Parameterized aspects of team-based formalisms and logical inference

Parameterized complexity is an interesting subfield of complexity theory that has received a lot of attention in recent years. Such an analysis characterizes the complexity of (classically) intractable problems by pinpointing the computational hardness to some structural aspects of the input. In this thesis, we study the parameterized complexity of various problems from the area of team-based formalisms as well as logical inference. In the context of team-based formalism, we consider propositional dependence logic (PDL). The problems of interest are model checking (MC) and satisfiability (SAT). Peter Lohmann studied the classical complexity of these problems as a part of his Ph.D. thesis proving that both MC and SAT are NP-complete for PDL. This thesis addresses the parameterized complexity of these problems with respect to a wealth of different parameterizations. Interestingly, SAT for PDL boils down to the satisfiability of propositional logic as implied by the downwards closure of PDL-formulas. We propose an interesting satisfiability variant (mSAT) asking for a satisfiable team of size m. The problem mSAT restores the ‘team semantic’ nature of satisfiability for PDL-formulas. We propose another problem (MaxSubTeam) asking for a maximal satisfiable team if a given team does not satisfy the input formula. From the area of logical inference, we consider (logic-based) abduction and argumentation. The problem of interest in abduction (ABD) is to determine whether there is an explanation for a manifestation in a knowledge base (KB). Following Pfandler et al., we also consider two of its variants by imposing additional restrictions over the size of an explanation (ABD and ABD=). In argumentation, our focus is on the argument existence (ARG), relevance (ARG-Rel) and verification (ARG-Check) problems. The complexity of these problems have been explored already in the classical setting, and each of them is known to be complete for the second level of the polynomial hierarchy (except for ARG-Check which is DP-complete) for propositional logic. Moreover, the work by Nord and Zanuttini (resp., Creignou et al.) explores the complexity of these problems with respect to various restrictions over allowed KBs for ABD (ARG). In this thesis, we explore a two-dimensional complexity analysis for these problems. The first dimension is the restrictions over KB in Schaefer’s framework (the same direction as Nord and Zanuttini and Creignou et al.). What differentiates the work in this thesis from an existing research on these problems is that we add another dimension, the parameterization. The results obtained in this thesis are interesting for two reasons. First (from a theoretical point of view), ideas used in our reductions can help in developing further reductions and prove (in)tractability results for related problems. Second (from a practical point of view), the obtained tractability results might help an agent designing an instance of a problem come up with the one for which the problem is tractable

Using Event Calculus to Formalise Policy Specification and Analysis

As the interest in using policy-based approaches for systems management grows, it is becoming increasingly important to develop methods for performing analysis and refinement of policy specifications. Although this is an area that researchers have devoted some attention to, none of the proposed solutions address the issues of analysing specifications that combine authorisation and management policies; analysing policy specifications that contain constraints on the applicability of the policies; and performing a priori analysis of the specification that will both detect the presence of inconsistencies and explain the situations in which the conflict will occur. We present a method for transforming both policy and system behaviour specifications into a formal notation that is based on event calculus. Additionally it describes how this formalism can be used in conjunction with abductive reasoning techniques to perform a priori analysis of policy specifications for the various conflict types identified in the literature. Finally, it presents some initial thoughts on how this notation and analysis technique could be used to perform policy refinement

Measuring axiomatic soundness of counterfactual image models

We use the axiomatic definition of counterfactual to derive metrics that enable quantifying the correctness of approximate counterfactual inference models. Abstract: We present a general framework for evaluating image counterfactuals. The power and flexibility of deep generative models make them valuable tools for learning mechanisms in structural causal models. However, their flexibility makes counterfactual identifiability impossible in the general case. Motivated by these issues, we revisit Pearl's axiomatic definition of counterfactuals to determine the necessary constraints of any counterfactual inference model: composition, reversibility, and effectiveness. We frame counterfactuals as functions of an input variable, its parents, and counterfactual parents and use the axiomatic constraints to restrict the set of functions that could represent the counterfactual, thus deriving distance metrics between the approximate and ideal functions. We demonstrate how these metrics can be used to compare and choose between different approximate counterfactual inference models and to provide insight into a model's shortcomings and trade-offs

