Multi-objective reinforcement learning (MORL) is an excellent framework for multi-objective sequential decision-making. MORL employs a utility function to aggregate multiple objectives into one that expresses a user's preferences. However, MORL still misses two crucial theoretical analyses of the properties of utility functions: (1) a characterisation of the utility functions for which an associated optimal policy exists, and (2) a characterisation of the types of preferences that can be expressed as utility functions. As a result, we formally characterise the families of preferences and utility functions that MORL should focus on: those for which an optimal policy is guaranteed to exist. We expect our theoretical results to promote the development of novel MORL algorithms that exploit our theoretical findings.

Global digital platforms are software systems designed to serve entire populations, with some already serving billions of people. We propose atomic transactions-based multiagent transition systems and protocols as a formal framework to study them; introduce essential agents -- minimal sets of agents the removal of which makes communication impossible; and show that the cardinality of essential agents partitions all global platforms into four classes: 1. Centralised -- one (the server) 2. Decentralised -- finite $>1$ (bootstrap nodes) 3. Federated -- infinite but not universal (all servers) 4. Grassroots -- universal (all agents) Our illustrative formal example is a global social network, for which we provide centralised, decentralised, federated, and grassroots specifications via multiagent atomic transactions, and prove they all satisfy the same basic correctness properties. We discuss informally additional global platforms -- currencies, ``sharing economy'' apps, AI, and more. While this may be the first characterisation of centralised, decentralised, and federated global platforms, grassroots platforms have been formally defined previously, but using different notions. Here, we prove that their original definition implies that all agents are essential, placing grassroots platforms in a distinct class within the broader formal context that includes all global platforms. This work provides the first mathematical framework for classifying any global platform -- existing or imagined -- by providing a multiagent atomic-transactions specification of it and determining the cardinality of the minimal set of essential agents in the ensuing multiagent protocol. It thus provides a unifying mathematical approach for the study of global digital platforms, perhaps the most important class of computer systems today.

Multi-objective reinforcement learning (MORL) is an excellent framework for multi-objective sequential decision-making. MORL employs a utility function to aggregate multiple objectives into one that expresses a user's preferences. However, MORL still misses two crucial theoretical analyses of the properties of utility functions: (1) a characterisation of the utility functions for which an associated optimal policy exists, and (2) a characterisation of the types of preferences that can be expressed as utility functions. As a result, we formally characterise the families of preferences and utility functions that MORL should focus on: those for which an optimal policy is guaranteed to exist. We expect our theoretical results to promote the development of novel MORL algorithms that exploit our theoretical findings.

We consider the Schrödinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely" evolution of the system compatible with the data. Most existing literature assume Brownian reference dynamics and are implicitly limited to potential-driven dynamics. We depart from this regime and consider reference processes described by a multivariate Ornstein-Uhlenbeck process with generic drift matrix $\mathbf{A} \in \mathbb{R}^{d \times d}$. When $\mathbf{A}$ is asymmetric, this corresponds to a non-equilibrium system with non-conservative forces at play: this is important for applications to biological systems, which are naturally exist out-of-equilibrium. In the case of Gaussian marginals, we derive explicit expressions that characterise the solution of both the static and dynamic Schrödinger bridge. For general marginals, we propose mvOU-OTFM, a simulation-free algorithm based on flow and score matching for learning the Schrödinger bridge. In application to a range of problems based on synthetic and real single cell data, we demonstrate that mvOU-OTFM achieves higher accuracy compared to competing methods, whilst being significantly faster to train.

Answer-set programming (ASP) is a successful problem-solving approach in logic-based AI. In ASP, problems are represented as declarative logic programs, and solutions are identified through their answer sets. Equilibrium logic (EL) is a general-purpose nonmonotonic reasoning formalism, based on a monotonic logic called here-and-there logic. EL was basically proposed by Pearce as a foundational framework of ASP. Epistemic specifications (ES) are extensions of ASP-programs with subjective literals. These new modal constructs in the ASP-language make it possible to check whether a regular literal of ASP is true in every (or some) answer-set of a program. ES-programs are interpreted by world-views, which are essentially collections of answer-sets. (Reflexive) autoepistemic logic is a nonmonotonic formalism, modeling self-belief (knowledge) of ideally rational agents. A relatively new semantics for ES is based on a combination of EL and (reflexive) autoepistemic logic. In this paper, we first propose an overarching framework in the epistemic ASP domain. We then establish a correspondence between existing (reflexive) (auto)epistemic equilibrium logics and our easily-adaptable comprehensive framework, building on Pearce's characterisation of answer-sets as equilibrium models. We achieve this by extending Ferraris' work on answer sets for propositional theories to the epistemic case and reveal the relationship between some ES-semantic proposals.

