Profile of Digital Literacy Skills of Class IX Students on Online Learning Mathematics

This study aims to determine the profile of digital literacy skills possessed by students in online learning mathematics. This research is a quantitative study. The subjects in this study were students of 9th Grade Imam Syafi'i Junior High School Batam, which may amount to 30 students. The data technique used was a questionnaire, with descriptive data analysis. Based on the research results, it can be seen that the level of digital literacy skills possessed by students is 80% and is in the good category. Where the skill level of each digital literacy indicator, namely internet search skills, was 86% in the very good category, while the hypertext direction guideline skills were 73%, information content evaluation was 82%, and knowledge compilation skills were 82%, the total was in the good category. Furthermore, the results also showed that the most ICT devices used by students in accessing the internet were smartphones 21 students, with 22 students private ownership. The purpose of most students in accessing the internet was to find information 14 students, and the most students accessed in using the internet were academic content 14 students.

Properties of Switch-List Representations of Boolean Functions

In this paper, we focus on a less usual way to represent Boolean functions, namely on representations by switch-lists, which are closely related to interval representations. Given a truth table representation of a Boolean function f the switch-list representation of f is a list of Boolean vectors from the truth table which have a different function value than the preceding Boolean vector in the truth table. The main aim of this paper is to include this type of representation in the Knowledge Compilation Map by Darwiche and Marquis and to argue that switch-lists may in certain situations constitute a reasonable choice for a target language in knowledge compilation. First, we compare switch-list representations with a number of standard representations (such as CNF, DNF, and OBDD) with respect to their relative succinctness. As a by-product of this analysis, we also give a short proof of a longstanding open question proposed by Darwiche and Marquis, namely the incomparability of MODS (models) and PI (prime implicates) representations. Next, using the succinctness result between switch-lists and OBDDs, we develop a polynomial time compilation algorithm from switch-lists to OBDDs. Finally, we analyze which standard transformations and queries (those considered by Darwiche and Marquis) can be performed in polynomial time with respect to the size of the input if the input knowledge is represented by a switch-list. We show that this collection is very broad and the combination of polynomial time transformations and queries is quite unique. Some of the queries can be answered directly using the switch-list input, others require a compilation of the input to OBDD representations which are then used to answer the queries.

Explanatory Diagnosis of Discrete-Event Systems with Temporal Information and Smart Knowledge-Compilation

Model-based diagnosis is typically set-oriented. In static systems, such as combinational circuits, a candidate (or diagnosis) is a set of faulty components that explains a set of observations. In discrete-event systems (DESs), a candidate is a set of faulty events occurring in a sequence of state changes that conforms with a sequence of observations. Invariably, a candidate is a set. This set-oriented perspective makes diagnosis of DESs narrow in explainability, owing to the lack of any temporal knowledge relevant to the faults within a candidate, along with the inability to discriminate between single and multiple occurrences of the same fault. Embedding temporal knowledge in a candidate, such as the relative temporal ordering of faults and the multiplicity of the same fault, may be essential for critical decision making. To favor explainability, the notions of temporal fault, explanation, and explainer are introduced in diagnosis of DESs. The explanation engine reacts to a given sequence of observations by generating and refining in real-time a sequence of regular expressions, where the language of each expression is a set of temporal faults. Moreover, to avoid total knowledge compilation, the explainer can be generated incrementally either offline, based on meaningful behavioral scenarios, or online, when being operated in solving specific diagnosis problems.

On Tractable XAI Queries based on Compiled Representations

One of the key purposes of eXplainable AI (XAI) is to develop techniques for understanding predictions made by Machine Learning (ML) models and for assessing how much reliable they are. Several encoding schemas have recently been pointed out, showing how ML classifiers of various types can be mapped to Boolean circuits exhibiting the same input-output behaviours. Thanks to such mappings, XAI queries about classifiers can be delegated to the corresponding circuits. In this paper, we define new explanation and/or verification queries about classifiers. We show how they can be addressed by combining queries and transformations about the associated Boolean circuits. Taking advantage of previous results from the knowledge compilation map, this allows us to identify a number of XAI queries that are tractable provided that the circuit has been first turned into a compiled representation.

Switch-List Representations in a Knowledge Compilation Map

In this paper we focus on a less usual way to represent Boolean functions, namely on representations by switch-lists. Given a truth table representation of a Boolean function f the switch-list representation (SLR) of f is a list of Boolean vectors from the truth table which have a different function value than the preceding Boolean vector in the truth table. The main aim of this paper is to include the language SL of all SLR in the Knowledge Compilation Map [Darwiche and Marquis, 2002] and to argue, that SL may in certain situations constitute a reasonable choice for a target language in knowledge compilation. First we compare SL with a number of standard representation languages (such as CNF, DNF, and OBDD) with respect to their relative succinctness. As a by-product of this analysis we also give a short proof of a long standing open question from [Darwiche and Marquis, 2002], namely the incomparability of MODS (models) and PI (prime implicates) languages. Next we analyze which standard transformations and queries (those considered in [Darwiche and Marquis, 2002] can be performed in poly-time with respect to the size of the input SLR. We show that this collection is quite broad and the combination of poly-time transformations and queries is quite unique.

Lower Bounds for Approximate Knowledge Compilation

Knowledge compilation studies the trade-off between succinctness and efficiency of different representation languages. For many languages, there are known strong lower bounds on the representation size, but recent work shows that, for some languages, one can bypass these bounds using approximate compilation. The idea is to compile an approximation of the knowledge for which the number of errors can be controlled. We focus on circuits in deterministic decomposable negation normal form (d-DNNF), a compilation language suitable in contexts such as probabilistic reasoning, as it supports efficient model counting and probabilistic inference. Moreover, there are known size lower bounds for d-DNNF which by relaxing to approximation one might be able to avoid. In this paper we formalize two notions of approximation: weak approximation which has been studied before in the decision diagram literature and strong approximation which has been used in recent algorithmic results. We then show lower bounds for approximation by d-DNNF, complementing the positive results from the literature.