33 research outputs found
Consistency proof of a fragment of PV with substitution in bounded arithmetic
This paper presents proof that Buss's can prove the consistency of a
fragment of Cook and Urquhart's from which induction has been
removed but substitution has been retained.
This result improves Beckmann's result, which proves the consistency of such
a system without substitution in bounded arithmetic .
Our proof relies on the notion of "computation" of the terms of
.
In our work, we first prove that, in the system under consideration, if an
equation is proved and either its left- or right-hand side is computed, then
there is a corresponding computation for its right- or left-hand side,
respectively.
By carefully computing the bound of the size of the computation, the proof of
this theorem inside a bounded arithmetic is obtained, from which the
consistency of the system is readily proven.
This result apparently implies the separation of bounded arithmetic because
Buss and Ignjatovi\'c stated that it is not possible to prove the consistency
of a fragment of without induction but with substitution in
Buss's .
However, their proof actually shows that it is not possible to prove the
consistency of the system, which is obtained by the addition of propositional
logic and other axioms to a system such as ours.
On the other hand, the system that we have considered is strictly equational,
which is a property on which our proof relies.Comment: Submitted versio
Evaluation of A Resilience Embedded System Using Probabilistic Model-Checking
If a Micro Processor Unit (MPU) receives an external electric signal as
noise, the system function will freeze or malfunction easily. A new resilience
strategy is implemented in order to reset the MPU automatically and stop the
MPU from freezing or malfunctioning. The technique is useful for embedded
systems which work in non-human environments. However, evaluating resilience
strategies is difficult because their effectiveness depends on numerous,
complex, interacting factors.
In this paper, we use probabilistic model checking to evaluate the embedded
systems installed with the above mentioned new resilience strategy. Qualitative
evaluations are implemented with 6 PCTL formulas, and quantitative evaluations
use two kinds of evaluation. One is system failure reduction, and the other is
ADT (Average Down Time), the industry standard. Our work demonstrates the
benefits brought by the resilience strategy. Experimental results indicate that
our evaluation is cost-effective and reliable.Comment: In Proceedings ESSS 2014, arXiv:1405.055
On the notion of validity for the bilateral classical logic
This paper considers Rumfitt’s bilateral classical logic (BCL), which is proposed to counter Dummett’s challenge to classical logic. First, agreeing with several authors, we argue that Rumfitt’s notion of harmony, used to justify logical rules by a purely proof theoretical manner, is not sufficient to justify coordination rules in BCL purely proof-theoretically. For the central part of this paper, we propose a notion of proof-theoretical validity similar to Prawitz for BCL and proves that BCL is sound and complete respect to this notion of validity. The major difficulty in defining validity for BCL is that validity of positive +A appears to depend on negative −A, and vice versa. Thus, the straightforward inductive definition does not work because of this circular dependance. However, Knaster-Tarski’s fixed point theorem can resolve this circularity. Finally, we discuss the philosophical relevance of our work, in particular, the impact of the use of fixed point theorem and the issue of decidability
Log-based Anomaly Detection of CPS Using a Statistical Method
Detecting anomalies of a cyber physical system (CPS), which is a complex
system consisting of both physical and software parts, is important because a
CPS often operates autonomously in an unpredictable environment. However,
because of the ever-changing nature and lack of a precise model for a CPS,
detecting anomalies is still a challenging task. To address this problem, we
propose applying an outlier detection method to a CPS log. By using a log
obtained from an actual aquarium management system, we evaluated the
effectiveness of our proposed method by analyzing outliers that it detected. By
investigating the outliers with the developer of the system, we confirmed that
some outliers indicate actual faults in the system. For example, our method
detected failures of mutual exclusion in the control system that were unknown
to the developer. Our method also detected transient losses of functionalities
and unexpected reboots. On the other hand, our method did not detect anomalies
that were too many and similar. In addition, our method reported rare but
unproblematic concurrent combinations of operations as anomalies. Thus, our
approach is effective at finding anomalies, but there is still room for
improvement
On the Metric Temporal Logic for Continuous Stochastic Processes
In this paper, we prove measurability of event for which a general
continuous-time stochastic process satisfies continuous-time Metric Temporal
Logic (MTL) formula. Continuous-time MTL can define temporal constrains for
physical system in natural way. Then there are several researches that deal
with probability of continuous MTL semantics for stochastic processes. However,
proving measurability for such events is by no means an obvious task, even
though it is essential. The difficulty comes from the semantics of "until
operator", which is defined by logical sum of uncountably many propositions.
Since it is difficult to prove the measurability of such an event by a
classical measure-theoretic method, we solve it using a theorem in stochastic
analysis used to prove the measurability of hitting times for stochastic
processes. Specifically, we prove the measurability of hitting times using a
profound result of theory of capacity. Next, we provide an example that
illustrates the failure of probability approximation when discretizing the
continuous semantics of MTL formulas with respect to time. Additionally, we
prove that the probability of the discretized semantics converges to that of
the continuous semantics when we impose restrictions on diamond operators to
prevent nesting.Comment: 33 page
Anomaly detection for a water treatment system using unsupervised machine learning
National Research Foundation (NRF) Singapor
Bounded Arithmetic in Free Logic
One of the central open questions in bounded arithmetic is whether Buss'
hierarchy of theories of bounded arithmetic collapses or not. In this paper, we
reformulate Buss' theories using free logic and conjecture that such theories
are easier to handle. To show this, we first prove that Buss' theories prove
consistencies of induction-free fragments of our theories whose formulae have
bounded complexity. Next, we prove that although our theories are based on an
apparently weaker logic, we can interpret theories in Buss' hierarchy by our
theories using a simple translation. Finally, we investigate finitistic G\"odel
sentences in our systems in the hope of proving that a theory in a lower level
of Buss' hierarchy cannot prove consistency of induction-free fragments of our
theories whose formulae have higher complexity