26,405 research outputs found
Dependence Logic vs. Constraint Satisfaction
Leibniz international proceedings in informatics. Vol. 62
From Uncertainty Data to Robust Policies for Temporal Logic Planning
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
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
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
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?
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
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
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