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Behavioural distances generally offer more fine-grained means of comparing quantitative systems than two-valued behavioural equivalences. They often relate to quantitative modalities, which generate quantitative modal logics that characterize a given behavioural distance in terms of the induced logical distance. We develop a unified framework for behavioural distances and logics induced by a special type of modalities that lift two-valued predicates to quantitative predicates. A typical example is the probability operator, which maps a two-valued predicate $A$ to a quantitative predicate on probability distributions assigning to each distribution the respective probability of $A$. Correspondingly, the prototypical example of our framework is $ε$-bisimulation distance of Markov chains, which has recently been shown to coincide with the behavioural distance induced by the popular Lévy-Prokhorov distance on distributions. Other examples include behavioural distance on metric transition systems and Hausdorff behavioural distance on fuzzy transition systems. Our main generic results concern the polynomial-time extraction of distinguishing formulae in two characteristic modal logics: A t
The 1mm roundworm C. elegans is a model organism used in many sub-areas of biology to investigate different types of biological processes. In order to complement the n-vivo analysis with computer-based investigations, several methods have been proposed to simulate the worm behaviour. These methods extract discrete behavioural units from the flow of the worm movements using different types of tracking techniques. Nevertheless, these techniques require a clear view of the entire worm body, which is not always achievable. For example, this happens in high density worm conditions, which are particularly informative to understand the influence of the social context on the single worm behaviour. In this paper, we illustrate and evaluate a method to extract behavioural units from recordings of C. elegans movements which do not necessarily require a clear view of the entire worm body. Moreover, the behavioural units are defined by an unsupervised automatic pipeline which frees the process from predefined assumptions that inevitably bias the behavioural analysis. The behavioural units resulting from the automatic method are interpreted by comparing them with hand-designed behavioural units.
Behavioural conformances -- e.g. behavioural equivalences, distances, preorders -- on a wide range of system types (non-deterministic, probabilistic, weighted etc.) can be dealt with uniformly in the paradigm of universal coalgebra. One of the most commonly used constructions for defining behavioural distances on coalgebras arises as a generalization of the well-known Wasserstein metric. In this construction, couplings of probability distributions are replaced with couplings of more general objects, depending on the functor describing the system type. In many cases, however, the set of couplings of two functor elements is empty, which causes such elements to have infinite distance even in situations where this is not desirable. We propose an approach to defining behavioural distances and preorders based on a more liberal notion of coupling where the coupled elements are matched laxly rather than on-the-nose. We thereby substantially broaden the range of behavioural conformances expressible in terms of couplings, covering, e.g., refinement of modal transition systems and behavioural distance on metric labelled Markov chains.
This PhD thesis discusses how European law could improve privacy protection in the area of behavioural targeting. Behavioural targeting, also referred to as online profiling, involves monitoring people's online behaviour, and using the collected information to show people individually targeted advertisements. To protect privacy in the area of behavioural targeting, the EU lawmaker mainly relies on the consent requirement for the use of tracking technologies in the e-Privacy Directive, and on general data protection law. With informed consent requirements, the law aims to empower people to make choices in their best interests. But behavioural studies cast doubt on the effectiveness of the empowerment approach as a privacy protection measure. Many people click "I agree" to any statement that is presented to them. Therefore, to mitigate privacy problems such as chilling effects, this study argues for a combined approach of protecting and empowering the individual. Compared to the current approach, the lawmaker should focus more on protecting people. The PhD thesis is a legal study, but it also incorporates insights from other disciplines, such as computer science, behavioural economic
Coinduction is a widely used technique for establishing behavioural equivalence of programs in higher-order languages. In recent years, the rise of languages with quantitative (e.g.~probabilistic) features has led to extensions of coinductive methods to more refined types of behavioural conformances, most notably notions of behavioural distance. To guarantee soundness of coinductive reasoning, one needs to show that the behavioural conformance at hand forms a program congruence, i.e. it is suitably compatible with the operations of the language. This is usually achieved by a complex proof technique known as \emph{Howe's method}, which needs to be carefully adapted to both the specific language and the targeted notion of behavioural conformance. We develop a uniform categorical approach to Howe's method that features two orthogonal dimensions of abstraction: (1) the underlying higher-order language is modelled by an \emph{abstract higher-order specification} (AHOS), a novel and very general categorical account of operational semantics, and (2) notions of behavioural conformance (such as relations or metrics) are modelled via fibrations over the base category of an AHOS. Our main res
The paper introduces a novel behavioural translation style space (BTSS) that describes possible behavioural translation patterns. The suggested BTSS is organized as a hierarchical structure that entails various embedded processing layers. We posit that observable translation behaviour - i.e. eye and finger movements - is fundamental when executing the physical act of translation but it is caused and shaped by higher-order cognitive processes and affective translation states. We analyse records of keystrokes and gaze data as indicators of the hidden mental processing structure and organize the behavioural patterns as a multi-layered embedded BTSS. We develop a perspective in which the BTSS serves as the basis for a computational translation agent to simulate the temporal dynamics of affect, behavioural routines and cognition during human translation production.
