相关论文: n-Valued Refined Neutrosophic Logic and Its Applic…

The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal…

The article discusses some applications of fuzzy logic ideas to formalizing of the Case-Based Reasoning (CBR) process and to measuring the effectiveness of CBR systems

A presentation is provided of the basic notions and operations of a) the propositional calculus of a variant of fuzzy logic -- canonical fuzzy logic, CFL -- and in a more succinct and introductory way, of b) the theory of fuzzy sets…

Let function $f$ be normalized, analytic and univalent in the unit disk ${\mathbb D}=\{z:|z|<1\}$ and $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. Using a method based on Grusky coefficients we study several problems over that class of univalent…

Humans have the ability to seamlessly combine low-level visual input with high-level symbolic reasoning often in the form of recognising objects, learning relations between them and applying rules. Neuro-symbolic systems aim to bring a…

We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the (n+1)-valued Kripke models and a corresponding language based on a modal extension of {\L}ukasiewicz many-valued…

This paper explores the integration of symbolic logic knowledge into deep neural networks for learning from noisy crowd labels. We introduce Logic-guided Learning from Noisy Crowd Labels (Logic-LNCL), an EM-alike iterative logic knowledge…

This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…

We briefly introduce noise-based logic. After describing the main motivations we outline classical, instantaneous (squeezed and non-squeezed), continuum, spike and random-telegraph-signal based schemes with applications such as circuits…

This work describes a methodology to combine logic-based systems and connectionist systems. Our approach uses finite truth valued {\L}ukasiewicz logic, where we take advantage of fact what in this type of logics every connective can be…

Combining symbolic and neural approaches has gained considerable attention in the AI community, as it is often argued that the strengths and weaknesses of these approaches are complementary. One such trend in the literature are weakly…

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to…

In this book, for the first time we introduce the notion of neutrosophic algebraic structures for groups, loops, semigroups and groupoids; and also their neutrosophic N-algebraic structures. One is fully aware of the fact that many…

To deal with uncertainty in reasoning, interval-valued logic has been developed. But uniform intervals cannot capture the difference in degrees of belief for different values in the interval. To salvage the problem triangular and…

Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the…

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;…

We introduce two-dimensional logics based on \L{}ukasiewicz and G\"{o}del logics to formalize paraconsistent fuzzy reasoning. The logics are interpreted on matrices, where the common underlying structure is the bi-lattice (twisted) product…

Most fuzzy systems including fuzzy decision support and fuzzy control systems provide out-puts in the form of fuzzy sets that represent the inferred conclusions. Linguistic interpretation of such outputs often involves the use of linguistic…

We contribute a theoretical and operational framework for neurosymbolic AI called DeepLog. DeepLog introduces building blocks and primitives for neurosymbolic AI that make abstraction of commonly used representations and computational…

Modern applications combine information from a great variety of sources. Oftentimes, some of these sources, like Machine-Learning systems, are not strictly binary but associated with some degree of (lack of) confidence in the observation.…