Uncertainty is unavoidable when modeling most application domains. In medicine, for example, symptoms (such as pain, dizziness, or nausea) are always subjective, and hence imprecise and incomparable. Additionally, concepts and their relationships may be inexpressible in a crisp, clear-cut manner. We extend the description logic ALC with multi-valued semantics based on lattices that can handle uncertainty on concepts as well as on the axioms of the ontology. We introduce reasoning methods for this logic w.r.t. general concept inclusions and show that the complexity of reasoning is not increased by this new semantics.

A tree decomposition We construct an homogeneous (and ω-categorical) of a constraint network is a tree decomposition of its constraint representation of the relation algebra RCC8, which graph: roughly speaking, a decomposition defines a is one of the fundamental formalisms for spatial set of subnetworks that can be glued together in a treelike reasoning. As a consequence we obtain that the manner. The width of such a decomposition, then, is the size network consistency problem for RCC8 can be of the largest subnetwork in the decomposition (in terms of solved in polynomial time for networks of bounded the variables in the network).

Many AI applications are based on some underlying logic that tolerates inconsistent information in a non-trivial way. However, it is not always clear what should be the exact nature of such a logic, and how to choose one for a specific application. In this paper, we formulate a list of desirable properties of `ideal' logics for reasoning with inconsistency, identify a variety of logics that have these properties, and provide a systematic way of constructing, for every n>2, a family of such n-valued logics.

One of main difficulties of multi-dimensional packing problems is the fragmentation of free space into several unusable small parts after a few items are packed. This study proposes a defragmentation technique to combine the fragmented space into a continuous usable space, which potentially allows the packing of additional items. We illustrate the effectiveness of this technique on the two- and three-dimensional Bin Packing Problems. In conjunction with a bin shuffling strategy for incremental improvement, our resultant algorithm outperforms all leading meta-heuristic approaches.

Balanced multi-way number partitioning (BMNP) seeks to split a collection of numbers into subsets with (roughly) the same cardinality and subset sum. The problem is NP-hard, and there are several exact and approximate algorithms for it. However, existing exact algorithms solve only the simpler, balanced two-way number partitioning variant, whereas the most effective approximate algorithm, BLDM, may produce widely varying subset sums. In this paper, we introduce the LRM algorithm that lowers the expected spread in subset sums to one third that of BLDM for uniformly distributed numbers and odd subset cardinalities. We also propose Meld, a novel strategy for skewed number distributions. A combination of LRM and Meld leads to a heuristic technique that consistently achieves a narrower spread of subset sums than BLDM.

Heuristics are crucial tools in decreasing search effort in varied fields of AI. In order to be effective, a heuristic must be efficient to compute, as well as provide useful information to the search algorithm. However, some well-known heuristics which do well in reducing backtracking are so heavy that the gain of deploying them in a search algorithm might be outweighed by their overhead. We propose a rational metareasoning approach to decide when to deploy heuristics, using CSP backtracking search as a case study. In particular, a value of information approach is taken to adaptive deployment of solution-count estimation heuristics for value ordering. Empirical results show that indeed the proposed mechanism successfully balances the tradeoff between decreasing backtracking and heuristic computational overhead, resulting in a significant overall search time reduction.

Bounded suboptimal search algorithms offer shorter solving times bysacrificing optimality and instead guaranteeing solution costs withina desired factor of optimal. Typically these algorithms use a singleadmissible heuristic both for guiding search and bounding solutioncost. In this paper, we present a new approach to bounded suboptimalsearch, Explicit Estimation Search, that separates these roles,consulting potentially inadmissible information to determine searchorder and using admissible information to guarantee the cost bound.Unlike previous proposals, it successfully combines estimates ofsolution length and solution cost to predict which node will lead mostquickly to a solution within the suboptimality bound. An empiricalevaluation across six diverse benchmark domains shows that ExplicitEstimation Search is competitive with the previous state of the art indomains with unit-cost actions and substantially outperformspreviously proposed techniques for domains in which solution cost andlength can differ.

We address the problem of optimal path finding for multiple agents where agents must not collide and their total travel cost should be minimized. Previous work used traditional single-agent search variants of the A* algorithm. We present a novel formalization for this problem which includes a search tree called the increasing cost tree (ICT) and a corresponding search algorithm that finds optimal solutions. We analyze this new formalization and compare it to the previous state-of-the-art A*-based approach. Experimental results on various domains show the benefits and drawbacks of this approach. A speedup of up to 3 orders of magnitude was obtained in a number of cases.

We develop a real-time algorithm based on a Monte-Carlo game tree search for solving a quantified constraint satisfaction problem (QCSP), which is a CSP where some variables are universally quantified. A universally quantified variable represents a choice of nature or an adversary. The goal of a QCSP is to make a robust plan against an adversary. However, obtaining a complete plan off-line is intractable when the size of the problem becomes large. Thus, we need to develop a real-time algorithm that sequentially selects a promising value at each deadline. Such a problem has been considered in the field of game tree search. In a standard game tree search algorithm, developing a good static evaluation function is crucial. However, developing a good static evaluation function for a QCSP is very difficult since it must estimate the possibility that a partially assigned QCSP is solvable. Thus, we apply a Monte-Carlo game tree search technique called UCT. However, the simple application of the UCT algorithm does not work since the player and the adversary are asymmetric, i.e., finding a game sequence where the player wins is very rare. We overcome this difficulty by introducing constraint propagation techniques. We experimentally compare the winning probability of our UCT-based algorithm and the state-of-the-art alpha-beta search algorithm. Our results show that our algorithm outperforms the state-of-the-art algorithm in large-scale problems.

Consider random hypergraphs on n vertices, where each k -element subset of vertices is selected with probability $independently and randomly as a hyperedge. By sparse we mean that the total number of hyperedges is  O ( n) or O ( n  ln n ). When k = 2, these are exactly the classical Erdös-Rényi random graphs G(n,p ). We prove that with high probability, hinge width on these sparse random hypergraphs can grow linearly with the expected number of hyperedges. Some random constraint satisfaction problems such as Model RB and Model RD have satisfiability thresholds on these sparse constraint hypergraphs, thus the large hinge width results provide some theoretical evidence for random instances around satisfiability thresholds to be hard for a standard hinge-decomposition based algorithm. We also conduct experiments on these and other kinds of random graphs with several hundreds vertices, including regular random graphs and power law random graphs. The experimental results also show that hinge width can grow linearly with the number of edges on these different random graphs. These results may be of further interests.