The purpose of this study was to explore the electroencephalogram (EEG) features sensitive to situation awareness (SA) and then classify SA levels. Forty-eight participants were recruited to complete an SA standard test based on the multi-attribute task battery (MATB) II, and the corresponding EEG data and situation awareness global assessment technology (SAGAT) scores were recorded. The population with the top 25% of SAGAT scores was selected as the high-SA level (HSL) group, and the bottom 25% was the low-SA level (LSL) group. The results showed that (1) for the relative power of $\beta$1 (16–20Hz), $\beta$2 (20–24Hz) and $\beta$3 (24–30Hz), repeated measures analysis of variance (ANOVA) in three brain regions (Central Central-Parietal, and Parietal) × three brain lateralities (left, midline, and right) × two SA groups (HSL and LSL) showed a significant main effect for SA groups; post hoc comparisons revealed that compared with LSL, the above features of HSL were higher. (2) for most ratio features associated with $\beta$1 ∼ $\beta$3, ANOVA also revealed a main effect for SA groups. (3) EEG features sensitive to SA were selected to classify SA levels with small-sample data based on the general supervised machine learning classifiers. Five-fold cross-validation results showed that among the models with easy interpretability, logistic regression (LR) and decision tree (DT) presented the highest accuracy (both 92%), while among the models with hard interpretability, the accuracy of random forest (RF) was 88.8%, followed by an artificial neural network (ANN) of 84%. The above results suggested that (1) the relative power of $\beta$1 ∼ $\beta$3 and their associated ratios were sensitive to changes in SA levels; (2) the general supervised machine learning models all exhibited good accuracy (greater than 75%); and (3) furthermore, LR and DT are recommended by combining the interpretability and accuracy of the models.

Human gait trajectory prediction is a long-standing research topic in human–machine interaction. However, there are two shortcomings in the current gait trajectory prediction technology. The first shortcoming is that the neural network model of gait prediction only predicts dozens of future time frames of gait trajectory. The second shortcoming is that the gait prediction neural network model is uninterpretable. We propose the Interpretable-Concatenation former (IC-former) model, which can predict long-term gait trajectories and explain the prediction results by quantifying the importance of data at different positions in the input sequence. Experiments prove that the IC-former model we proposed not only makes a breakthrough in prediction accuracy but also successfully explains the data basis of the prediction.

Elementary first-order theories of trees allowing at most, exactly $\mathrm{m}$, and any finite number of immediate descendants are introduced and proved mutually interpretable among themselves and with Robinson arithmetic, Adjunctive Set Theory with Extensionality and other well-known weak theories of numbers, sets, and strings.

Kristiansen and Murwanashyaka recently proved that Robinson arithmetic, Q, is interpretable in an elementary theory of full binary trees, T. We prove that, conversely, T is interpretable in Q by producing a formal interpretation of T in an elementary concatenation theory QT+, thereby also establishing mutual interpretability of T with several well-known weak essentially undecidable theories of numbers, strings, and sets. We also introduce a “hybrid” elementary theory of strings and trees, WQT*, and establish its mutual interpretability with Robinson’s weak arithmetic R, the weak theory of trees WT of Kristiansen and Murwanashyaka, and the weak concatenation theory WTCε of Higuchi and Horihata.

Like a hydra, fraudsters adapt and circumvent increasingly sophisticated barriers erected by public or private institutions. Among these institutions, banks must quickly take measures to avoid losses while guaranteeing the satisfaction of law-abiding customers. Facing an expanding flow of operations, effective banking relies on data analytics to support established risk control processes, but also on a better understanding of the underlying fraud mechanism. In addition, fraud being a criminal offence, the evidential aspect of the process must also be considered. These legal, operational, and strategic constraints lead to compromises on the means to be implemented for fraud management. This paper first focuses on the translation of practical questions raised in the banking industry at each step of the fraud management process into performance evaluation required to design a fraud detection model. Secondly, it considers a range of machine learning approaches that address these specificities: the imbalance between fraudulent and nonfraudulent operations, the lack of fully trusted labels, the concept-drift phenomenon, and the unavoidable trade-off between accuracy and interpretability of detection. This state-of-the-art review sheds some light on a technology race between black box machine learning models improved by post-hoc interpretation and intrinsic interpretable models boosted to gain accuracy. Finally, it discusses how concrete and promising hybrid approaches can provide pragmatic, short-term answers to banks and policy makers without swallowing up stakeholders with economical and ethical stakes in this technological race.

