Belief systems are often treated as globally consistent sets of propositions or as scalar-valued probability distributions. Such representations tend to obscure the internal structure of belief, conflate external credibility with internal coherence, and preclude the modeling of fragmented or contradictory epistemic states. This paper introduces a minimal formalism for belief systems as directed, weighted graphs. In this framework, nodes represent individual beliefs, edges encode epistemic relationships (e.g., support or contradiction), and two distinct functions assign each belief a credibility (reflecting source trust) and a confidence (derived from internal structural support). Unlike classical probabilistic models, our approach does not assume prior coherence or require belief updating. Unlike logical and argumentation-based frameworks, it supports fine-grained structural representation without committing to binary justification status or deductive closure. The model is purely static and deliberately excludes inference or revision procedures. Its aim is to provide a foundational substrate for analyzing the internal organization of belief systems, including coherence conditions, epistemic tensions, and representational limits. By distinguishing belief structure from belief strength, this formalism enables a richer classification of epistemic states than existing probabilistic, logical, or argumentation-based approaches.

Robot-assisted surgery has revolutionized the healthcare industry by providing surgeons with greater precision, reducing invasiveness, and improving patient outcomes. However, the success of these surgeries depends heavily on the robotic system ability to accurately interpret the intentions of the surgical trainee or even surgeons. One critical factor impacting intent recognition is the cognitive workload experienced during the procedure. In our recent research project, we are building an intelligent adaptive system to monitor cognitive workload and improve learning outcomes in robot-assisted surgery. The project will focus on achieving a semantic understanding of surgeon intents and monitoring their mental state through an intelligent multi-modal assistive framework. This system will utilize brain activity, heart rate, muscle activity, and eye tracking to enhance intent recognition, even in mentally demanding situations. By improving the robotic system ability to interpret the surgeons intentions, we can further enhance the benefits of robot-assisted surgery and improve surgery outcomes.

Intelligence-biological, artificial, or collective-requires structural coherence across recursive reasoning processes to scale effectively. As complex systems grow, coherence becomes fragile unless a higher-order structure ensures semantic consistency. This paper introduces the Recursive Coherence Principle (RCP): a foundational constraint stating that for any reasoning system of order N, composed of systems operating over conceptual spaces of order N-1, semantic coherence is preserved only by a recursively evaluable generalization operator that spans and aligns those lower-order conceptual spaces. Crucially, this coherence enables structural alignment. Without recursive coherence, no system can reliably preserve goals, meanings, or reasoning consistency at scale. We formally define the Functional Model of Intelligence (FMI) as the only known operator capable of satisfying the RCP at any scale. The FMI is a minimal, composable architecture with internal functions (evaluation, modeling, adaptation, stability, decomposition, bridging) and external functions (storage, recall, System 1 and System 2 reasoning) vital for preserving semantic structure across inference and coordination layers. We prove that any system lacking the FMI will experience recursive coherence breakdown as it scales, arguing that common AI issues like misalignment, hallucination, and instability are symptoms of this structural coherence loss. Unlike other foundational principles, RCP uniquely captures the internal, recursive dynamics needed for coherent, alignable intelligence, modeling semantic coherence under recursion. This work significantly impacts AI alignment, advocating a shift from behavioral constraints to structural coherence, and offers a pathway for safely generalizable, robustly coherent AI at scale.

Dialectical systems are a mathematical formalism for modeling an agent updating a knowledge base seeking consistency. Introduced in the 1970s by Roberto Magari, they were originally conceived to capture how a working mathematician or a research community refines beliefs in the pursuit of truth. Dialectical systems also serve as natural models for the belief change of an automated agent, offering a unifying, computable framework for dynamic belief management. The literature distinguishes three main models of dialectical systems: (d-)dialectical systems based on revising beliefs when they are seen to be inconsistent, p-dialectical systems based on revising beliefs based on finding a counterexample, and q-dialectical systems which can do both. We answer an open problem in the literature by proving that q-dialectical systems are strictly more powerful than p-dialectical systems, which are themselves known to be strictly stronger than (d-)dialectical systems. This result highlights the complementary roles of counterexample and contradiction in automated belief revision, and thus also in the reasoning processes of mathematicians and research communities.

Within the formal setting of the Lockean thesis, an agent belief set is defined in terms of degrees of confidence and these are described in probabilistic terms. This approach is of established interest, notwithstanding some limitations that make its use troublesome in some contexts, like, for instance, in belief change theory. Precisely, Lockean belief sets are not generally closed under (classical) logical deduction. The aim of the present paper is twofold: on one side we provide two characterizations of those belief sets that are closed under classical logic deduction, and on the other we propose an approach to probabilistic update that allows us for a minimal revision of those beliefs, i.e., a revision obtained by making the fewest possible changes to the existing belief set while still accommodating the new information. In particular, we show how we can deductively close a belief set via a minimal revision.