We investigate the power soltera2 is a positive example for C, and of labeled examples for describing description-logic px10 and teslaY are negative examples for C concepts. Specifically, we systematically study the In fact, as it turns out, C is the only EL-concept (up to equivalence) existence and efficient computability of finite characterisations, that fits these three labeled examples. In other words, i.e., finite sets of labeled examples these three labeled examples "uniquely characterize" C within that uniquely characterize a single concept, for a the class of all EL-concepts. This shows that the above three wide variety of description logics between EL and labeled examples are a good choice of examples. Adding any ALCQI,both without an ontology and in the presence additional examples would be redundant. Note, however, that of a DL-Lite ontology. Finite characterisations this depends on the choice of description logic. For instance, are relevant for debugging purposes, and their existence the richer concept language ALC allows for other concept is a necessary condition for exact learnability expressions such as Bicycle Contains.Basket that also fit.

Formal Concept Analysis (FCA) is an approach to creating a conceptual hierarchy in which a \textit{concept lattice} is generated from a \textit{formal context}. That is, a triple consisting of a set of objects, $G$, a set of attributes, $M$, and an incidence relation $I$ on $G \times M$. A \textit{concept} is then modelled as a pair consisting of a set of objects (the \textit{extent}), and a set of shared attributes (the \textit{intent}). Implications in FCA describe how one set of attributes follows from another. The semantics of these implications closely resemble that of logical consequence in classical logic. In that sense, it describes a monotonic conditional. The contributions of this paper are two-fold. First, we introduce a non-monotonic conditional between sets of attributes, which assumes a preference over the set of objects. We show that this conditional gives rise to a consequence relation that is consistent with the postulates for non-monotonicty proposed by Kraus, Lehmann, and Magidor (commonly referred to as the KLM postulates). We argue that our contribution establishes a strong characterisation of non-monotonicity in FCA. Typical concepts represent concepts where the intent aligns with expectations from the extent, allowing for an exception-tolerant view of concepts. To this end, we show that the set of all typical concepts is a meet semi-lattice of the original concept lattice. This notion of typical concepts is a further introduction of KLM-style typicality into FCA, and is foundational towards developing an algebraic structure representing a concept lattice of prototypical concepts.

VMs provide a computing paradigm inspired by the transmission and replication networks of viruses. VMs consist of process units (called hosts) structured by a directed graph whose arcs are called channels and an instruction graph that controls the transmissions of virus objects among hosts. The present work complements our understanding of the computing power of VMs by introducing normal forms; these expressions restrict the features in a given computing model. Some of the features that we restrict in our normal forms include (a) the number of hosts, (b) the number of instructions, and (c) the number of virus objects in each host. After we recall some known results on the computing power of VMs we give our normal forms, such as the size of the loops in the network, proving new characterisations of family of sets, such as the finite sets, semilinear sets, or NRE.

Fish locomotion is enabled by fin rays-actively deformable boney rods, which manipulate the fin to facilitate complex interaction with surrounding water and enable propulsion. Replicating the performance and kinematics of the biological fin ray from an engineering perspective is a challenging task and has not been realised thus far. This work introduces a prototype of a fin ray-inspired origami electromagnetic tendon-driven (FOLD) actuator, designed to emulate the functional dynamics of fish fin rays. Constructed in minutes using origami/kirigami and paper joinery techniques from flat laser-cut polypropylene film, this actuator is low-cost at {\pounds}0.80 (\$1), simple to assemble, and durable for over one million cycles. We leverage its small size to embed eight into two fin membranes of a 135 mm long cuttlefish robot capable of four degrees of freedom swimming. We present an extensive kinematic and swimming parametric study with 1015 data points from 7.6 hours of video, which has been used to determine optimal kinematic parameters and validate theoretical constants observed in aquatic animals. Notably, the study explores the nuanced interplay between undulation patterns, power distribution, and locomotion efficiency, underscoring the potential of the actuator as a model system for the investigation of energy-efficient propulsion and control of bioinspired systems. The versatility of the actuator is further demonstrated by its integration into a fish and a jellyfish.

Many enhancements to Monte-Carlo Tree Search (MCTS) have been proposed over almost two decades of general game playing and other artificial intelligence research. However, our ability to characterise and understand which variants work well or poorly in which games is still lacking. This paper describes work on an initial dataset that we have built to make progress towards such an understanding: 268,386 plays among 61 different agents across 1494 distinct games. We describe a preliminary analysis and work on training predictive models on this dataset, as well as lessons learned and future plans for a new and improved version of the dataset.