A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz hierarchy. In particular, it is proved that the classes of truth-equational and assertional logics are meet-prime in the Leibniz hierarchy, while the classes of protoalgebraic and equivalential logics are meet-reducible. However, the last two classes are shown to be determined by Leibniz conditions consisting of meet-prime logics only.

A notion of interpretation between arbitrary logics is introduced, and the poset $\mathsf {Log}$ of all logics ordered under interpretability is studied. It is shown that in $\mathsf {Log}$ infima of arbitrarily large sets exist, but binary suprema in general do not. On the other hand, the existence of suprema of sets of equivalential logics is established. The relations between $\mathsf {Log}$ and the lattice of interpretability types of varieties are investigated.

We investigate which part of Brouwer’s Intuitionistic Mathematics is finitistically justifiable or guaranteed in Hilbert’s Finitism, in the same way as similar investigations on Classical Mathematics (i.e., which part is equiconsistent with $\textbf {PRA}$ or consistent provably in $\textbf {PRA}$ ) already done quite extensively in proof theory and reverse mathematics. While we already knew a contrast from the classical situation concerning the continuity principle, more contrasts turn out: we show that several principles are finitistically justifiable or guaranteed which are classically not. Among them are: (i) fan theorem for decidable fans but arbitrary bars; (ii) continuity principle and the axiom of choice both for arbitrary formulae; and (iii) $\Sigma _2$ induction and dependent choice. We also show that Markov’s principle MP does not change this situation; that neither does lesser limited principle of omniscience LLPO (except the choice along functions); but that limited principle of omniscience LPO makes the situation completely classical.

As a ubiquitous method in natural language processing, word embeddings are extensively employed to map semantic properties of words into a dense vector representation. They capture semantic and syntactic relations among words, but the vectors corresponding to the words are only meaningful relative to each other. Neither the vector nor its dimensions have any absolute, interpretable meaning. We introduce an additive modification to the objective function of the embedding learning algorithm that encourages the embedding vectors of words that are semantically related to a predefined concept to take larger values along a specified dimension, while leaving the original semantic learning mechanism mostly unaffected. In other words, we align words that are already determined to be related, along predefined concepts. Therefore, we impart interpretability to the word embedding by assigning meaning to its vector dimensions. The predefined concepts are derived from an external lexical resource, which in this paper is chosen as Roget’s Thesaurus. We observe that alignment along the chosen concepts is not limited to words in the thesaurus and extends to other related words as well. We quantify the extent of interpretability and assignment of meaning from our experimental results. Manual human evaluation results have also been presented to further verify that the proposed method increases interpretability. We also demonstrate the preservation of semantic coherence of the resulting vector space using word-analogy/word-similarity tests and a downstream task. These tests show that the interpretability-imparted word embeddings that are obtained by the proposed framework do not sacrifice performances in common benchmark tests.

In a recent article, Barrett & Halvorson (2016) define a notion of equivalence for first-order theories, which they call “Morita equivalence.” To argue that Morita equivalence is a reasonable measure of “theoretical equivalence,” they make use of the claim that Morita extensions “say no more” than the theories they are extending. The goal of this article is to challenge this central claim by raising objections to their argument for it and by showing why there is good reason to think that the claim itself is false. In light of these criticisms, this article develops a natural way for the advocate of Morita equivalence to respond. I prove that this response makes her criterion a special case of bi-interpretability, an already well-established barometer of theoretical equivalence. I conclude by providing reasons why the advocate of Morita equivalence should opt for a notion of theoretical equivalence that is defined in terms of interpretability rather than Morita extensions.

