1 Revising Qualitative Constraint Networks: Definition and Implementation Julien Hu´ e and Matthias Westphal Institut f¨ ur Informatik Albert-Ludwigs-Universit¨ at Freiburg Georges-K¨ ohler-Allee 52 79110 Freiburg, Germany {hue,westpham}@informatik.uni-freiburg.de Abstract—Qualitative Spatial and Temporal Reasoning is a central topic in Artificial Intelligence. In particular, it is aimed at application scenarios dealing with uncertain information and thus needs to be able to handle dynamic beliefs. This makes merging and revision of qualitative information important topics. While merging has been studied extensively, revision which describes what is happening when one learns new information about a static world has been overlooked. In this paper, we propose to fill the gap by providing two revision operations for qualitative calculi. In order to implement these operations, we give algo- rithms for revision and analyze the computational complexity of these problems. Finally, we present an implementation of these algorithms based on a qualitative constraint solver and provide an experimental evaluation. I. I NTRODUCTION Qualitative Spatial and Temporal Reasoning (QSTR) is a research field which studies relation languages for representing information about infinitely-valued domains. For example, temporal relations between events (defined on the domain Q) can be described by qualitative terms like a happened before b or a takes place during b. Since spatial and temporal aspects are usually concerned with infinite, continuous domains, many computational tasks are undecidable in the general case. Thus, focusing on the qualitative relations between entities is a convenient method for crafting a calculus that can actually be used for reasoning. Qualitative information is then represented as constraint networks defined over such qualitative terms, so- called qualitative constraint networks (QCNs). As qualitative information deals with vague and uncertain information, representing Qualitative Spatial and Temporal beliefs is an important topic for several fields in or related to Artificial Intelligence, e.g., Geographic Information Sys- tems or robot navigation. So far, mainly the central task of deciding satisfiability of QCNs has been extensively studied. Nevertheless, many practical applications of such qualitative languages require the ability to deal with changing beliefs, i.e., if one only knows uncertain or incomplete information about the world then what happens when a more reliable piece of information about the world arises or when the world changes? The first problem is known as belief revision and the latter problem is known as belief update. For this paper, we will only concentrate on the revision problem (differences with possible treatments of update operations will be discussed in the conclusion). A good revision operation must solve conflicts between the new and the old information while saving as much as possible from the old information and respecting the new one. Such issues arise in, e.g., the context of robots learning a map of their surroundings [Wal10]. Several operators have been studied for merging QCNs (see [WD10], [CKMS09a], [CKMS10], [CKMS09b]). These merging operators are based on the distance between solutions of each source (called semantic operators) or based on the number of violated con- straints (called syntactic operators). These distances in turn can either be based on a drastic distance or a more fine- grained distance based on proximity of the different relations [CKS08]. To the authors knowledge, with the exception of a bachelor’s thesis [Dos11] on classical revision operations (partial meet and cut revisions) for QCNs, no operations for revision of QCNs have been proposed. Moreover, in the context of QCNs, to the authors knowledge no such revision or merging operation has been implemented despite some proposals such as [WD10]. In this paper, we propose revision operations for QCNs based on the merging operations previously defined in the literature. We show that these operations behave well with respect to the AGM postulates which state how a correct revision operator must behave [AGM85]. We then provide an algorithm for revision operations of QCNs and analyze its computational complexity. We finally exhibit an implementa- tion of these revision operations based on qualitative constraint reasoning techniques and provide an experimental study. We based this implementation on the qualitative constraint solver GQR [WWG09] since it is considered as the state-of-the-art constraint solver for QCNs and compares favorably with other possibilities such as SAT encodings [WW09]. The structure of this paper is as follows. In Section II a reminder about QCNs and revision is given. Then, a formal definition of our revision operations is provided in Section III where their formal properties are also studied. This is followed by a description of our implementation in Section IV as well as a theoretical study of its complexity. In Section V we then show first experimental results of our implementation. We conclude the paper in Section VI with a summary and outlook on future work.