This paper focuses on the expressive power of disjunctive and normal logic programs under the stable model semantics over finite, infinite, or arbitrary structures. A translation from disjunctive logic programs into normal logic programs is proposed and then proved to be sound over infinite structures. The equivalence of expressive power of two kinds of logic programs over arbitrary structures is shown to coincide with that over finite structures, and coincide with whether or not NP is closed under complement. Over finite structures, the intranslatability from disjunctive logic programs to normal logic programs is also proved if arities of auxiliary predicates and functions are bounded in a certain way.

So-called combined approaches answer a conjunctive query over a description logic ontology in three steps: first, they materialise certain consequences of the ontology and the data; second, they evaluate the query over the data; and third, they filter the result of the second phase to eliminate unsound answers. Such approaches were developed for various members of the DL-Lite and the EL families of languages, but none of them can handle ontologies containing nominals. In our work, we bridge this gap and present a combined query answering approach for ELHO---a logic that contains all features of the OWL 2 EL standard apart from transitive roles and complex role inclusions. This extension is nontrivial because nominals require equality reasoning, which introduces complexity into the first and the third step. Our empirical evaluation suggests that our technique is suitable for practical application, and so it provides a practical basis for conjunctive query answering in a large fragment of OWL 2 EL.

This paper presents a model-based planner called the Probabilistic Sulu Planner or the p-Sulu Planner, which controls stochastic systems in a goal directed manner within user-specified risk bounds. The objective of the p-Sulu Planner is to allow users to command continuous, stochastic systems, such as unmanned aerial and space vehicles, in a manner that is both intuitive and safe. To this end, we first develop a new plan representation called a chance-constrained qualitative state plan (CCQSP), through which users can specify the desired evolution of the plant state as well as the acceptable level of risk. An example of a CCQSP statement is ``go to A through B within 30 minutes, with less than 0.001% probability of failure." We then develop the p-Sulu Planner, which can tractably solve a CCQSP planning problem. In order to enable CCQSP planning, we develop the following two capabilities in this paper: 1) risk-sensitive planning with risk bounds, and 2) goal-directed planning in a continuous domain with temporal constraints. The first capability is to ensures that the probability of failure is bounded. The second capability is essential for the planner to solve problems with a continuous state space such as vehicle path planning. We demonstrate the capabilities of the p-Sulu Planner by simulations on two real-world scenarios: the path planning and scheduling of a personal aerial vehicle as well as the space rendezvous of an autonomous cargo spacecraft.

A fundamental question in Computer Science is understanding when a specific class of problems go from being computationally easy to hard. Because of its generality and applications, the problem of Boolean Satisfiability (aka SAT) is often used as a vehicle for investigating this question. A signal result from these studies is that the hardness of SAT problems exhibits a dramatic easy-to-hard phase transition with respect to the problem constrainedness. Past studies have however focused mostly on SAT instances generated using uniform random distributions, where all constraints are independently generated, and the problem variables are all considered of equal importance. These assumptions are unfortunately not satisfied by most real problems. Our project aims for a deeper understanding of hardness of SAT problems that arise in practice. We study two key questions: (i) How does easy-to-hard transition change with more realistic distributions that capture neighborhood sensitivity and rich-get-richer aspects of real problems and (ii) Can these changes be explained in terms of the network properties (such as node centrality and small-worldness) of the clausal networks of the SAT problems. Our results, based on extensive empirical studies and network analyses, provide important structural and computational insights into realistic SAT problems. Our extensive empirical studies show that SAT instances from realistic distributions do exhibit phase transition, but the transition occurs sooner (at lower values of constrainedness) than the instances from uniform random distribution. We show that this behavior can be explained in terms of their clausal network properties such as eigenvector centrality and small-worldness (measured indirectly in terms of the clustering coefficients and average node distance).

This paper presents a structured power and energy-flow-based qualitative modelling approach that is applicable to a variety of system types including electrical and fluid flow. The modelling is split into two parts. Power flow is a global phenomenon and is therefore naturally represented and analysed by a network comprised of the relevant structural elements from the components of a system. The power flow analysis is a platform for higher-level behaviour prediction of energy related aspects using local component behaviour models to capture a state-based representation with a global time. The primary application is Failure Modes and Effects Analysis (FMEA) and a form of exaggeration reasoning is used, combined with an order of magnitude representation to derive the worst case failure modes. The novel aspects of the work are an order of magnitude(OM) qualitative network analyser to represent any power domain and topology, including multiple power sources, a feature that was not required for earlier specialised electrical versions of the approach. Secondly, the representation of generalised energy related behaviour as state-based local models is presented as a modelling strategy that can be more vivid and intuitive for a range of topologically complex applications than qualitative equation-based representations. The two-level modelling strategy allows the broad system behaviour coverage of qualitative simulation to be exploited for the FMEA task, while limiting the difficulties of qualitative ambiguity explanation that can arise from abstracted numerical models. We have used the method to support an automated FMEA system with examples of an aircraft fuel system and domestic a heating system discussed in this paper.