The belief revision field is opulent in new proposals and indigent in analyses of existing approaches. Much work hinge on postulates, employed as syntactic characterizations: some revision mechanism is equivalent to some properties. Postulates constraint specific revision instances: certain revisions update certain beliefs in a certain way. As an example, if the revision is consistent with the current beliefs, it is incorporated with no other change. A postulate like this tells what revisions must do and neglect what they can do. Can they reach a certain state of beliefs? Can they reach all possible states of beliefs? Can they reach all possible states of beliefs from no previous belief? Can they reach a dogmatic state of beliefs, where everything not believed is impossible? Can they make two conditions equally believed? An application where every possible state of beliefs is sensible requires each state of beliefs to be reachable. An application where conditions may be equally believed requires such a belief state to be reachable. An application where beliefs may become dogmatic requires a way to make them dogmatic. Such doxastic states need to be reached in a way or another. Not in specific way, as dictated by a typical belief revision postulate. This is an ability, not a constraint: the ability of being plastic, equating, dogmatic. Amnesic, correcting, believer, damascan, learnable are other abilities. Each revision mechanism owns some of these abilities and lacks the others: lexicographic, natural, restrained, very radical, full meet, radical, severe, moderate severe, deep severe, plain severe and deep severe revisions, each of these revisions is proved to possess certain abilities.

We introduce a mathematically rigorous framework for an artificial intelligence system composed of probabilistic agents evolving through structured competition and belief revision. The architecture, grounded in Bayesian inference, measure theory, and population dynamics, defines agent fitness as a function of alignment with a fixed external oracle representing ground truth. Agents compete in a discrete-time environment, adjusting posterior beliefs through observed outcomes, with higher-rated agents reproducing and lower-rated agents undergoing extinction. Ratings are updated via pairwise truth-aligned utility comparisons, and belief updates preserve measurable consistency and stochastic convergence. We introduce hash-based cryptographic identity commitments to ensure traceability, alongside causal inference operators using do-calculus. Formal theorems on convergence, robustness, and evolutionary stability are provided. The system establishes truth as an evolutionary attractor, demonstrating that verifiable knowledge arises from adversarial epistemic pressure within a computable, self-regulating swarm.

This paper outlines a comprehensive theoretical and architectural framework for constructing epistemically grounded artificial intelligence systems capable of propositional commitment, metacognitive reasoning, contradiction detection, and normative truth maintenance. Moving beyond the constraints of stochastic language generation, we propose a model in which artificial agents engage in structured, rule-governed reasoning that adheres to explicit epistemic norms. The approach integrates insights from epistemology, formal logic, inferential semantics, knowledge graph structuring, probabilistic justification, and immutable blockchain evidence to create systems that do not merely simulate knowledge, but operate under explicit, verifiable constraints on belief, justification, and truth. We begin with an analysis of epistemic norms in artificial reasoning, contrasting evi-dentialist, Bayesian, and logical foundations, and establishing a requirement for internal consistency and constraint against falsehood. Central to the proposed system is a prohibition against internal deception: no model component may assert what it internally contradicts.

The crisis of epistemic overload in modern scientific inquiry has exposed a critical deficiency in how truth claims are assessed, validated, and integrated across time and domain. The exponential growth in peer-reviewed publications, accompanied by inconsistent replication rates, entrenched citation biases, and the sociological entanglements of scientific authorship, has rendered traditional mechanisms of epistemic filtering increasingly obsolete. Simultaneously, artificial intelligence--while having demonstrated capacity in data correlation and language generation--remains fundamentally ill-equipped to perform rigorous epistemic reasoning. This gap is not merely technical but conceptual: current AI systems lack any principled framework for evaluating the truth-promoting value of claims, discerning authoritative sources, or understanding belief as a structured probabilistic relation between agents, claims, and contexts. The present work introduces a formal architecture--Bayesian Epistemology with Weighted Authority (BEW A)--which systematically encodes the logic of belief formation, update, and decay, guided by the core axioms of Bayesian rationality, tempered by structural mechanisms for authority weighting, replication scoring, and temporal reassessment.

People regularly make inferences about objects in the world that they cannot see by flexibly integrating information from multiple sources: auditory and visual cues, language, and our prior beliefs and knowledge about the scene. How are we able to so flexibly integrate many sources of information to make sense of the world around us, even if we have no direct knowledge? In this work, we propose a neurosymbolic model that uses neural networks to parse open-ended multi-modal inputs and then applies a Bayesian model to integrate different sources of information to evaluate different hypotheses. We evaluate our model with a novel object guessing game called "What's in the Box?" where humans and models watch a video clip of an experimenter shaking boxes and then try to guess the objects inside the boxes. Through a human experiment, we show that our model correlates strongly with human judgments, whereas unimodal ablated models and large multi-modal neural model baselines showed poor correlation.