Knowledge Representation

We prove The Equivalence Theorem: structurally complete knowledge representation requires exactly four mutually entailing capabilities -- n-ary relationships with attributes, temporal validity, uncertainty quantification, and causal relationships between relationships -- collectively equivalent to treating relationships as first-class objects. Any system implementing one capability necessarily requires all four; any system missing one cannot achieve structural completeness. This result is constructive: we exhibit an Attributed Temporal Causal Hypergraph (ATCH) framework satisfying all four conditions simultaneously. The theorem yields a strict expressiveness hierarchy -- SQL < LPG < TypeDB < ATCH -- with witness queries that are structurally inexpressible at each lower level. We establish computational complexity bounds showing NP-completeness for general queries but polynomial-time tractability for practical query classes (acyclic patterns, bounded-depth causal chains, windowed temporal queries). As direct corollaries, we derive solutions to classical AI problems: the Frame Problem (persistence by default from temporal validity), conflict resolution (contradictions as unresolved metadata with hidden variable discovery), and common sense reasoning (defaults with causal inhibitors). A prototype PostgreSQL extension in C validates practical feasibility within the established complexity bounds.

We present Elenchus, a dialogue system for knowledge base construction grounded in inferentialist semantics, where knowledge engineering is re-conceived as explicitation rather than extraction from expert testimony or textual content. A human expert develops a bilateral position (commitments and denials) about a topic through prover-skeptic dialogue with a large language model (LLM) opponent. The LLM proposes tensions (claims that parts of the position are jointly incoherent) which the expert resolves by retraction, refinement, or contestation. The LLM thus serves as a defeasible derivability oracle whose unreliability is structurally contained by the expert's authority. Our main technical contribution is a mapping from Elenchus dialectical states to material bases in Hlobil and Brandom's NonMonotonic MultiSuccedent (NMMS) logic, satisfying Containment and enabling the elaboration of logical vocabulary that makes explicit the inferential relationships negotiated in the dialectic. We demonstrate the approach on the W3C PROV-O provenance ontology, where a single dialogue session elicits and structures design tensions that a domain expert can articulate, corresponding to decisions documented in a retrospective analysis of the ontology's design. Using pyNMMS, an automated NMMS reasoner, we verify that the structural properties of the resulting material base (nontransitivity, nonmonotonicity, and independence) correspond to specific PROV design rationales, demonstrating end-to-end integration from dialogue through formal reasoning.

ODRL's six set-based operators -- isA, isPartOf, hasPart, isAnyOf, isAllOf, isNoneOf -- depend on external domain knowledge that the W3C specification leaves unspecified. Without it, every cross-dataspace policy comparison defaults to Unknown. We present a denotational semantics that maps each ODRL constraint to the set of knowledge-base concepts satisfying it. Conflict detection reduces to denotation intersection under a three-valued verdict -- Conflict, Compatible, or Unknown -- that is sound under incomplete knowledge. The framework covers all three ODRL composition modes (and, or, xone) and all three semantic domains arising in practice: taxonomic (class subsumption), mereological (part-whole containment), and nominal (identity). For cross-dataspace interoperability, we define order-preserving alignments between knowledge bases and prove two guarantees: conflicts are preserved across different KB standards, and unmapped concepts degrade gracefully to Unknown -- never to false conflicts. A runtime soundness theorem ensures that design-time verdicts hold for all execution contexts. The encoding stays within the decidable EPR fragment of first-order logic. We validate it with 154 benchmarks across six knowledge base families (GeoNames, ISO 3166, W3C DPV, a GDPR-derived taxonomy, BCP 47, and ISO 639-3) and four structural KBs targeting adversarial edge cases. Both the Vampire theorem prover and the Z3 SMT solver agree on all 154 verdicts. A key finding is that exclusive composition (xone) requires strictly stronger KB axioms than conjunction or disjunction: open-world semantics blocks exclusivity even when positive evidence appears to satisfy exactly one branch.

Climate change impacts a broad spectrum of human resources and activities, necessitating the use of climate models to project long-term effects and inform mitigation and adaptation strategies. These models generate multiple datasets by running simulations across various scenarios and configurations, thereby covering a range of potential future outcomes. Currently, researchers rely on traditional search interfaces and APIs to retrieve such datasets, often piecing together information from metadata and community vocabularies. The Climate Change Knowledge Graph is designed to address these challenges by integrating diverse data sources related to climate simulations into a coherent and interoperable knowledge graph. This innovative resource allows for executing complex queries involving climate models, simulations, variables, spatio-temporal domains, and granularities. Developed with input from domain experts, the knowledge graph and its underlying ontology are published with open access license and provide a comprehensive framework that enhances the exploration of climate data, facilitating more informed decision-making in addressing climate change issues.

