Note: This blog should have been named bitwise operator, but yes will correct it after some time. Renaming it now will break the link and will leave many with a a 404 page. Okay, today let's look at Boolean algebra with Julia. In Julia, something true is represented by a constant true and something false is represented by a constant false. These two things are inbuilt in Julia and you can't keep a variable like true 1, Julia will throw an error.

Humans constantly restructure knowledge to use it more efficiently. Our goal is to give a machine learning system similar abilities so that it can learn more efficiently. We introduce the \textit{knowledge refactoring} problem, where the goal is to restructure a learner's knowledge base to reduce its size and to minimise redundancy in it. We focus on inductive logic programming, where the knowledge base is a logic program. We introduce Knorf, a system which solves the refactoring problem using constraint optimisation. We evaluate our approach on two program induction domains: real-world string transformations and building Lego structures. Our experiments show that learning from refactored knowledge can improve predictive accuracies fourfold and reduce learning times by half.

Inductive programming (IP) is a field whose main goal is synthesising programs that respect a set of examples, given some form of background knowledge. This paper is concerned with a subfield of IP, inductive functional programming (IFP). We explore the idea of generating modular functional programs, and how those allow for function reuse, with the aim to reduce the size of the programs. We introduce two algorithms that attempt to solve the problem and explore type based pruning techniques in the context of modular programs. By experimenting with the implementation of one of those algorithms, we show reuse is important (if not crucial) for a variety of problems and distinguished two broad classes of programs that will generally benefit from function reuse.

We study query answering in the description logic $\mathcal{SQ}$ supporting qualified number restrictions on both transitive and non-transitive roles. Our main contributions are a tree-like model property for $\mathcal{SQ}$ knowledge bases and, building upon this, an optimal automata-based algorithm for answering positive existential regular path queries in 2ExpTime.

We propose answer-set programs that specify and compute counterfactual interventions as a basis for causality-based explanations to the outcomes from classification models. They can be applied with black-box models, and also with models that can be specified as logic programs, such as rule-based classifiers. The main focus is on the specification and computation of maximum-responsibility counterfactual explanations, with responsibility becoming an explanation score for features of entities under classification. We also extend the programs to bring into the picture semantic or domain knowledge. We show how the approach could be extended by means of probabilistic methods, and how the underlying probability distributions could be modified through the use of constraints.

Motivated by the needs of resource constrained dialog policy learning, we introduce dialog policy via differentiable inductive logic (DILOG). We explore the tasks of one-shot learning and zero-shot domain transfer with DILOG on SimDial and MultiWoZ. Using a single representative dialog from the restaurant domain, we train DILOG on the SimDial dataset and obtain 99 % in-domain test accuracy. We also show that the trained DILOG zero-shot transfers to all other domains with 99 % accuracy, proving the suitability of DILOG to slot-filling dialogs. We further extend our study to the MultiWoZ dataset achieving 90 % inform and success metrics. We also observe that these metrics are not capturing some of the shortcomings of DILOG in terms of false positives, prompting us to measure an auxiliary Action F1 score. We show that DILOG is 100x more data efficient than state-of-the-art neural approaches on MultiWoZ while achieving similar performance metrics. We conclude with a discussion on the strengths and weaknesses of DILOG.

Therefore, our work alliances through multiple means: diplomatic, economic, seeks to advance capabilities in explainable AI/ML to allow conventional and unconventional warfare, including information a human operative to'calibrate their trust' in an AI/ML asset warfare. A critical requirement for allies is potentially provided by a different coalition partner (Tomsett rapid and continuous integration of capabilities to collect, et al. 2020). The purpose of human-machine teaming is process, disseminate and exploit actionable information and to aim for each party to exploit the strengths of, and compensate intelligence. To achieve this, the MDO layered ISR concept for the weaknesses of, the other (Cummings 2014).

Recently, the notions of subjective constraint monotonicity, epistemic splitting, and foundedness have been introduced for epistemic logic programs, with the aim to use them as main criteria respectively intuitions to compare different answer set semantics proposed in the literature on how they comply with these intuitions. In this note, we consider these three notions and demonstrate on some examples that they may be too strong in general and may exclude some desired answer sets respectively world views. In conclusion, these properties should not be regarded as mandatory properties that every answer set semantics must satisfy in general.

Weighted First Order Model Counting (WFOMC) computes the weighted sum of the models of a first order theory on a domain of a given finite size. WFOMC has emerged as a fundamental tool for probabilistic inference. Algorithms for WFOMC that run in polynomial time w.r.t. the domain size are called lifted inference algorithms. Such algorithms have been developed for multiple extensions of FO$^2$(the fragment of First Order Logic with two variables) for the special case of symmetric weight functions. In this paper, instead of developing a specific algorithm, we derive a closed form formula for WFOMC in FO$^2$. The three key advantages of our proposal are: (i) it deals with existential quantifiers without introducing negative weights; (ii) it easily extends to FO$^2$ with cardinality constraints and counting quantifiers (aka C$^2$); finally, (iii) it supports WFOMC for a class of weight functions strictly larger than symmetric weight functions, which can model count distributions, without introducing complex or negative weights.

We provide a comprehensive analysis of the computational complexity of the outcome determination problem for the most important aggregation rules proposed in the literature on logic-based judgment aggregation. Judgment aggregation is a powerful and flexible framework for studying problems of collective decision making that has attracted interest in a range of disciplines, including Legal Theory, Philosophy, Economics, Political Science, and Artificial Intelligence. The problem of computing the outcome for a given list of individual judgments to be aggregated into a single collective judgment is the most fundamental algorithmic challenge arising in this context. Our analysis applies to several different variants of the basic framework of judgment aggregation that have been discussed in the literature, as well as to a new framework that encompasses all existing such frameworks in terms of expressive power and representational succinctness.