This chapter examines the policy implications of behavioural sciences insights for the regulation of privacy on the Internet, by focusing in particular on behavioural targeting. This marketing technique involves tracking people's online behaviour to use the collected information to show people individually targeted advertisements. Enforcing data protection law may not be enough to protect privacy in this area. I argue that, if society is better off when certain behavioural targeting practices do not happen, policymakers should consider banning them.
Reinforcement learning (RL) agents under partial observability often condition actions on internally accumulated information such as memory or inferred latent context. We formalise such information-conditioned interaction patterns as behavioural dependency: variation in action selection with respect to internal information under fixed observations. This induces a probe-relative notion of $ε$-behavioural equivalence and a within-policy behavioural distance that quantifies probe sensitivity. We establish three structural results. First, the set of policies exhibiting non-trivial behavioural dependency is not closed under convex aggregation. Second, behavioural distance contracts under convex combination. Third, we prove a sufficient local condition under which gradient ascent on a skewed mixture objective decreases behavioural distance when a dominant-mode gradient aligns with the direction of steepest contraction. Minimal bandit and partially observable gridworld experiments provide controlled witnesses of these mechanisms. In the examined settings, behavioural distance decreases under convex aggregation and under continued optimisation with skewed latent priors, and in these experi
Federated Learning (FL), a privacy-aware approach in distributed deep learning environments, enables many clients to collaboratively train a model without sharing sensitive data, thereby reducing privacy risks. However, enabling human trust and control over FL systems requires understanding the evolving behaviour of clients, whether beneficial or detrimental for the training, which still represents a key challenge in the current literature. To address this challenge, we introduce Federated Behavioural Planes (FBPs), a novel method to analyse, visualise, and explain the dynamics of FL systems, showing how clients behave under two different lenses: predictive performance (error behavioural space) and decision-making processes (counterfactual behavioural space). Our experiments demonstrate that FBPs provide informative trajectories describing the evolving states of clients and their contributions to the global model, thereby enabling the identification of clusters of clients with similar behaviours. Leveraging the patterns identified by FBPs, we propose a robust aggregation technique named Federated Behavioural Shields to detect malicious or noisy client models, thereby enhancing secu
Behavioural metrics provide a quantitative refinement of classical two-valued behavioural equivalences on systems with quantitative data, such as metric or probabilistic transition systems. In analogy to the linear-time/branching-time spectrum of two-valued behavioural equivalences on transition systems, behavioural metrics vary in granularity, and are often characterized by fragments of suitable modal logics. In the latter respect, the quantitative case is, however, more involved than the two-valued one; in fact, we show that probabilistic metric trace distance cannot be characterized by any compositionally defined modal logic with unary modalities. We go on to provide a unifying treatment of spectra of behavioural metrics in the emerging framework of graded monads, working in coalgebraic generality, that is, parametrically in the system type. In the ensuing development of quantitative graded semantics, we introduce algebraic presentations of graded monads on the category of metric spaces. Moreover, we provide a general criterion for a given real-valued modal logic to characterize a given behavioural distance. As a case study, we apply this criterion to obtain a new characteristic