This paper is an extended version of Bílková et al. ((2023b). Logic, Language, Information, and Computation. WoLLIC 2023, Lecture Notes in Computer Science, vol. 13923, Cham, Springer Nature Switzerland, 101–117.). We discuss two-layered logics formalising reasoning with probabilities and belief functions that combine the Łukasiewicz $[0,1]$-valued logic with Baaz $\triangle$ operator and the Belnap–Dunn logic. We consider two probabilistic logics – $\mathsf {Pr}^{{\mathsf {\unicode {x0141}}}^2}_\triangle$ (introduced by Bílková et al. 2023d. Annals of Pure and Applied Logic, 103338.) and $\mathbf {4}\mathsf {Pr}^{{\mathsf {\unicode {x0141}}}_\triangle }$ (from Bílková et al. 2023b. Logic, Language, Information, and Computation. WoLLIC 2023, Lecture Notes in Computer Science, vol. 13923, Cham, Springer Nature Switzerland, 101–117.) – that present two perspectives on the probabilities in the Belnap–Dunn logic. In $\mathsf {Pr}^{{\mathsf {\unicode {x0141}}}^2}_\triangle$, every event $\phi$ has independent positive and negative measures that denote the likelihoods of $\phi$ and $\neg \phi$, respectively. In $\mathbf {4}\mathsf {Pr}^{{\mathsf {\unicode {x0141}}}_\triangle }$, the measures of the events are treated as partitions of the sample into four exhaustive and mutually exclusive parts corresponding to pure belief, pure disbelief, conflict and uncertainty of an agent in $\phi$. In addition to that, we discuss two logics for the paraconsistent reasoning with belief and plausibility functions from Bílková et al. ((2023d). Annals of Pure and Applied Logic, 103338.) – $\mathsf {Bel}^{{\mathsf {\unicode {x0141}}}^2}_\triangle$ and $\mathsf {Bel}^{\mathsf {N}{\mathsf {\unicode {x0141}}}}$. Both these logics equip events with two measures (positive and negative) with their main difference being that in $\mathsf {Bel}^{{\mathsf {\unicode {x0141}}}^2}_\triangle$, the negative measure of $\phi$ is defined as the belief in $\neg \phi$ while in $\mathsf {Bel}^{\mathsf {N}{\mathsf {\unicode {x0141}}}}$, it is treated independently as the plausibility of $\neg \phi$. We provide a sound and complete Hilbert-style axiomatisation of $\mathbf {4}\mathsf {Pr}^{{\mathsf {\unicode {x0141}}}_\triangle }$ and establish faithful translations between it and $\mathsf {Pr}^{\mathsf {\unicode {x0141}}^2}_\triangle$. We also show that the validity problem in all the logics is $\mathsf {coNP}$-complete.

The newly introduced discipline of Population-Based Structural Health Monitoring (PBSHM) has been developed in order to circumvent the issue of data scarcity in “classical” SHM. PBSHM does this by using data across an entire population, in order to improve diagnostics for a single data-poor structure. The improvement of inferences across populations uses the machine-learning technology of transfer learning. In order that transfer makes matters better, rather than worse, PBSHM assesses the similarity of structures and only transfers if a threshold of similarity is reached. The similarity measures are implemented by embedding structures as models —Irreducible-Element (IE) models— in a graph space. The problem with this approach is that the construction of IE models is subjective and can suffer from author-bias, which may induce dissimilarity where there is none. This paper proposes that IE-models be transformed to a canonical form through reduction rules, in which possible sources of ambiguity have been removed. Furthermore, in order that other variations —outside the control of the modeller— are correctly dealt with, the paper introduces the idea of a reality model, which encodes details of the environment and operation of the structure. Finally, the effects of the canonical form on similarity assessments are investigated via a numerical population study. A final novelty of the paper is in the implementation of a neural-network-based similarity measure, which learns reduction rules from data; the results with the new graph-matching network (GMN) are compared with a previous approach based on the Jaccard index, from pure graph theory.

We show that the principal types of the closed terms of the affine fragment of λ-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry of Interaction model à la Abramsky. This permits to explain in elementary terms the somewhat awkward notion of linear application arising in Geometry of Interaction, simply as the resolution between principal types using an alternate unification algorithm. As a consequence, we provide an answer, for the purely affine fragment, to the open problem raised by Abramsky of characterizing those partial involutions which are denotations of combinatory terms.

We present an axiom system for what we call Prior’s Ideal Language and prove its completeness and pure completeness with respect to general models. With this is done, we explain, with examples, why this system provides a useful setting for exploring Arthur Prior’s work.

We revisit the communication primitive in ambient calculi. Previously, such communication was confined to first-order (FO) mode (e.g., merely names or capabilities of ambients can be sent), local mode (e.g., the communication only occurs inside an ambient), or particular cross-hierarchy mode (e.g., parent-child communication). In this work, we explore further higher-order (HO) communication in ambient calculi. Specifically, such a communication mechanism allows sending a whole piece of a program across the borders of ambients and is the only form of communication that can happen exactly between ambients. Since ambients are basically of HO nature (i.e., those being moved may be ambients themselves), in a sense, it appears more natural to have HO communication than FO communication. We stipulate that communications merely occur between equally positioned ambients in a peer-to-peer fashion (e.g., between sibling ambients). Following this line, we drop the local or other forms of communication that violate this criterion. As the workbench, we work on a variant of Fair Ambients extended with HO communication, FAHO. This variant also strengthens the original version in that entirely real-identity interaction is guaranteed. We study the semantics, bisimulation, and expressiveness of FAHO. Particularly, we provide the operational semantics using a labeled transition system. Over the semantics, we define the bisimulation in line with the standard notion of bisimulation for ambients and prove that the bisimulation equivalence (i.e., bisimilarity) is a congruence. In addition, we demonstrate that bisimilarity coincides with observational congruence (i.e., barbed congruence). Moreover, we show that FAHO can encode a minimal Turing-complete HO calculus and thus is computationally complete.

