Related papers: A New Connective in Natural Deduction, and its App…
We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a…
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…
Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles' heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We…
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…
We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…
We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…
Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…
Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke (NAND) and Peirce's…
I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction…
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…
This work describes a methodology that combines logic-based systems and connectionist systems. Our approach uses finite truth-valued {\L}ukasiewicz logic, wherein every connective can be defined by a neuron in an artificial network. This…
Reynold's parametricity theory captures the property that parametrically polymorphic functions behave uniformly: they produce related results on related instantiations. In dependently-typed programming languages, such relations and…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
Starting from a simple estimation problem, here we propose a general approach for decoding quantum measurements from the perspective of information extraction. By virtue of the estimation fidelity only, we provide surprisingly simple…
The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…
This paper presents a novel explanation of the cause of quantum probabilities and the Born rule based on the intuitionistic interpretation of quantum mechanics where propositions obey constructive (intuitionistic) logic. The use of…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…