Related papers: On Quantifying Literals in Boolean Logic and Its A…
Recent years have witnessed a renewed interest in Boolean function in explaining binary classifiers in the field of explainable AI (XAI). The standard approach of Boolean function is propositional logic. We present a modal language of a…
In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic…
Fuzzy quantification is a subtopic of fuzzy logic which deals with the modelling of the quantified expressions we can find in natural language. Fuzzy quantifiers have been successfully applied in several fields like fuzzy, control, fuzzy…
The inclusion of universal quantification and a form of implication in goals in logic programming is considered. These additions provide a logical basis for scoping but they also raise new implementation problems. When universal and…
The logic which describes quantum robots is not orthodox quantum logic, but a deductive calculus which reproduces the quantum tasks (computational processes, and actions) taking into account quantum superposition and quantum entanglement. A…
In this paper we show that there is a direct correspondence between quantum Boolean operations and certain forms of classical (non-quantum) logic known as Reed-Muller expansions. This allows us to readily convert Boolean circuits into their…
Quantified constraints over the reals appear in numerous contexts. Usually existential quantification occurs when some parameter can be chosen by the user of a system, and univeral quantification when the exact value of a parameter is…
Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…
Artificial Intelligence (AI) has become an integral part of domains such as security, finance, healthcare, medicine, and criminal justice. Explaining the decisions of AI systems in human terms is a key challenge--due to the high complexity…
We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\alpha), where \alpha is a Boolean variable. Intuitively, with Boolean dependence…
The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform…
We investigate the applicability of the formalism of quantum mechanics to everyday life. It seems to be directly relevant for situations in which the very act of coming to a conclusion or decision on one issue affects one's confidence about…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a…
Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be…
A first-order logic with quantum variables is needed as an assertion language for specifying and reasoning about various properties (e.g. correctness) of quantum programs. Surprisingly, such a logic is missing in the literature, and the…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical…
This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions.…
Quantization enables efficient deployment of large language models (LLMs) in resource-constrained environments by significantly reducing memory and computation costs. While quantized LLMs often maintain performance on perplexity and…