such solvers and left to the user. This shortcoming is addressed by multi-shot solvers that embrace the dynamicity of nonmonotonic reasoning by allowing a reactive procedure to loop on solving while acquiring changes in the problem specification. In this paper, we provide a hands-on introduction to multi-shot solving with clingoi¾?4 by modeling the popular board game of Ricochet Robots. Our particular focus lies on capturing the underlying turn based playing through the procedural-declarative interplay offered by the Python-ASP integration of clingoi¾?4. From a technical perspective, we provide semantic underpinnings for multi-shot solving with clingoi¾?4 by means of a simple stateful semantics along with operations reflecting clingoi¾?4 functionalities.

Ricochet Robots: A Transverse ASP Benchmark

A distinguishing feature of Answer Set Programming is its versatility. In addition to satisfiability testing, it offers various forms of model enumeration, intersection or unioning, as well as optimization. Moreover, there is an increasing interest in incremental and reactive solving due to their applicability to dynamic domains. However, so far no comparative studies have been conducted, contrasting the respective modeling capacities and their computational impact. To assess the variety of different forms of ASP solving, we propose Alex Randolphs board game Ricochet Robots as a transverse benchmark problem that allows us to compare various approaches in a uniform setting. To begin with, we consider alternative ways of encoding ASP planning problems and discuss the underlying modeling techniques. In turn, we conduct an empirical analysis contrasting traditional solving, optimization, incremental, and reactive approaches. In addition, we study the impact of some boosting techniques in the realm of our case study.

Generalized Target Assignment and Path Finding Using Answer Set Programming

Multi-Agent Path Finding (MAPF) deals with teams of agents that need to find collision-free paths from their respective starting locations to their respective goal locations on a graph. This model can be applied to a number of applications (e.g., autonomous warehouse systems (Wurman, D’Andrea, and Mountz 2008)). For example, in an autonomous warehouse system (illustrated by Figure 1), robots (in orange) navigate around a warehouse to pick up inventory pods from their storage locations (in green) and drop them off at designated inventory stations (in purple) in the warehouse. Several extensions of MAPF have been proposed (e.g., combined Target Assignment and Path Finding or TAPF). While TAPF better reflects real-world systems with homogeneous agents, such as our motivating application, it still has a key limitation: It assumes that the number of agents equals the number of tasks to be allocated. In our motivating application, there are typically more tasks than agents. As such, agents have to move towards a new task after completing their current task. Therefore, we propose Generalized TAPF (G-TAPF), a generalization of TAPF that allows the number of tasks to be greater than the number of agents. We also propose a new objective, which better captures more applications including our motivating warehouse application: Each task has an associated deadline that indicates the time at which it must be completed. We also propose use answer set programming (ASP) (Lifschitz 2002) as the general framework for solving the new G-TAPF problems.

Advanced Solving Technology for Dynamic and Reactive Applications

The project Advanced Solving Technology for Dynamic and Reactive Applications (henceforth called ASTRA) is part of the DFG-funded Research Unit HYBRIS: Hybrid Reasoning for Intelligent Systems (www.hybrid-reasoning.org/). The Unit started in 2012 with the aim of investigating different combinations of both qualitative and quantitative reasoning. Among the quantitative aspects addressed are time, uncertainty, preferences, continuous state spaces, and quantitative data such as point clouds or text, from which meaningful symbolic descriptions can be extracted. The principal investigators of ASTRA are Gerhard Brewka (Leipzig), Gabriele Kern-Isberner (Dortmund) and Torsten Schaub (Potsdam). In a nutshell, the project aims to provide hybrid reasoning methods that are sufficiently expressive to handle complex decision-making problems. So far our research focused on answer set solving technology for incremental and reactive reasoning, preferential reasoning, and finite linear constraint solving. Also, basic techniques for reactive multi-context systems and argumentative reasoning were developed. Currently we are realizing new methods to be built on top of the existing systems, extending the range of reasoning methods and addressing in particular uncertain reasoning. In particular, we study combinations of uncertain reasoning and answer set programming (ASP), respectively argumentation. In addition we want to substantially generalize existing preferential reasoning methods. We also study new forms of theory-based reasoning, and further investigate reactive and interactive forms of reasoning. On top of the advanced reasoning methods, we will build a general framework for complex hybrid problem solving, focusing on interactive, hybrid methods for decision making and for argumentation. The developed methods and frameworks will be tested in applications from the field of logistics, namely logistic systems design, autonomous logistic vehicles, and RoboCup logistics. To provide a clearer idea of our research we focus in what follows on two of the various aspects of the project, namely on extensions of answer set programming with constraints and on applications in logistics.