Related papers: {\L}ukasiewicz Logic with Actions for Neural Netwo…
Modal logics for reasoning about the power of coalitions capture the notion of effectivity functions associated with game forms. The main goal of coalition logics is to provide formal tools for modeling the dynamics of a game frame whose…
The implementation of analog neural network and online analog learning circuits based on memristive crossbar has been intensively explored in recent years. The implementation of various activation functions is important, especially for deep…
The human reasoning process is seldom a one-way process from an input leading to an output. Instead, it often involves a systematic deduction by ruling out other possible outcomes as a self-checking mechanism. In this paper, we describe the…
Logic Tensor Networks (LTN) is a Neuro-Symbolic framework that effectively incorporates deep learning and logical reasoning. In particular, LTN allows defining a logical knowledge base and using it as the objective of a neural model. This…
Pooling operations, which can be calculated at low cost and serve as a linear or nonlinear transfer function for data reduction, are found in almost every modern neural network. Countless modern approaches have already tackled replacing the…
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…
In this paper, we present a gradient-free approach for training multi-layered neural networks based upon quantum perceptrons. Here, we depart from the classical perceptron and the elemental operations on quantum bits, i.e. qubits, so as to…
In 1929 Jan Lukasiewicz used, apparently for the first time, his Polish notation to represent the operations of formal logic. This is a parenthesis-free notation, which also implies that logical functions are operators preceding the…
This article studies (multilayer perceptron) neural networks with an emphasis on the transformations involved --- both forward and backward --- in order to develop a semantical/logical perspective that is in line with standard program…
A learning algorithm for multilayer perceptrons is presented which is based on finding the principal components of a correlation matrix computed from the example inputs and their target outputs. For large networks our procedure needs far…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
In this paper we introduce the convex fragment of {\L}ukasiewicz Logic and discuss its possible applications in different learning schemes. Indeed, the provided theoretical results are highly general, because they can be exploited in any…
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…
The paper explores properties of {\L}ukasiewicz mu-calculus, a version of the quantitative/probabilistic modal mu-calculus containing both weak and strong conjunctions and disjunctions from {\L}ukasiewicz (fuzzy) logic. We show that this…
The current state-of-the-art in many natural language processing and automated knowledge base completion tasks is held by representation learning methods which learn distributed vector representations of symbols via gradient-based…
The paper discusses the capabilities of multilayer perceptron neural networks implementing metric recognition methods, for which the values of the weights are calculated analytically by formulas. Comparative experiments in training a neural…
Majority of research in learning based methods has been towards designing and training networks for specific tasks. However, many of the learning based tasks, across modalities, share commonalities and could be potentially tackled in a…
Artificial Intelligence agents are required to learn from their surroundings and to reason about the knowledge that has been learned in order to make decisions. While state-of-the-art learning from data typically uses sub-symbolic…
Combining neural networks with continuous logic and multicriteria decision making tools can reduce the black box nature of neural models. In this study, we show that nilpotent logical systems offer an appropriate mathematical framework for…
The paper explores properties of the {\L}ukasiewicz {\mu}-calculus, or {\L}{\mu} for short, an extension of {\L}ukasiewicz logic with scalar multiplication and least and greatest fixed-point operators (for monotone formulas). We observe…