Complexity of Prioritized Default Logics

In default reasoning, usually not all possible ways of resolving conflicts between default rules are acceptable. Criteria expressing acceptable ways of resolving the conflicts may be hardwired in the inference mechanism, for example specificity in inheritance reasoning can be handled this way, or they may be given abstractly as an ordering on the default rules. In this article we investigate formalizations of the latter approach in Reiter's default logic. Our goal is to analyze and compare the computational properties of three such formalizations in terms of their computational complexity: the prioritized default logics of Baader and Hollunder, and Brewka, and a prioritized default logic that is based on lexicographic comparison. The analysis locates the propositional variants of these logics on the second and third levels of the polynomial hierarchy, and identifies the boundary between tractable and intractable inference for restricted classes of prioritized default theories

Constructing Conditional Plans by a Theorem-Prover

The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of operations that achieve the goals depend on the initial state and the outcomes of nondeterministic changes in the system. This setting raises the questions of how to represent the plans and how to perform plan search. The answers are quite different from those in the simpler classical framework. In this paper, we approach conditional planning from a new viewpoint that is motivated by the use of satisfiability algorithms in classical planning. Translating conditional planning to formulae in the propositional logic is not feasible because of inherent computational limitations. Instead, we translate conditional planning to quantified Boolean formulae. We discuss three formalizations of conditional planning as quantified Boolean formulae, and present experimental results obtained with a theorem-prover

Understanding Gentzen and Frege Systems for QBF

Recently Beyersdorff, Bonacina, and Chew [10] introduced a natural class of Frege systems for quantified Boolean formulas (QBF) and showed strong lower bounds for restricted versions of these systems. Here we provide a comprehensive analysis of the new extended Frege system from [10], denoted EF + ∀red, which is a natural extension of classical extended Frege EF. Our main results are the following: Firstly, we prove that the standard Gentzen-style system G*1 p-simulates EF + ∀red and that G*1 is strictly stronger under standard complexity-theoretic hardness assumptions. Secondly, we show a correspondence of EF + ∀red to bounded arithmetic: EF + ∀red can be seen as the non-uniform propositional version of intuitionistic S12. Specifically, intuitionistic S12 proofs of arbitrary statements in prenex form translate to polynomial-size EF + ∀red proofs, and EF + ∀red is in a sense the weakest system with this property. Finally, we show that unconditional lower bounds for EF + ∀red would imply either a major breakthrough in circuit complexity or in classical proof complexity, and in fact the converse implications hold as well. Therefore, the system EF + ∀red naturally unites the central problems from circuit and proof complexity. Technically, our results rest on a formalised strategy extraction theorem for EF + ∀red akin to witnessing in intuitionistic S12 and a normal form for EF + ∀red proofs

AMPLE: an anytime planning and execution framework for dynamic and uncertain problems in robotics

Acting in robotics is driven by reactive and deliberative reasonings which take place in the competition between execution and planning processes. Properly balancing reactivity and deliberation is still an open question for harmonious execution of deliberative plans in complex robotic applications. We propose a flexible algorithmic framework to allow continuous real-time planning of complex tasks in parallel of their executions. Our framework, named AMPLE, is oriented towards robotic modular architectures in the sense that it turns planning algorithms into services that must be generic, reactive, and valuable. Services are optimized actions that are delivered at precise time points following requests from other modules that include states and dates at which actions are needed. To this end, our framework is divided in two concurrent processes: a planning thread which receives planning requests and delegates action selection to embedded planning softwares in compliance with the queue of internal requests, and an execution thread which orchestrates these planning requests as well as action execution and state monitoring. We show how the behavior of the execution thread can be parametrized to achieve various strategies which can differ, for instance, depending on the distribution of internal planning requests over possible future execution states in anticipation of the uncertain evolution of the system, or over different underlying planners to take several levels into account. We demonstrate the flexibility and the relevance of our framework on various robotic benchmarks and real experiments that involve complex planning problems of different natures which could not be properly tackled by existing dedicated planning approaches which rely on the standard plan-then-execute loop

Parallel Encodings of Classical Planning as Satisfiability

We consider a number of semantics for plans with parallel operator application. The standard semantics used most often in earlier work requires that parallel operators are independent and can therefore be executed in any order. We consider a more relaxed definition of parallel plans, first proposed by Dimopoulos et al., as well as normal forms for parallel plans that require every operator to be executed as early as possible. We formalize the semantics of parallel plans emerging in this setting, and propose effective translations of these semantics into the propositional logic. And finally we show that one of the semantics yields an approach to classical planning that is sometimes much more efficient than the existing SAT-based planners

QUBE: A system for deciding quantified boolean formulas satisfiability

Deciding the satisfiability of a Quantified Boolean Formula (QBF) is an important research issue in Artificial Intelligence. Many reasoning tasks involving planning [1], abduction, reasoning about knowledge, non monotonic reasoning [2], can be directly mapped into the problem of deciding the satisfiability of a QBF. In this paper we present quBE, a system for deciding QBFs satisfiability. We start our presentation is Section 2 with some terminology and definitions necessary for the rest of the paper. In Section 3 we present a high level description of QuBE's basic algorithm. QuBE's available options are described in Section 4. We end our presentation is Section 5 with some experimental results showing QuBE effectiveness in comparison with other systems. QuBE, and more information about QuBE are available at www.mrg.dist.unige.it/star/qub