Related papers: Quantitative Separation Logic - A Logic for Reason…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
A first-order conditional logic is considered, with semantics given by a variant of epsilon-semantics, where p -> q means that Pr(q | p) approaches 1 super-polynomially --faster than any inverse polynomial. This type of convergence is…
Separation Logic (SL) is a well-known assertion language used in Hoare-style modular proof systems for programs with dynamically allocated data structures. In this paper we investigate the fragment of first-order SL restricted to the…
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
Classical planning asks for a sequence of operators reaching a given goal. While the most common case is to compute a plan, many scenarios require more than that. However, quantitative reasoning on the plan space remains mostly unexplored.…
The main contribution of this paper is the introduction of a dynamic logic formalism for reasoning about information flow in composite quantum systems. This builds on our previous work on a complete quantum dynamic logic for single systems.…
We investigate an unsuspected connection between logical connectives with non-harmonious deduction rules, such as Prior's tonk, and quantum computing. We argue that these connectives model the information-erasure, the non-reversibility, and…
Many important functional and security properties--including non-interference, determinism, and generalized non-interference (GNI)--are hyperproperties, i.e., properties relating multiple executions of a program. Existing separation logics…
Lawvere showed that generalised metric spaces are categories enriched over $[0, \infty]$, the quantale of the positive extended reals. The statement of enrichment is a quantitative analogue of being a preorder. Towards seeking a logic for…
We have proposed in several recent papers a critical view of some parts of quantum mechanics (QM) that is methodologically unusual because it rests on analysing the language of QM by using some elementary but fundamental tools of…
We apply the notion of quantum predicate proposed by D'Hondt and Panangaden to analyze a purely quantum language fragment which describes the quantum part of a future quantum computer in Knill's architecture. The denotational semantics,…
Probabilistic couplings are the foundation for many probabilistic relational program logics and arise when relating random sampling statements across two programs. In relational program logics, this manifests as dedicated coupling rules…
The list segment predicate ls used in separation logic for verifying programs with pointers is well-suited to express properties on singly-linked lists. We study the effects of adding ls to the full quantifier-free separation logic with the…
Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…
We present a logic for reasoning about pairs of interactive quantum programs - quantum relational Hoare logic (qRHL). This logic follows the spirit of probabilistic relational Hoare logic (Barthe et al. 2009) and allows us to formulate how…
The quantum logical `or' is analyzed from a physical perspective. We show that it is the existence of EPR-like correlation states for the quantum mechanical entity under consideration that make it nonequivalent to the classical situation.…
Existing work on theorem proving for the assertion language of separation logic (SL) either focuses on abstract semantics which are not readily available in most applications of program verification, or on concrete models for which…
In order to reason about effects, we can define quantitative formulas to describe behavioural aspects of effectful programs. These formulas can for example express probabilities that (or sets of correct starting states for which) a program…
Verifying fine-grained optimistic concurrent programs remains an open problem. Modern program logics provide abstraction mechanisms and compositional reasoning principles to deal with the inherent complexity. However, their use is mostly…