Related papers: On Logic Gates with Complex Numbers

We offer an alternative to the conventional network formulation of quantum computing. We advance the analog approach to quantum logic gate/circuit construction. As an illustration, we consider the spatially extended NOT gate as the first…

Logic programming is sometimes described as relational programming: a paradigm in which the programmer specifies and composes n-ary relations using systems of constraints. An advanced logic programming environment will provide tools that…

Explaining neural network computation in terms of probabilistic/fuzzy logical operations has attracted much attention due to its simplicity and high interpretability. Different choices of logical operators such as AND, OR and XOR give rise…

We consider a simple extension of logic programming where variables may range over goals and goals may be arguments of predicates. In this language we can write logic programs which use goals as data. We give practical evidence that, by…

Landauer's principle places a fundamental lower limit on the work required to perform a logically irreversible operation. Logically reversible gates provide a way to avoid these work costs, and also simplify the task of making the…

This article exhibits a particular encoding of logic circuits into a sheaf formalism. The central result of this article is that there exists strictly more information available to a circuit designer in this setting than exists in static…

Temporal logics are an obvious high-level descriptive companion formalism to dynamical systems which model behavior as deterministic evolution of state over time. A wide variety of distinct temporal logics applicable to dynamical systems…

Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…

We propose a general architecture for universal logic operations using NAND and NOR gates on classical information encoded in period-doubled states of periodically-driven systems. The protocol involves applying a single pulse that…

We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…

This article is a short review on the concept of information. We show the strong relation between Information Theory and Physics, and the differences between classical and quantum information, with emphasis in their manipulation through…

A rotation-based synthesis framework for reversible logic is proposed. We develop a canonical representation based on binary decision diagrams and introduce operators to manipulate the developed representation model. Furthermore, a…

In this paper we present methods of transition from one perspective on logic to others, and apply this in particular to obtain a coalgebraic presentation of logic. The central ingredient in this process is to view consequence relations as…

Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…

Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with…

Self-sustaining nonlinear oscillators of practically any type can function as latches and registers if Boolean logic states are represented physically as the phase of oscillatory signals. Combinational operations on such phase-encoded logic…

Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed…

We propose an implementation of quantum logic gates via virtual vibrational excitations in an ion trap quantum computer. Transition paths involving unpopulated, vibrational states interfere destructively to eliminate the dependence of rates…