Abductive knowledge induction from raw data

For many reasoning-heavy tasks with raw inputs, it is challenging to design an appropriate end-to-end pipeline to formulate the problem-solving process. Some modern AI systems, e.g., Neuro-Symbolic Learning, divide the pipeline into sub-symbolic perception and symbolic reasoning, trying to utilise data-driven machine learning and knowledge-driven problem-solving simultaneously. However, these systems suffer from the exponential computational complexity caused by the interface between the two components, where the sub-symbolic learning model lacks direct supervision, and the symbolic model lacks accurate input facts. Hence, they usually focus on learning the sub-symbolic model with a complete symbolic knowledge base while avoiding a crucial problem: where does the knowledge come from? In this paper, we present Abductive Meta-Interpretive Learning (MetaAbd) that unites abduction and induction to learn neural networks and logic theories jointly from raw data. Experimental results demonstrate that MetaAbd not only outperforms the compared systems in predictive accuracy and data efficiency but also induces logic programs that can be re-used as background knowledge in subsequent learning tasks. To the best of our knowledge, MetaAbd is the first system that can jointly learn neural networks from scratch and induce recursive first-order logic theories with predicate invention

Advancing probabilistic and causal deep learning in medical image analysis

The power and flexibility of deep learning have made it an indispensable tool for tackling modern machine learning problems. However, this flexibility comes at the cost of robustness and interpretability, which can lead to undesirable or even harmful outcomes. Deep learning models often fail to generalise to real-world conditions and produce unforeseen errors that hinder wide adoption in safety-critical critical domains such as healthcare. This thesis presents multiple works that address the reliability problems of deep learning in safety-critical domains by being aware of its vulnerabilities and incorporating more domain knowledge when designing and evaluating our algorithms. We start by showing how close collaboration with domain experts is necessary to achieve good results in a real-world clinical task - the multiclass semantic segmentation of traumatic brain injuries (TBI) lesions in head CT. We continue by proposing an algorithm that models spatially coherent aleatoric uncertainty in segmentation tasks by considering the dependencies between pixels. The lack of proper uncertainty quantification is a robustness issue which is ubiquitous in deep learning. Tackling this issue is of the utmost importance if we want to deploy these systems in the real world. Lastly, we present a general framework for evaluating image counterfactual inference models in the absence of ground-truth counterfactuals. Counterfactuals are extremely useful to reason about models and data and to probe models for explanations or mistakes. As a result, their evaluation is critical for improving the interpretability of deep learning models.Open Acces

Declarative Specification

Deriving formal specifications from informal requirements is extremely difficult since one has to overcome the conceptual gap between an application domain and the domain of formal specification methods. To reduce this gap we introduce application-specific specification languages, i.e., graphical and textual notations that can be unambiguously mapped to formal specifications in a logic language. We describe a number of realised approaches based on this idea, and evaluate them with respect to their domain specificity vs. generalit

Reachable Workspace and Proximal Function Measures for Quantifying Upper Limb Motion.

There are a lack of quantitative measures for clinically assessing upper limb function. Conventional biomechanical performance measures are restricted to specialist labs due to hardware cost and complexity, while the resulting measurements require specialists for analysis. Depth cameras are low cost and portable systems that can track surrogate joint positions. However, these motions may not be biologically consistent, which can result in noisy, inaccurate movements. This paper introduces a rigid body modelling method to enforce biological feasibility of the recovered motions. This method is evaluated on an existing depth camera assessment: the reachable workspace (RW) measure for assessing gross shoulder function. As a rigid body model is used, position estimates of new proximal targets can be added, resulting in a proximal function (PF) measure for assessing a subject's ability to touch specific body landmarks. The accuracy, and repeatability of these measures is assessed on ten asymptomatic subjects, with and without rigid body constraints. This analysis is performed both on a low-cost depth camera system and a gold-standard active motion capture system. The addition of rigid body constraints was found to improve accuracy and concordance of the depth camera system, particularly in lateral reaching movements. Both RW and PF measures were found to be feasible candidates for clinical assessment, with future analysis needed to determine their ability to detect changes within specific patient populations