26,405 research outputs found

    Dependence Logic vs. Constraint Satisfaction

    Get PDF
    Leibniz international proceedings in informatics. Vol. 62

    From Uncertainty Data to Robust Policies for Temporal Logic Planning

    Full text link
    We consider the problem of synthesizing robust disturbance feedback policies for systems performing complex tasks. We formulate the tasks as linear temporal logic specifications and encode them into an optimization framework via mixed-integer constraints. Both the system dynamics and the specifications are known but affected by uncertainty. The distribution of the uncertainty is unknown, however realizations can be obtained. We introduce a data-driven approach where the constraints are fulfilled for a set of realizations and provide probabilistic generalization guarantees as a function of the number of considered realizations. We use separate chance constraints for the satisfaction of the specification and operational constraints. This allows us to quantify their violation probabilities independently. We compute disturbance feedback policies as solutions of mixed-integer linear or quadratic optimization problems. By using feedback we can exploit information of past realizations and provide feasibility for a wider range of situations compared to static input sequences. We demonstrate the proposed method on two robust motion-planning case studies for autonomous driving

    Generalizing Consistency and other Constraint Properties to Quantified Constraints

    Full text link
    Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the usual notion of solution inappropriate. As a consequence, basic properties of Constraint Satisfaction Problems (CSP), such as consistency or substitutability, are not completely understood in the quantified case. These properties are important because they are the basis of most of the reasoning methods used to solve classical (existentially quantified) constraints, and one would like to benefit from similar reasoning methods in the resolution of quantified constraints. In this paper, we show that most of the properties that are used by solvers for CSP can be generalized to quantified CSP. This requires a re-thinking of a number of basic concepts; in particular, we propose a notion of outcome that generalizes the classical notion of solution and on which all definitions are based. We propose a systematic study of the relations which hold between these properties, as well as complexity results regarding the decision of these properties. Finally, and since these problems are typically intractable, we generalize the approach used in CSP and propose weaker, easier to check notions based on locality, which allow to detect these properties incompletely but in polynomial time

    Learning and Designing Stochastic Processes from Logical Constraints

    Get PDF
    Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics must be known exactly. As this is seldom the case, many methods have been devised over the last decade to infer (learn) such parameters from observations of the state of the system. In this paper, we depart from this approach by assuming that our observations are {\it qualitative} properties encoded as satisfaction of linear temporal logic formulae, as opposed to quantitative observations of the state of the system. An important feature of this approach is that it unifies naturally the system identification and the system design problems, where the properties, instead of observations, represent requirements to be satisfied. We develop a principled statistical estimation procedure based on maximising the likelihood of the system's parameters, using recent ideas from statistical machine learning. We demonstrate the efficacy and broad applicability of our method on a range of simple but non-trivial examples, including rumour spreading in social networks and hybrid models of gene regulation

    The Futility of Utility: how market dynamics marginalize Adam Smith

    Get PDF
    Econometrics is based on the nonempiric notion of utility. Prices, dynamics, and market equilibria are supposed to be derived from utility. Utility is usually treated by economists as a price potential, other times utility rates are treated as Lagrangians. Assumptions of integrability of Lagrangians and dynamics are implicitly and uncritically made. In particular, economists assume that price is the gradient of utility in equilibrium, but I show that price as the gradient of utility is an integrability condition for the Hamiltonian dynamics of an optimization problem in econometric control theory. One consequence is that, in a nonintegrable dynamical system, price cannot be expressed as a function of demand or supply variables. Another consequence is that utility maximization does not describe equiulibrium. I point out that the maximization of Gibbs entropy would describe equilibrium, if equilibrium could be achieved, but equilibrium does not describe real markets. To emphasize the inconsistency of the economists' notion of 'equilibrium', I discuss both deterministic and stochastic dynamics of excess demand and observe that Adam Smith's stabilizing hand is not to be found either in deterministic or stochastic dynamical models of markets, nor in the observed motions of asset prices. Evidence for stability of prices of assets in free markets simply has not been found.Comment: 46 pages. accepte

    Logic Programming Applications: What Are the Abstractions and Implementations?

    Full text link
    This article presents an overview of applications of logic programming, classifying them based on the abstractions and implementations of logic languages that support the applications. The three key abstractions are join, recursion, and constraint. Their essential implementations are for-loops, fixed points, and backtracking, respectively. The corresponding kinds of applications are database queries, inductive analysis, and combinatorial search, respectively. We also discuss language extensions and programming paradigms, summarize example application problems by application areas, and touch on example systems that support variants of the abstractions with different implementations

    A Policy Search Method For Temporal Logic Specified Reinforcement Learning Tasks

    Full text link
    Reward engineering is an important aspect of reinforcement learning. Whether or not the user's intentions can be correctly encapsulated in the reward function can significantly impact the learning outcome. Current methods rely on manually crafted reward functions that often require parameter tuning to obtain the desired behavior. This operation can be expensive when exploration requires systems to interact with the physical world. In this paper, we explore the use of temporal logic (TL) to specify tasks in reinforcement learning. TL formula can be translated to a real-valued function that measures its level of satisfaction against a trajectory. We take advantage of this function and propose temporal logic policy search (TLPS), a model-free learning technique that finds a policy that satisfies the TL specification. A set of simulated experiments are conducted to evaluate the proposed approach
    • …
    corecore