Toward a Functional Geometric Algebra for Natural Language Semantics

Distributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable empirical success, yet they face persistent structural limitations in compositional semantics, type sensitivity, and interpretability. I argue in this paper that geometric algebra (GA) -- specifically, Clifford algebras -- provides a mathematically superior foundation for semantic representation, and that a Functional Geometric Algebra (FGA) framework extends GA toward a typed, compositional semantics capable of supporting inference, transformation, and interpretability while retaining full compatibility with distributional learning and modern neural architectures. I develop the formal foundations, identify three core capabilities that GA provides and linear algebra does not, present a detailed worked example illustrating operator-level semantic contrasts, and show how GA-based operations already implicit in current transformer architectures can be made explicit and extended. The central claim is not merely increased dimensionality but increased structural organization: GA expands an $n$-dimensional embedding space into a $2^n$ multivector algebra where base semantic concepts and their higher-order interactions are represented within a single, principled algebraic framework.

Frictive Policy Optimization for LLMs: Epistemic Intervention, Risk-Sensitive Control, and Reflective Alignment

We propose Frictive Policy Optimization (FPO), a framework for learning language model policies that regulate not only what to say, but when and how to intervene in order to manage epistemic and normative risk. Unlike standard alignment methods that optimize surface-level preference or task utility, FPO treats clarification, verification, challenge, redirection, and refusal as explicit control actions whose purpose is to shape the evolution of belief, commitment, and uncertainty over time. We formalize alignment as a risk-sensitive epistemic control problem in which intervention decisions are selected based on their expected effect on downstream epistemic quality rather than on immediate reward alone. We introduce a compact taxonomy of frictive interventions, a structured friction functional that operationalizes multiple alignment failure modes, and a unified family of FPO methods spanning reward shaping, preference pairing, group-relative ranking, and risk-conditioned trust regions. We further propose an evaluation framework that measures epistemic competence directly through clarification behavior, calibration, contradiction repair, refusal proportionality, and information efficiency. Together, these results provide a formal and algorithmic foundation for learning agents that are aligned not only in outcome, but in epistemic conduct.

Distributed Partial Information Puzzles: Examining Common Ground Construction Under Epistemic Asymmetry

Establishing common ground, a shared set of beliefs and mutually recognized facts, is fundamental to collaboration, yet remains a challenge for current AI systems, especially in multimodal, multiparty settings, where the collaborators bring different information to the table. We introduce the Distributed Partial Information Puzzle (DPIP), a collaborative construction task that elicits rich multimodal communication under epistemic asymmetry. We present a multimodal dataset of these interactions, annotated and temporally aligned across speech, gesture, and action modalities to support reasoning over propositional content and belief dynamics. We then evaluate two paradigms for modeling common ground (CG): (1) state-of-the-art large language models (LLMs), prompted to infer shared beliefs from multimodal updates, and (2) an axiomatic pipeline grounded in Dynamic Epistemic Logic (DEL) that incrementally performs the same task. Results on the annotated DPIP data indicate that it poses a challenge to modern LLMs' abilities to track both task progression and belief state.

Dynamic Epistemic Friction in Dialogue

Recent developments in aligning Large Language Models (LLMs) with human preferences have significantly enhanced their utility in human-AI collaborative scenarios. However, such approaches often neglect the critical role of "epistemic friction," or the inherent resistance encountered when updating beliefs in response to new, conflicting, or ambiguous information. In this paper, we define dynamic epistemic friction as the resistance to epistemic integration, characterized by the misalignment between an agent's current belief state and new propositions supported by external evidence. We position this within the framework of Dynamic Epistemic Logic (Van Benthem and Pacuit, 2011), where friction emerges as nontrivial belief-revision during the interaction. We then present analyses from a situated collaborative task that demonstrate how this model of epistemic friction can effectively predict belief updates in dialogues, and we subsequently discuss how the model of belief alignment as a measure of epistemic resistance or friction can naturally be made more sophisticated to accommodate the complexities of real-world dialogue scenarios.

TRACE: Real-Time Multimodal Common Ground Tracking in Situated Collaborative Dialogues

We present TRACE, a novel system for live *common ground* tracking in situated collaborative tasks. With a focus on fast, real-time performance, TRACE tracks the speech, actions, gestures, and visual attention of participants, uses these multimodal inputs to determine the set of task-relevant propositions that have been raised as the dialogue progresses, and tracks the group's epistemic position and beliefs toward them as the task unfolds. Amid increased interest in AI systems that can mediate collaborations, TRACE represents an important step forward for agents that can engage with multiparty, multimodal discourse.