Data-based methods have gained increasing importance in engineering. Success stories are prevalent in areas such as data-driven modeling, control, and automation, as well as surrogate modeling for accelerated simulation. Beyond engineering, generative and large-language models are increasingly helping with tasks that, previously, were solely associated with creative human processes. Thus, it seems timely to seek artificial-intelligence-support for engineering design tasks to automate, help with, or accelerate purpose-built designs of engineering systems for instance in mechanics and dynamics, where design so far requires a lot of specialized knowledge. Compared with established, predominantly first-principles-based methods, the datasets used for training, validation, and test become an almost inherent part of the overall methodology. Thus, data publishing becomes just as important in (data-driven) engineering science as appropriate descriptions of conventional methodology in publications in the past. However, in mechanics and dynamics, quite widely, still traditional publishing practices are prevalent that largely do not yet take into account the rising role of data as much as that may already be the case in pure data-scientific research. This article analyzes the value and challenges of data publishing in mechanics and dynamics, in particular regarding engineering design tasks, showing that the latter raise also challenges and considerations not typical in fields where data-driven methods have been booming originally. Researchers currently find barely any guidance to overcome these challenges. Thus, ways to deal with these challenges are discussed and a set of examples from across different design problems shows how data publishing can be put into practice.

We provide a fine classification of bisimilarities between states of possibly different labelled Markov processes (LMP). We show that a bisimilarity relation proposed by Panangaden that uses direct sums coincides with “event bisimilarity” from his joint work with Danos, Desharnais, and Laviolette. We also extend Giorgio Bacci’s notions of bisimilarity between two different processes to the case of nondeterministic LMP and generalize the game characterization of state bisimilarity by Clerc et al. for the latter.

Online customer feedback management (CFM) is becoming increasingly important for businesses. Providing timely and effective responses to guest reviews can be challenging, especially as the volume of reviews grows. This paper explores the response process and the potential for artificial intelligence (AI) augmentation in response formulation. We propose an orchestration concept for human–AI collaboration in co-writing within the hospitality industry, supported by a novel NLP-based solution that combines the strengths of both human and AI. Although complete automation of the response process remains out of reach, our findings offer practical implications for improving response speed and quality through human–AI collaboration. Additionally, we formulate policy recommendations for businesses and regulators in CFM. Our study provides transferable design knowledge for developing future CFM products.

In the wake of the recent resurgence of the Datalog language of databases, together with its extensions for ontological reasoning settings, this work aims to bridge the gap between the theoretical studies of DatalogMTL (Datalog extended with metric temporal logic) and the development of production-ready reasoning systems. In particular, we lay out the functional and architectural desiderata of a modern reasoner and propose our system, Temporal Vadalog. Leveraging the vast amount of experience from the database community, we go beyond the typical chase-based implementations of reasoners, and propose a set of novel techniques and a system that adopts a modern data pipeline architecture. We discuss crucial architectural choices, such as how to guarantee termination when infinitely many time intervals are possibly generated, how to merge intervals, and how to sustain a limited memory footprint. We discuss advanced features of the system, such as the support for time series, and present an extensive experimental evaluation. This paper is a substantially extended version of “The Temporal Vadalog System” as presented at RuleML+RR ’22.

The formal theory of monads shows that much of the theory of monads can be developed in the abstract at the level of 2-categories. This means that results about monads can be established once and for all and simply instantiated in settings such as enriched category theory.

Unfortunately, these results can be hard to reason about as they involve more abstract machinery. In this paper, we present the formal theory of monads in terms of string diagrams — a graphical language for 2-categorical calculations. Using this perspective, we show that many aspects of the theory of monads, such as the Eilenberg–Moore and Kleisli resolutions of monads, liftings, and distributive laws, can be understood in terms of systematic graphical calculational reasoning.

This paper will serve as an introduction both to the formal theory of monads and to the use of string diagrams, in particular, their application to calculations in monad theory.

This study introduces an innovative deep learning method for intelligent healthcare emotion analysis, specifically targeting the recognition of pain based on facial expressions. The suggested approach combines cloud-based mobile applications, utilising separate front-end and back-end elements to optimise data processing. The main contributions consist of a Smart Automated System (SASys) that integrates statistical and deep learning methods to extract features, thereby guaranteeing both resilience and efficiency. Image preprocessing encompasses the tasks of detecting faces and normalising them, which is crucial for extracting features with high accuracy. The comparison of statistical feature representation using Histogram of Oriented Gradients and Local Binary Pattern, along with machine learning classifiers, against an enhanced deep learning-based approach with an integrated multi-tasking feature known as multi-task convolutional neural network, demonstrates encouraging outcomes that support the superiority of the convolutional neural network architecture. Statistical and deep learning-based classification scores, when combined, greatly enhance the system’s overall performance. The results of the experiments prove that the method is effective, outperforming traditional classifiers and exhibiting comparable accuracy to cutting-edge healthcare SASys.