Generalising weighted model counting

Given a formula in propositional or (finite-domain) first-order logic and some non-negative weights, weighted model counting (WMC) is a function problem that asks to compute the sum of the weights of the models of the formula. Originally used as a flexible way of performing probabilistic inference on graphical models, WMC has found many applications across artificial intelligence (AI), machine learning, and other domains. Areas of AI that rely on WMC include explainable AI, neural-symbolic AI, probabilistic programming, and statistical relational AI. WMC also has applications in bioinformatics, data mining, natural language processing, prognostics, and robotics. In this work, we are interested in revisiting the foundations of WMC and considering generalisations of some of the key definitions in the interest of conceptual clarity and practical efficiency. We begin by developing a measure-theoretic perspective on WMC, which suggests a new and more general way of defining the weights of an instance. This new representation can be as succinct as standard WMC but can also expand as needed to represent less-structured probability distributions. We demonstrate the performance benefits of the new format by developing a novel WMC encoding for Bayesian networks. We then show how existing WMC encodings for Bayesian networks can be transformed into this more general format and what conditions ensure that the transformation is correct (i.e., preserves the answer). Combining the strengths of the more flexible representation with the tricks used in existing encodings yields further efficiency improvements in Bayesian network probabilistic inference. Next, we turn our attention to the first-order setting. Here, we argue that the capabilities of practical model counting algorithms are severely limited by their inability to perform arbitrary recursive computations. To enable arbitrary recursion, we relax the restrictions that typically accompany domain recursion and generalise circuits (used to express a solution to a model counting problem) to graphs that are allowed to have cycles. These improvements enable us to find efficient solutions to counting fundamental structures such as injections and bijections that were previously unsolvable by any available algorithm. The second strand of this work is concerned with synthetic data generation. Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm’s superiority over another. However, benchmarks are often limited and fail to reveal differences among the algorithms. First, we show how random instances of probabilistic logic programs (that typically use WMC algorithms for inference) can be generated using constraint programming. We also introduce a new constraint to control the independence structure of the underlying probability distribution and provide a combinatorial argument for the correctness of the constraint model. This model allows us to, for the first time, experimentally investigate inference algorithms on more than just a handful of instances. Second, we introduce a random model for WMC instances with a parameter that influences primal treewidth—the parameter most commonly used to characterise the difficulty of an instance. We show that the easy-hard-easy pattern with respect to clause density is different for algorithms based on dynamic programming and algebraic decision diagrams than for all other solvers. We also demonstrate that all WMC algorithms scale exponentially with respect to primal treewidth, although at differing rates

On the role of Computational Logic in Data Science: representing, learning, reasoning, and explaining knowledge

In this thesis we discuss in what ways computational logic (CL) and data science (DS) can jointly contribute to the management of knowledge within the scope of modern and future artificial intelligence (AI), and how technically-sound software technologies can be realised along the path. An agent-oriented mindset permeates the whole discussion, by stressing pivotal role of autonomous agents in exploiting both means to reach higher degrees of intelligence. Accordingly, the goals of this thesis are manifold. First, we elicit the analogies and differences among CL and DS, hence looking for possible synergies and complementarities along 4 major knowledge-related dimensions, namely representation, acquisition (a.k.a. learning), inference (a.k.a. reasoning), and explanation. In this regard, we propose a conceptual framework through which bridges these disciplines can be described and designed. We then survey the current state of the art of AI technologies, w.r.t. their capability to support bridging CL and DS in practice. After detecting lacks and opportunities, we propose the notion of logic ecosystem as the new conceptual, architectural, and technological solution supporting the incremental integration of symbolic and sub-symbolic AI. Finally, we discuss how our notion of logic ecosys- tem can be reified into actual software technology and extended towards many DS-related directions

Technical Education in 'Lived Markets': University Technical College leaders' perceptions of and responses to competitive pressure

This study analyses the complexities of competition and competitive practices within lived markets across nine University Technical College (UTC) case studies. The research built upon Jabbar’s (2015) conceptual framework of school competition in the USA to conceptualise how competition and competitive practices may be conceived in England. Despite the growth in UTC numbers since 2010, with 50 operating (July 2019) and each with a capacity for between 500 and 800 students aged from 14 to 19 years, relatively little was known about how these providers interacted with existing local provision. The research analysed UTC leaders’ perceptions of competition, the mediating factors they believe have contributed to perceived competition and competitive pressure, the range of strategies they developed in response to those perceptions, and the resulting outcomes. The findings indicated that these leaders’ perceptions of competition and the associated competitive pressures were broadly in tension with their belief in technical education, the national ethos and vision for UTCs, the government’s national accountability measures, and partnership working with local providers. The findings analyse the consequences of these tensions and, in so doing, contribute to a greater theoretical and conceptual understanding of the contemporary expansion of the tenets of the quasi-market into mainstream and technical schooling. The main contributions of this thesis are that it provides; a greater understanding of the ways in which competition and supply side liberalisation operate at a local level, and offers a new conceptual framework for researching school-to-school competition in England. The study highlights the need for further research of the impact of competition on all schools and students within a given region, and highlights the importance of strengthening policy ‘memory’ with regards to technical education. The findings will be of broad interest to researchers interested in technical education, leadership roles, quasi-markets and competition, parental choice, and social segregation. Key words: Competition, competitive practices, lived market, parental choice, quasi-market, social segregation, technical education

Foster care for unaccompanied refugee children in the Netherlands; what about the placement success?

There is hardly any knowledge on the outcomes of foster placements of unaccompanied refugee children. Especially, knowledge on the stability of foster placements for unaccompanied refugee children is lacking. Because placements in regular foster care change and develop over time, including the occurrence of placement breakdowns, the need for a study focusing on the stability of foster placements for unaccompanied refugee children is indicated. This study explores the association between the success of foster placements for unaccompanied refugee children and cultural, child and fostering factors, and examines the stability of these factors over time

Advancing the field of decision making and judgement in child welfare and protection:A look back and forward

Our knowledge of decision making in child welfare has evolved concurrent with the recognition that there is variability in the rates at which children and families experience no involvement to deeper involvement in the system from jurisdiction to jurisdiction and person to person. In this synthesis of concepts and studies we recap the reasons it is important and challenging to identify systematic causes for variability in decisions and what can be learned about them. Child protection systems have a history of relying on both formal and informal assessments of children and families. While research indicates that emphasis on assessment is warranted, errors and mistakes can happen in all the stages of the assessment and decision processes due to a range of system and human factors. We present some examples here