35,476 research outputs found
Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems
The paper presents probabilistic extensions of interval temporal logic (ITL)
and duration calculus (DC) with infinite intervals and complete Hilbert-style
proof systems for them. The completeness results are a strong completeness
theorem for the system of probabilistic ITL with respect to an abstract
semantics and a relative completeness theorem for the system of probabilistic
DC with respect to real-time semantics. The proposed systems subsume
probabilistic real-time DC as known from the literature. A correspondence
between the proposed systems and a system of probabilistic interval temporal
logic with finite intervals and expanding modalities is established too.Comment: 43 page
Robust Online Monitoring of Signal Temporal Logic
Signal Temporal Logic (STL) is a formalism used to rigorously specify
requirements of cyberphysical systems (CPS), i.e., systems mixing digital or
discrete components in interaction with a continuous environment or analog com-
ponents. STL is naturally equipped with a quantitative semantics which can be
used for various purposes: from assessing the robustness of a specification to
guiding searches over the input and parameter space with the goal of falsifying
the given property over system behaviors. Algorithms have been proposed and
implemented for offline computation of such quantitative semantics, but only
few methods exist for an online setting, where one would want to monitor the
satisfaction of a formula during simulation. In this paper, we formalize a
semantics for robust online monitoring of partial traces, i.e., traces for
which there might not be enough data to decide the Boolean satisfaction (and to
compute its quantitative counterpart). We propose an efficient algorithm to
compute it and demonstrate its usage on two large scale real-world case studies
coming from the automotive domain and from CPS education in a Massively Open
Online Course (MOOC) setting. We show that savings in computationally expensive
simulations far outweigh any overheads incurred by an online approach
Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)
Oxford, UK, 26 August 200
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
Temporal Landscapes: A Graphical Temporal Logic for Reasoning
We present an elementary introduction to a new logic for reasoning about
behaviors that occur over time. This logic is based on temporal type theory.
The syntax of the logic is similar to the usual first-order logic; what differs
is the notion of truth value. Instead of reasoning about whether formulas are
true or false, our logic reasons about temporal landscapes. A temporal
landscape may be thought of as representing the set of durations over which a
statement is true. To help understand the practical implications of this
approach, we give a wide variety of examples where this logic is used to reason
about autonomous systems.Comment: 20 pages, lots of figure
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