Computational Complexity of Strong Admissibility for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments arecalled semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. Recently, the notion of strong admissibility has been introduced for ADFs. In the current work we study the computational complexityof the following reasoning tasks under strong admissibility semantics. We address 1. the credulous/skeptical decision problem; 2. the verification problem; 3. the strong justification problem; and 4. the problem of finding a smallest witness of strong justification of a queried argument

Neutrosophic SuperHyperAlgebra and New Types of Topologies

In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P2(S) } and so on. That’s why the n-th PowerSet of a Set S { defined recursively and denoted by Pn(S) = P(Pn-1(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world. The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

Quadruple Neutrosophic Theory And Applications Volume I

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Smarandache introduce for the first time the neutrosophic quadruple numbers (of the form + + + ) and the refined neutrosophic quadruple numbers

The Road to General Intelligence

Humans have always dreamed of automating laborious physical and intellectual tasks, but the latter has proved more elusive than naively suspected. Seven decades of systematic study of Artificial Intelligence have witnessed cycles of hubris and despair. The successful realization of General Intelligence (evidenced by the kind of cross-domain flexibility enjoyed by humans) will spawn an industry worth billions and transform the range of viable automation tasks.The recent notable successes of Machine Learning has lead to conjecture that it might be the appropriate technology for delivering General Intelligence. In this book, we argue that the framework of machine learning is fundamentally at odds with any reasonable notion of intelligence and that essential insights from previous decades of AI research are being forgotten. We claim that a fundamental change in perspective is required, mirroring that which took place in the philosophy of science in the mid 20th century. We propose a framework for General Intelligence, together with a reference architecture that emphasizes the need for anytime bounded rationality and a situated denotational semantics. We given necessary emphasis to compositional reasoning, with the required compositionality being provided via principled symbolic-numeric inference mechanisms based on universal constructions from category theory. • Details the pragmatic requirements for real-world General Intelligence. • Describes how machine learning fails to meet these requirements. • Provides a philosophical basis for the proposed approach. • Provides mathematical detail for a reference architecture. • Describes a research program intended to address issues of concern in contemporary AI. The book includes an extensive bibliography, with ~400 entries covering the history of AI and many related areas of computer science and mathematics.The target audience is the entire gamut of Artificial Intelligence/Machine Learning researchers and industrial practitioners. There are a mixture of descriptive and rigorous sections, according to the nature of the topic. Undergraduate mathematics is in general sufficient. Familiarity with category theory is advantageous for a complete understanding of the more advanced sections, but these may be skipped by the reader who desires an overall picture of the essential concepts This is an open access book