Symmetry-Based Search Space Reduction For Grid Maps

In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles, removing from each rectangle all interior nodes and possibly some from along the perimeter. We then add a series of macro-edges between selected pairs of remaining perimeter nodes to facilitate provably optimal traversal through each rectangle. We also develop a novel online pruning technique to further speed up search. Our algorithm is fast, memory efficient and retains the same optimality and completeness guarantees as searching on an unmodified grid map

Growing a Tree in the Forest: Constructing Folksonomies by Integrating Structured Metadata

Many social Web sites allow users to annotate the content with descriptive metadata, such as tags, and more recently to organize content hierarchically. These types of structured metadata provide valuable evidence for learning how a community organizes knowledge. For instance, we can aggregate many personal hierarchies into a common taxonomy, also known as a folksonomy, that will aid users in visualizing and browsing social content, and also to help them in organizing their own content. However, learning from social metadata presents several challenges, since it is sparse, shallow, ambiguous, noisy, and inconsistent. We describe an approach to folksonomy learning based on relational clustering, which exploits structured metadata contained in personal hierarchies. Our approach clusters similar hierarchies using their structure and tag statistics, then incrementally weaves them into a deeper, bushier tree. We study folksonomy learning using social metadata extracted from the photo-sharing site Flickr, and demonstrate that the proposed approach addresses the challenges. Moreover, comparing to previous work, the approach produces larger, more accurate folksonomies, and in addition, scales better.Comment: 10 pages, To appear in the Proceedings of ACM SIGKDD Conference on Knowledge Discovery and Data Mining(KDD) 201

A Graphical Language for Proof Strategies

Complex automated proof strategies are often difficult to extract, visualise, modify, and debug. Traditional tactic languages, often based on stack-based goal propagation, make it easy to write proofs that obscure the flow of goals between tactics and are fragile to minor changes in input, proof structure or changes to tactics themselves. Here, we address this by introducing a graphical language called PSGraph for writing proof strategies. Strategies are constructed visually by "wiring together" collections of tactics and evaluated by propagating goal nodes through the diagram via graph rewriting. Tactic nodes can have many output wires, and use a filtering procedure based on goal-types (predicates describing the features of a goal) to decide where best to send newly-generated sub-goals. In addition to making the flow of goal information explicit, the graphical language can fulfil the role of many tacticals using visual idioms like branching, merging, and feedback loops. We argue that this language enables development of more robust proof strategies and provide several examples, along with a prototype implementation in Isabelle

A Branching Time Model of CSP

I present a branching time model of CSP that is finer than all other models of CSP proposed thus far. It is obtained by taking a semantic equivalence from the linear time - branching time spectrum, namely divergence-preserving coupled similarity, and showing that it is a congruence for the operators of CSP. This equivalence belongs to the bisimulation family of semantic equivalences, in the sense that on transition systems without internal actions it coincides with strong bisimilarity. Nevertheless, enough of the equational laws of CSP remain to obtain a complete axiomatisation for closed, recursion-free terms.Comment: Dedicated to Bill Roscoe, on the occasion of his 60th birthda

Practical Reasoning for Very Expressive Description Logics

Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSPACE. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the worst-case complexity of the problem, exhibit good performance with real-life problems