Speech Is Not Enough: Interpreting Nonverbal Indicators of Common Knowledge and Engagement

Our goal is to develop an AI Partner that can provide support for group problem solving and social dynamics. In multi-party working group environments, multimodal analytics is crucial for identifying non-verbal interactions of group members. In conjunction with their verbal participation, this creates an holistic understanding of collaboration and engagement that provides necessary context for the AI Partner. In this demo, we illustrate our present capabilities at detecting and tracking nonverbal behavior in student task-oriented interactions in the classroom, and the implications for tracking common ground and engagement.

Linguistically Conditioned Semantic Textual Similarity

Semantic textual similarity (STS) is a fundamental NLP task that measures the semantic similarity between a pair of sentences. In order to reduce the inherent ambiguity posed from the sentences, a recent work called Conditional STS (C-STS) has been proposed to measure the sentences' similarity conditioned on a certain aspect. Despite the popularity of C-STS, we find that the current C-STS dataset suffers from various issues that could impede proper evaluation on this task. In this paper, we reannotate the C-STS validation set and observe an annotator discrepancy on 55% of the instances resulting from the annotation errors in the original label, ill-defined conditions, and the lack of clarity in the task definition. After a thorough dataset analysis, we improve the C-STS task by leveraging the models' capability to understand the conditions under a QA task setting. With the generated answers, we present an automatic error identification pipeline that is able to identify annotation errors from the C-STS data with over 80% F1 score. We also propose a new method that largely improves the performance over baselines on the C-STS data by training the models with the answers. Finally we discuss the conditionality annotation based on the typed-feature structure (TFS) of entity types. We show in examples that the TFS is able to provide a linguistic foundation for constructing C-STS data with new conditions.

Computational Thought Experiments for a More Rigorous Philosophy and Science of the Mind

We offer philosophical motivations for a method we call Virtual World Cognitive Science (VW CogSci), in which researchers use virtual embodied agents that are embedded in virtual worlds to explore questions in the field of Cognitive Science. We focus on questions about mental and linguistic representation and the ways that such computational modeling can add rigor to philosophical thought experiments, as well as the terminology used in the scientific study of such representations. We find that this method forces researchers to take a god's-eye view when describing dynamical relationships between entities in minds and entities in an environment in a way that eliminates the need for problematic talk of belief and concept types, such as the belief that cats are silly, and the concept CAT, while preserving belief and concept tokens in individual cognizers' minds. We conclude with some further key advantages of VW CogSci for the scientific study of mental and linguistic representation and for Cognitive Science more broadly.

ChainNet: Structured Metaphor and Metonymy in WordNet

The senses of a word exhibit rich internal structure. In a typical lexicon, this structure is overlooked: a word's senses are encoded as a list without inter-sense relations. We present ChainNet, a lexical resource which for the first time explicitly identifies these structures. ChainNet expresses how senses in the Open English Wordnet are derived from one another: every nominal sense of a word is either connected to another sense by metaphor or metonymy, or is disconnected in the case of homonymy. Because WordNet senses are linked to resources which capture information about their meaning, ChainNet represents the first dataset of grounded metaphor and metonymy.

Common Ground Tracking in Multimodal Dialogue

Within Dialogue Modeling research in AI and NLP, considerable attention has been spent on ``dialogue state tracking'' (DST), which is the ability to update the representations of the speaker's needs at each turn in the dialogue by taking into account the past dialogue moves and history. Less studied but just as important to dialogue modeling, however, is ``common ground tracking'' (CGT), which identifies the shared belief space held by all of the participants in a task-oriented dialogue: the task-relevant propositions all participants accept as true. In this paper we present a method for automatically identifying the current set of shared beliefs and ``questions under discussion'' (QUDs) of a group with a shared goal. We annotate a dataset of multimodal interactions in a shared physical space with speech transcriptions, prosodic features, gestures, actions, and facets of collaboration, and operationalize these features for use in a deep neural model to predict moves toward construction of common ground. Model outputs cascade into a set of formal closure rules derived from situated evidence and belief axioms and update operations. We empirically assess the contribution of each feature type toward successful construction of common ground relative to ground truth, establishing a benchmark in this novel, challenging task.