Knowledge representation formalisms are aimed to represent general conceptual information and are typically used in the construction of the knowledge base of reasoning agent. A knowledge base can be thought of as representing the beliefs of such an agent. Like a child, a strong-AI (AGI) robot would have to learn through input and experiences, constantly progressing and advancing its abilities over time. Both with statistical AI generated by neural networks we need also the concept of causality of events traduced into directionality of logic entailments and deductions in order to give to robots the emulation of human intelligence. Moreover, by using the axioms we can guarantee the controlled security about robot's actions based on logic inferences. For AGI robots we consider the 4-valued Belnap's bilattice of truth-values with knowledge ordering as well, where the value "unknown" is the bottom value, the sentences with this value are indeed unknown facts, that is, the missed knowledge in the AGI robots. Thus, these unknown facts are not part of the robot's knowledge database, and by learn through input and experiences, the robot's knowledge would be naturally expanded over time. Consequently, this phenomena can be represented by the Closed Knowledge Assumption and Logic Inference provided by this paper. Moreover, the truth-value "inconsistent", which is the top value in the knowledge ordering of Belnap's bilattice, is necessary for strong-AI robots to be able to support such inconsistent information and paradoxes, like Liar paradox, during deduction processes.

This paper presents a novel approach for ontological heterogeneity that draws heavily from Carnapian-Goguenism, as presented by Kutz, Mossakowski and Lücke (2010). The approach is provisionally designated da Costian-Tarskianism, named after da Costa's Principle of Tolerance in Mathematics and after Alfred Tarski's work on the concept of a consequence operator. The approach is based on the machinery of consequence systems, as developed by Carnielli et al. (2008) and Citkin and Muravitsky (2022), and it introduces the idea of an extended consequence system, which is a consequence system extended with ontological axioms. The paper also defines the concept of an extended development graph, which is a graph structure that allows ontologies to be related via morphisms of extended consequence systems, and additionally via other operations such as fibring and splitting. Finally, we discuss the implications of this approach for the field of applied ontology and suggest directions for future research.

Agent memory systems must accommodate continuously growing information while supporting efficient, context-aware retrieval for downstream tasks. Abstraction is essential for scaling agent memory, yet it often comes at the cost of specificity, obscuring the fine-grained details required for effective reasoning. We introduce Memora, a harmonic memory representation that structurally balances abstraction and specificity. Memora organizes information via its primary abstractions that index concrete memory values and consolidate related updates into unified memory entries, while cue anchors expand retrieval access across diverse aspects of the memory and connect related memories. Building on this structure, we employ a retrieval policy that actively exploits these memory connections to retrieve relevant information beyond direct semantic similarity. Theoretically, we show that standard Retrieval-Augmented Generation (RAG) and Knowledge Graph (KG)-based memory systems emerge as special cases of our framework. Empirically, Memora establishes a new state-of-the-art on the LoCoMo and LongMemEval benchmarks, demonstrating better retrieval relevance and reasoning effectiveness as memory scales.

Language models (LMs) increasingly drive real-world applications that require world knowledge. However, the internal processes through which models turn data into representations of knowledge and beliefs about the world are poorly understood. To facilitate such studies, we present LMEnt, a suite including (1) a knowledge-rich pretraining corpus, fully annotated with entity mentions based on Wikipedia, (2) an entity-based retrieval method over pretraining data that outperforms existing tools by as much as 80.4%, and (3) 12 pretrained LMs with up to 1B parameters and 4K intermediate checkpoints, with comparable performance to popular open-source models on knowledge tasks. Together, these resources provide a controlled environment for analyzing connections between entity mentions in pretraining data and downstream performance. We show the utility of LMEnt by studying knowledge acquisition over training, finding that entity co-occurrence and mention forms-which are difficult to study with existing tools-affect learning trends. Moreover, as LMs form stronger associations between entities, their facts are harder to edit in-context, whereas inconsistencies in model predictions over training are indicative of editing success. We release LMEnt to support studies of knowledge in LMs, including knowledge representations, plasticity, editing, attribution, hallucinations, and learning dynamics.

After learning a multiple paired-association (MPA) navigation task, rodents can rapidly learn new cue-location associations after a single exposure, a phenomenon proposed to be facilitated by cognitive schemas. However, it remains unclear what schemas support this behavior and how they could be implemented in biological neural circuits. Here, we identify a set of schemas sufficient for gradual then one-shot paired-association navigation, and implement them in a fully neural agent using biologically plausible plasticity rules. The agent gradually acquires a low-dimensional spatial metric representation using a path-integration based temporal-difference error, enabling self-localization across different environments. It also contains a memory network that forms one-shot associations between sensory cues and goal locations, implemented using reward-modulated exploratory Hebbian (EH) plasticity. A third network performs vector subtraction between the agent's current and goal location to compute goal-directed actions. Supplementing these schemas with an actor-critic enables one-shot navigation past obstacles. Lastly, learning a working-memory gating mechanism using the temporal-difference error enables one-shot learning even with brief cue and distractor presentation. The model reproduces key behavioral features of rodent learning in the MPA task and generates testable predictions about the neural mechanisms underlying schema-based one-shot learning.