Related papers: Symbolic Neutrosophic Theory
We introduce the concept of a \textbf{neuro-symbolic pair} -- neural and symbolic approaches that are linked through a common knowledge representation. Next, we present \textbf{taxonomic networks}, a type of discrimination network in which…
This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a…
We give a precise definition of a formal mathematical object as any symbol for an individual constant, predicate letter, or a function letter that can be introduced through definition into a formal mathematical language without inviting…
Initial Semantics aims at interpreting the syntax associated to a signature as the initial object of some category of 'models', yielding induction and recursion principles for abstract syntax. Zsid\'o proves an initiality result for…
In this paper, we present a generalization of the relational data model based on interval neutrosophic set. Our data model is capable of manipulating incomplete as well as inconsistent information. Fuzzy relation or intuitionistic fuzzy…
A new symbol theory for pseudodifferential operators in the complex analytic category is given. This theory provides a cohomological foundation of symbolic calculus.
Neurosymbolic (NeSy) AI studies the integration of neural networks (NNs) and symbolic reasoning based on logic. Usually, NeSy techniques focus on learning the neural, probabilistic and/or fuzzy parameters of NeSy models. Learning the…
Similarly to other connectionist models, Graph Neural Networks (GNNs) lack transparency in their decision-making. A number of sub-symbolic approaches have been developed to provide insights into the GNN decision making process. These are…
Symbolic reasoning, rule-based symbol manipulation, is a hallmark of human intelligence. However, rule-based systems have had limited success competing with learning-based systems outside formalized domains such as automated theorem…
In this book, the authors define several new types of soft neutrosophic algebraic structures over neutrosophic algebraic structures and we study their generalizations. These soft neutrosophic algebraic structures are basically parameterized…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
As a core element of culture, images transform perception into structured representations and undergo evolution similar to natural languages. Given that visual input accounts for 60% of human sensory experience, it is natural to ask whether…
One generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic logic (NL). The distinctions between IFL and NL {and the corresponding intuitionistic fuzzy set (IFS) and neutrosophic set (NS) respectively} are…
Neurosymbolic artificial intelligence (AI) is an emerging branch of AI that combines the strengths of symbolic AI and sub-symbolic AI. A major drawback of sub-symbolic AI is that it acts as a "black box", meaning that predictions are…
Symbolic summation as an active research topic of symbolic computation provides efficient algorithmic tools for evaluating and simplifying different types of sums arising from mathematics, computer science, physics and other areas. Most of…
We study the interpretability issue of task-oriented dialogue systems in this paper. Previously, most neural-based task-oriented dialogue systems employ an implicit reasoning strategy that makes the model predictions uninterpretable to…
We present a neurosymbolic approach, i.e., combining symbolic and subsymbolic artificial intelligence, to validating offer documents in regulated public institutions. We employ a language model to extract information and then aggregate with…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
The complete optimal systems of subalgebras of all nonisomorphic three- and four-dimensional real Lie algebras are analyzed by the program \symbolie running in the computer algebra system \emph{Wolfram Mathematica}\texttrademark. The…
Thirty-three new definitions are presented, derived from neutrosophic set, neutrosophic probability, neutrosophic statistics, and neutrosophic logic. Each one is independent, short, with references and cross references like in a dictionary…