Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Logic Theory Pattern for Linearized Control Systems
62
0
0.0
(
0
)
Added by
EPTCS
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Authors
Andrea Domenici
Ask ChatGPT about the research
No Arabic abstract
This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find constraints on design parameters, with the support of computer-assisted theorem proving. This method contributes to the integration of formal verification methods into the standard model-driven development processes for control systems. The theories obtained through its application comprise a set of assumptions that the system equations must satisfy, and a translation of the equations into the logic language of the Prototype Verification System theorem-proving environment. The method is illustrated with a standard case study from control theory.
rate research
Read More
The high availability and scalability of weakly-consistent systems attracts system designers. Yet, writing correct application code for this type of systems is difficult; even how to specify the intended behavior of such systems is still an open question. There has not been established any standard method to specify the intended dynamic behavior of a weakly consistent system. There exist specifications of various consistency models for distributed and concurrent systems; and the semantics of replicated datatypes like CRDTs have been specified in axiomatic and operational models based on visibility relations. In this paper, we present a temporal logic, EPTL, that is tailored to specify properties of weakly consistent systems. In contrast to LTL and CTL, EPTL takes into account that operations of weakly consistent systems are in many cases not serializable and have to be treated respectively to capture the behavior. We embed our temporal logic in Isabelle/HOL and can thereby leverage strong semi-automatic proving capabilities.
We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside the host language. Our categorical semantics for the host language is standard, and involves cartesian closed categories and monads. We interpret the circuit language not in an ordinary category, but in a category that is enriched in the host category. We show that this structure is also related to linear/non-linear models. As an extended example, we recall an earlier result that the category of W*-algebras is dcpo-enriched, and we use this model to extend the circuit language with some recursive types.
The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other. Left and right algebras over a clone are covariant and contravariant functors from the category to that of sets respectively. In this paper we show that first-order logic can be studied effectively using the notions of right and left algebras over a clone. It is easy to translate the classical treatment of logic into our setting and prove all the fundamental theorems of first-order theory algebraically.
We consider the pressing question of how to model, verify, and ensure that autonomous systems meet certain textit{obligations} (like the obligation to respect traffic laws), and refrain from impermissible behavior (like recklessly changing lanes). Temporal logics are heavily used in autonomous system design; however, as we illustrate here, temporal (alethic) logics alone are inappropriate for reasoning about obligations of autonomous systems. This paper proposes the use of Dominance Act Utilitarianism (DAU), a deontic logic of agency, to encode and reason about obligations of autonomous systems. We use DAU to analyze Intels Responsibility-Sensitive Safety (RSS) proposal as a real-world case study. We demonstrate that DAU can express well-posed RSS rules, formally derive undesirable consequences of these rules, illustrate how DAU could help design systems that have specific obligations, and how to model-check DAU obligations.
We propose a model of the substructural logic of Bunched Implications (BI) that is suitable for reasoning about quantum states. In our model, the separating conjunction of BI describes separable quantum states. We develop a program logic where pre- and post-conditions are BI formulas describing quantum states -- the program logic can be seen as a counterpart of separation logic for imperative quantum programs. We exercise the logic for proving the security of quantum one-time pad and secret sharing, and we show how the program logic can be used to discover a flaw in Google Cirqs tutorial on the Variational Quantum Algorithm (VQA).
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
