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

Mathematical Foundations of Consciousness

We employ the Zermelo-Fraenkel Axioms that characterize sets as mathematical primitives. The Anti-foundation Axiom plays a significant role in our development, since among other of its features, its replacement for the Axiom of Foundation in the Zermelo-Fraenkel Axioms motivates Platonic interpretations. These interpretations also depend on such allied notions for sets as pictures, graphs, decorations, labelings and various mappings that we use. A syntax and semantics of operators acting on sets is developed. Such features enable construction of a theory of non-well-founded sets that we use to frame mathematical foundations of consciousness. To do this we introduce a supplementary axiomatic system that characterizes experience and consciousness as primitives. The new axioms proceed through characterization of so- called consciousness operators. The Russell operator plays a central role and is shown to be one example of a consciousness operator. Neural networks supply striking examples of non-well-founded graphs the decorations of which generate associated sets, each with a Platonic aspect. Employing our foundations, we show how the supervening of consciousness on its neural correlates in the brain enables the framing of a theory of consciousness by applying appropriate consciousness operators to the generated sets in question

Scaffolding type-2 classifier for incremental learning under concept drifts

© 2016 Elsevier B.V. The proposal of a meta-cognitive learning machine that embodies the three pillars of human learning: what-to-learn, how-to-learn, and when-to-learn, has enriched the landscape of evolving systems. The majority of meta-cognitive learning machines in the literature have not, however, characterized a plug-and-play working principle, and thus require supplementary learning modules to be pre-or post-processed. In addition, they still rely on the type-1 neuron, which has problems of uncertainty. This paper proposes the Scaffolding Type-2 Classifier (ST2Class). ST2Class is a novel meta-cognitive scaffolding classifier that operates completely in local and incremental learning modes. It is built upon a multivariable interval type-2 Fuzzy Neural Network (FNN) which is driven by multivariate Gaussian function in the hidden layer and the non-linear wavelet polynomial in the output layer. The what-to-learn module is created by virtue of a novel active learning scenario termed the uncertainty measure; the how-to-learn module is based on the renowned Schema and Scaffolding theories; and the when-to-learn module uses a standard sample reserved strategy. The viability of ST2Class is numerically benchmarked against state-of-the-art classifiers in 12 data streams, and is statistically validated by thorough statistical tests, in which it achieves high accuracy while retaining low complexity

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