Related papers: Symbolic Neutrosophic Theory
Artificial Intelligence (AI) is a powerful new language of science as evidenced by recent Nobel Prizes in chemistry and physics that recognized contributions to AI applied to those areas. Yet, this new language lacks semantics, which makes…
In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of T-norms/T-conorms in fuzzy logic and set. Also, as an extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic Topologies.
This paper presents NEUROSPF, a tool for the symbolic analysis of neural networks. Given a trained neural network model, the tool extracts the architecture and model parameters and translates them into a Java representation that is amenable…
Neurosymbolic AI is an increasingly active area of research that combines symbolic reasoning methods with deep learning to leverage their complementary benefits. As knowledge graphs are becoming a popular way to represent heterogeneous and…
Subatomic systems were recently introduced to identify the structural principles underpinning the normalization of proofs. "Subatomic" means that we can reformulate logical systems in accordance with two principles. Their atomic formulas…
In this paper we generalize the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Several examples are presented. Also, a geometric interpretation of the Neutrosophic Set is given using…
We show how fundamental ideas from signal processing, multiscale theory and wavelets may be applied to non-linear dynamics. The problems from dynamics include iterated function systems (IFS), dynamical systems based on substitution such as…
A key objective in the field of artificial intelligence is to develop cognitive models that can exhibit human-like intellectual capabilities. One promising approach to achieving this is through neural-symbolic systems, which combine the…
Error: Peer-review process exposed an error in Theorem 1 that, unfourtunately, is not repairable. Idempotent semigroups are always finite. See Green and Rees [1952], Siekmann and Szab\'o [1981] for details Anti-unification is a fundamental…
In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…
Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of…
To improve the explainability of leading Transformer networks used in NLP, it is important to tease apart genuine symbolic rules from merely associative input-output patterns. However, we identify several inconsistencies in how…
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
To handle AI tasks that combine perception and logical reasoning, recent work introduces Neurosymbolic Deep Neural Networks (NS-DNNs), which contain -- in addition to traditional neural layers -- symbolic layers: symbolic expressions (e.g.,…
In this paper titled A Symbolic Approach for Counterfactual Explanations we propose a novel symbolic approach to provide counterfactual explanations for a classifier predictions. Contrary to most explanation approaches where the goal is to…
The field of neuro-symbolic AI aims to benefit from the combination of neural networks and symbolic systems. A cornerstone of the field is the translation or encoding of symbolic knowledge into neural networks. Although many neuro-symbolic…
In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…
Binary semirings such as the tropical, log, and probability semirings form a core algebraic tool in classical and modern neural inference systems, supporting tasks like Viterbi decoding, dynamic programming, and probabilistic reasoning.…
We present a procedure which allows us to recover classical and nonclassical logical structures as \emph{concrete logics} associated with physical theories expressed by means of classical languages. This procedure consists in choosing, for…
Despite the extensive investment and impressive recent progress at reasoning by similarity, deep learning continues to struggle with more complex forms of reasoning such as non-monotonic and commonsense reasoning. Non-monotonicity is a…