This article presents the state-of-the-art in optimal solution methods for decentralized partially observable Markov decision processes (Dec-POMDPs), which are general models for collaborative multiagent planning under uncertainty. Building off the generalized multiagent A* (GMAA*) algorithm, which reduces the problem to a tree of one-shot collaborative Bayesian games (CBGs), we describe several advances that greatly expand the range of Dec-POMDPs that can be solved optimally. First, we introduce lossless incremental clustering of the CBGs solved by GMAA*, which achieves exponential speedups without sacrificing optimality. Second, we introduce incremental expansion of nodes in the GMAA* search tree, which avoids the need to expand all children, the number of which is in the worst case doubly exponential in the node's depth. This is particularly beneficial when little clustering is possible. In addition, we introduce new hybrid heuristic representations that are more compact and thereby enable the solution of larger Dec-POMDPs. We provide theoretical guarantees that, when a suitable heuristic is used, both incremental clustering and incremental expansion yield algorithms that are both complete and search equivalent. Finally, we present extensive empirical results demonstrating that GMAA*-ICE, an algorithm that synthesizes these advances, can optimally solve Dec-POMDPs of unprecedented size.

The paper briefly describes a basic set of special combinatorial engineering frameworks for solving complex problems in the field of hierarchical modular systems. The frameworks consist of combinatorial problems (and corresponding models), which are interconnected/linked (e.g., by preference relation). Mainly, hierarchical morphological system model is used. The list of basic standard combinatorial engineering (technological) frameworks is the following: (1) design of system hierarchical model, (2) combinatorial synthesis ('bottom-up' process for system design), (3) system evaluation, (4) detection of system bottlenecks, (5) system improvement (re-design, upgrade), (6) multi-stage design (design of system trajectory), (7) combinatorial modeling of system evolution/development and system forecasting. The combinatorial engineering frameworks are targeted to maintenance of some system life cycle stages. The list of main underlaying combinatorial optimization problems involves the following: knapsack problem, multiple-choice problem, assignment problem, spanning trees, morphological clique problem.

Orthogonality is a discipline of programming that in a syntactic manner guarantees determinism of functional specifications. Essentially, orthogonality avoids, on the one side, the inherent ambiguity of non determinism, prohibiting the existence of different rules that specify the same function and that may apply simultaneously (non-ambiguity), and, on the other side, it eliminates the possibility of occurrence of repetitions of variables in the left-hand side of these rules (left linearity). In the theory of term rewriting systems (TRSs) determinism is captured by the well-known property of confluence, that basically states that whenever different computations or simplifications from a term are possible, the computed answers should coincide. Although the proofs are technically elaborated, confluence is well-known to be a consequence of orthogonality. Thus, orthogonality is an important mathematical discipline intrinsic to the specification of recursive functions that is naturally applied in functional programming and specification. Starting from a formalization of the theory of TRSs in the proof assistant PVS, this work describes how confluence of orthogonal TRSs has been formalized, based on axiomatizations of properties of rules, positions and substitutions involved in parallel steps of reduction, in this proof assistant. Proofs for some similar but restricted properties such as the property of confluence of non-ambiguous and (left and right) linear TRSs have been fully formalized.

We present a principled approach for detecting overlapping temporal community structure in dynamic networks. Our method is based on the following framework: find the overlapping temporal community structure that maximizes a quality function associated with each snapshot of the network subject to a temporal smoothness constraint. A novel quality function and a smoothness constraint are proposed to handle overlaps, and a new convex relaxation is used to solve the resulting combinatorial optimization problem. We provide theoretical guarantees as well as experimental results that reveal community structure in real and synthetic networks. Our main insight is that certain structures can be identified only when temporal correlation is considered and when communities are allowed to overlap. In general, discovering such overlapping temporal community structure can enhance our understanding of real-world complex networks by revealing the underlying stability behind their seemingly chaotic evolution.

We introduce a graceful approach to probabilistic inference called bounded conditioning. Bounded conditioning monotonically refines the bounds on posterior probabilities in a belief network with computation, and converges on final probabilities of interest with the allocation of a complete resource fraction. The approach allows a reasoner to exchange arbitrary quantities of computational resource for incremental gains in inference quality. As such, bounded conditioning holds promise as a useful inference technique for reasoning under the general conditions of uncertain and varying reasoning resources. The algorithm solves a probabilistic bounding problem in complex belief networks by breaking the problem into a set of mutually exclusive, tractable subproblems and ordering their solution by the expected effect that each subproblem will have on the final answer. We introduce the algorithm, discuss its characterization, and present its performance on several belief networks, including a complex model for reasoning about problems in intensive-care medicine.