The Empirical Methods in Natural Language Processing (EMNLP) 2018 workshop BlackboxNLP was dedicated to resources and techniques specifically developed for analyzing and understanding the inner-workings and representations acquired by neural models of language. Approaches included: systematic manipulation of input to neural networks and investigating the impact on their performance, testing whether interpretable knowledge can be decoded from intermediate representations acquired by neural networks, proposing modifications to neural network architectures to make their knowledge state or generated output more explainable, and examining the performance of networks on simplified or formal languages. Here we review a number of representative studies in each category.

This paper explores the relationship borne by the traditional paradoxes of set theory and semantics to formal incompleteness phenomena. A central tool is the application of the Arithmetized Completeness Theorem to systems of second-order arithmetic and set theory in which various “paradoxical notions” for first-order languages can be formalized. I will first discuss the setting in which this result was originally presented by Hilbert & Bernays (1939) and also how it was later adapted by Kreisel (1950) and Wang (1955) in order to obtain formal undecidability results. A generalization of this method will then be presented whereby Russell’s paradox, a variant of Mirimanoff’s paradox, the Liar, and the Grelling–Nelson paradox may be uniformly transformed into incompleteness theorems. Some additional observations are then framed relating these results to the unification of the set theoretic and semantic paradoxes, the intensionality of arithmetization (in the sense of Feferman, 1960), and axiomatic theories of truth.

In this paper, we study finitely axiomatizable conservative extensions of a theory U in the case where U is recursively enumerable and not finitely axiomatizable. Stanisław Krajewski posed the question whether there are minimal conservative extensions of this sort. We answer this question negatively.

Consider a finite expansion of the signature of U that contains at least one predicate symbol of arity ≥ 2. We show that, for any finite extension α of U in the expanded language that is conservative over U, there is a conservative extension β of U in the expanded language, such that $\alpha \vdash \beta$ and $\beta \not \vdash \alpha$. The result is preserved when we consider either extensions or model-conservative extensions of U instead of conservative extensions. Moreover, the result is preserved when we replace $\dashv$ as ordering on the finitely axiomatized extensions in the expanded language by a relevant kind of interpretability, to wit interpretability that identically translates the symbols of the U-language.

We show that the result fails when we consider an expansion with only unary predicate symbols for conservative extensions of U ordered by interpretability that preserves the symbols of U.

An elementary theory of concatenation, QT+, is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, quantifier-free part of Kirby’s finitary set theory, and Adjunctive Set Theory, with or without extensionality. The most basic arithmetic and simplest set theory thus turn out to be variants of string theory.

One way to study and understand the notion of truth is to examine principles that we are willing to associate with truth, often because they conform to a pre-theoretical or to a semi-formal characterization of this concept. In comparing different collections of such principles, one requires formally precise notions of inter-theoretic reduction that are also adequate to compare these conceptual aspects. In this work I study possible ways to make precise the relation of conceptual equivalence between notions of truth associated with collections of principles of truth. In doing so, I will consider refinements and strengthenings of the notion of relative truth-definability proposed by Fujimoto (2010): in particular I employ suitable variants of notions of equivalence of theories considered in Visser (2006) and Friedman & Visser (2014) to show that there are better candidates than mutual truth-definability for the role of sufficient condition for conceptual equivalence between the semantic notions associated with the theories. In the concluding part of the paper, I extend the techniques introduced in the first and show that there is a precise sense in which ramified truth (either disquotational or compositional) does not correspond to iterations of comprehension.

The objective of this article is to characterise elimination of finite generalised imaginaries as defined in [9] in terms of group cohomology. As an application, I consider series of Zariski geometries constructed [10, 23, 24] by Hrushovski and Zilber and indicate how their nondefinability in algebraically closed fields is connected to eliminability of certain generalised imaginaries.

This paper develops the very basic notions of analysis in a weak second-order theory of arithmetic BTFA whose provably total functions are the polynomial time computable functions. We formalize within BTFA the real number system and the notion of a continuous real function of a real variable. The theory BTFA is able to prove the intermediate value theorem, wherefore it follows that the system of real numbers is a real closed ordered field. In the last section of the paper, we show how to interpret the theory BTFA in Robinson's theory of arithmetic Q. This fact entails that the elementary theory of the real closed ordered fields is interpretable in Q.