Logic programming (LP) is typically understood through operational semantics (e.g., SLD-resolution) or model-theoretic interpretations (e.g., the least Herbrand model). This paper introduces a novel perspective on LP by defining a ``support'' relation that explicates what a program ``knows''. This interpretation is shown to express classical and intuitionistic logic, as well as an intermediate logic, depending on certain choices regarding LP and the meanings of disjunction and negation. These results are formalized using the idea of base-extension semantics within proof-theoretic semantics. Our approach offers new insights into the logical foundations of LP and has potential applications in knowledge representation, automated reasoning, and formal verification.

Understanding how information is represented in neural networks is a fundamental challenge in both neuroscience and artificial intelligence. Despite their nonlinear architectures, recent evidence suggests that neural networks encode features in superposition, meaning that input concepts are linearly overlaid within the network's representations. We present a perspective that explains this phenomenon and provides a foundation for extracting interpretable representations from neural activations. Our theoretical framework consists of three steps: (1) Identifiability theory shows that neural networks trained for classification recover latent features up to a linear transformation. (2) Sparse coding methods can extract disentangled features from these representations by leveraging principles from compressed sensing. (3) Quantitative interpretability metrics provide a means to assess the success of these methods, ensuring that extracted features align with human-interpretable concepts. By bridging insights from theoretical neuroscience, representation learning, and interpretability research, we propose an emerging perspective on understanding neural representations in both artificial and biological systems. Our arguments have implications for neural coding theories, AI transparency, and the broader goal of making deep learning models more interpretable.

When studying political communication, combining the information from text, audio, and video signals promises to reflect the richness of human communication more comprehensively than confining it to individual modalities alone. However, its heterogeneity, connectedness, and interaction are challenging to address when modeling such multimodal data. We argue that aligning the respective modalities can be an essential step in entirely using the potential of multimodal data because it informs the model with human understanding. Taking care of the data-generating process of multimodal data, our framework proposes four principles to organize alignment and, thus, address the challenges of multimodal data. We illustrate the utility of these principles by analyzing how German MPs address members of the far-right AfD in their speeches and predicting the tone of video advertising in the context of the 2020 US presidential race. Our paper offers important insights to all keen to analyze multimodal data effectively.

Our research investigates vibrotactile perception in four prosthetic hands with distinct kinematics and mechanical characteristics. We found that rigid and simple socket-based prosthetic devices can transmit tactile information and surprisingly enable users to identify the stimulated finger with high reliability. This ability decreases with more advanced prosthetic hands with additional articulations and softer mechanics. We conducted experiments to understand the underlying mechanisms. We assessed a prosthetic user's ability to discriminate finger contacts based on vibrations transmitted through the four prosthetic hands. We also performed numerical and mechanical vibration tests on the prostheses and used a machine learning classifier to identify the contacted finger. Our results show that simpler and rigid prosthetic hands facilitate contact discrimination (for instance, a user of a purely cosmetic hand can distinguish a contact on the index finger from other fingers with 83% accuracy), but all tested hands, including soft advanced ones, performed above chance level. Despite advanced hands reducing vibration transmission, a machine learning algorithm still exceeded human performance in discriminating finger contacts. These findings suggest the potential for enhancing vibrotactile feedback in advanced prosthetic hands and lay the groundwork for future integration of such feedback in prosthetic devices.

Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in different groups are distinguishable based on structural node characteristics such as centrality and clustering coefficient. We demonstrate, using various network datasets and random network models, that a classifier can be trained to accurately predict the network category of a given node (without seeing the whole network), implying that complex networks display distinct structural patterns even at the node level. Finally, we discuss two applications of node-level network classification: (i) whole-network classification from small samples of nodes, and (ii) network bootstrapping.

Quantum mechanical systems exist as superpositions of complementary states that collapse to classical, concrete states upon becoming entangled with the measurement apparatus of observer-participants. A musical composition and its performance constitute a quantum system. Historically, conventional musical notation has presented the appearance of a composition as a deterministic, concrete entity, with interpretation approached as an extrinsic act. This historical perspective inhabits a subspace of the available quantum space. A quantum musical system unifies the composition, instruments, situated performance and perception as a superposition of musical events that collapses to concrete musical events via the interactions and perceptions of performers and audience. A composer captures superposed musical events via implicit or explicit conditional event probabilities, and human and/or machine performers create music by collapsing interrelated probabilities to zeros and ones via observer-participancy.

An accepted belief is a proposition considered likely enough by an agent, to be inferred from as if it were true. This paper bridges the gap between probabilistic and logical representations of accepted beliefs. To this end, natural properties of relations on propositions, describing relative strength of belief are augmented with some conditions ensuring that accepted beliefs form a deductively closed set. This requirement turns out to be very restrictive. In particular, it is shown that the sets of accepted belief of an agent can always be derived from a family of possibility rankings of states. An agent accepts a proposition in a given context if this proposition is considered more possible than its negation in this context, for all possibility rankings in the family. These results are closely connected to the non-monotonic 'preferential' inference system of Kraus, Lehmann and Magidor and the so-called plausibility functions of Friedman and Halpern. The extent to which probability theory is compatible with acceptance relations is laid bare. A solution to the lottery paradox, which is considered as a major impediment to the use of non-monotonic inference is proposed using a special kind of probabilities (called lexicographic, or big-stepped). The setting of acceptance relations also proposes another way of approaching the theory of belief change after the works of Gärdenfors and colleagues. Our view considers the acceptance relation as a primitive object from which belief sets are derived in various contexts.

Non-deductive reasoning systems are often representation dependent: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For example, the principle of maximum entropyhas been subjected to much criticism due to its representation dependence. There has, however, been almost no work investigating representation dependence. In this paper, we formalize this notion and show that it is not a problem specific to maximum entropy. In fact, we show that any representation-independent probabilistic inference procedure that ignores irrelevant information is essentially entailment, in a precise sense. Moreover, we show that representation independence is incompatible with even a weak default assumption of independence. We then show that invariance under a restricted class of representation changes can form a reasonable compromise between representation independence and other desiderata, and provide a construction of a family of inference procedures that provides such restricted representation independence, using relative entropy.