Related papers: Birkhoff-von Neumann Quantum Logic as an Assertion…
To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem…
Reasoning about quantum programs remains a fundamental challenge, regardless of the programming model or computational paradigm. Despite extensive research, existing verification techniques are insufficient -- even for quantum circuits, a…
The model theory of a first-order logic called N^4 is introduced. N^4 does not eliminate double negations, as classical logic does, but instead reduces fourfold negations. N^4 is very close to classical logic: N^4 has two truth values;…
Relying on the formulae-as-types paradigm for classical logic, we define a program logic for an imperative language with higher-order procedural variables and non-local jumps. Then, we show how to derive a sound program logic for this…
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…
We present a new approach to automated reasoning about higher-order programs by endowing symbolic execution with a notion of higher-order, symbolic values. Our approach is sound and relatively complete with respect to a first-order solver…
Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…
This reports introduces a novel sound and complete semantics for first order intuitionistic logic, in the framework of category theory and by the computational interpretation of the logic based on the so-called Curry-Howard isomorphism.…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
A semantic embedding of (constant domain) quantified conditional logic in classical higher-order logic is presented.
We prescribe a choice of 18 variables in all that casts the equations of the fully nonlinear characteristic formulation of general relativity in first--order quasi-linear canonical form. At the analytical level, a formulation of this type…
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.…
Deductive verification techniques based on program logics (i.e., the family of Floyd-Hoare logics) are a powerful approach for program reasoning. Recently, there has been a trend of increasing the expressive power of such logics by…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
Because of the probabilistic/nondeterministic behavior of quantum programs, it is highly advisable to verify them formally to ensure that they correctly implement their specifications. Formal verification, however, also traditionally…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
In this paper, we propose Proq, a runtime assertion scheme for testing and debugging quantum programs on a quantum computer. The predicates in Proq are represented by projections (or equivalently, closed subspaces of the state space),…
Quantum computing is an emerging computational paradigm that leverages the laws of quantum mechanics to perform elementary logic operations. Existing programming models for quantum computing were designed with fault-tolerant hardware in…