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An Epistemic Perspective on Agent Awareness

Conference: AAAI 2026 arXiv: 2511.05977v1 Code: None Area: Other Keywords: epistemic logic, agent awareness, de re/de dicto, 2D semantics, completeness proof

TL;DR

This paper is the first to treat agent awareness as a form of knowledge, distinguishing two awareness modalities — de re (concerning physical objects) and de dicto (concerning concepts/descriptions) — and proposes a sound and complete logical system grounded in 2D semantics to characterize the interaction between these two modalities and the standard "factual knowledge" modality.

Background & Motivation

As AI agents increasingly participate in high-stakes decisions affecting human lives, correct decision-making often depends on awareness of the existence of other agents. For example: - Combat robots must minimize casualties upon becoming aware of civilians - Autonomous vehicles must stop at yield signs upon becoming aware of oncoming traffic - Medical AI must provide assistance upon becoming aware that someone is ill - Value-aligned robots must apologize upon becoming aware that someone has been offended

However, "awareness" is an ambiguous term treated as a standalone concept in existing literature. The Cambridge Dictionary defines it as "knowledge that something exists," implying an epistemic interpretation. This paper provides a formal account of awareness from precisely this epistemic perspective.

Core Problem

  1. How can two distinct forms of agent awareness be formally distinguished?
  2. How can a logical system be constructed to reason about both forms of awareness and their relationship to standard knowledge?
  3. Is such a logical system sound and complete?

Method

Overall Architecture

The paper constructs an epistemic logic system based on egocentric logic and 2D semantics, comprising three modal operators:

  • K φ ("knows φ about herself"): standard self-knowledge modality, expressing that an agent knows property φ about itself
  • R φ ("de re aware"): de re awareness modality, expressing that an agent, as a physical object, is aware of some agent with property φ
  • D φ ("de dicto aware"): de dicto awareness modality, expressing that an agent is aware, at the conceptual level, of some agent with property φ

Key Designs

  1. Dual-Modality Distinction between De Re and De Dicto Awareness:

    • Function: Decomposes "awareness" into two essentially distinct modal operators \(R\varphi\) (de re) and \(D\varphi\) (de dicto), forming a three-modality epistemic system together with the self-knowledge operator \(K\varphi\)
    • Mechanism: \(R\varphi\) expresses that an agent, as a physical object, perceives some agent with property \(\varphi\) — that agent holds \(\varphi\) in the current world and exists in all indistinguishable worlds ("seen but not identified"); \(D\varphi\) expresses that in every indistinguishable world there exists at least one agent with property \(\varphi\) ("the concept is known but the referent is unidentified"). Illustrative example: Ann seeing an unmarked police car is de re awareness; receiving a WeRide text message and knowing an autonomous vehicle is nearby is de dicto awareness
    • Design Motivation: Existing epistemic logics typically treat awareness as a single concept and cannot distinguish between "perceiving a physical object without knowing its properties" and "possessing a concept without being able to locate the referent." The dual-modality distinction fills this expressive gap

  2. Epistemic Models Based on 2D Semantics and the Ternary Satisfaction Relation:

    • Function: Provides a rigorous model-theoretic semantic foundation for the three-modality system
    • Mechanism: An epistemic model is defined as a quintuple \((W, A, P, {\sim}, \pi)\), where \(P \subseteq A \times W\) is an existence relation (specifying in which worlds an agent appears) and \(\sim_a\) is an indistinguishability equivalence relation. The key innovation is the adoption of a ternary satisfaction relation \(w, a \Vdash \varphi\) (world \(w\), agent \(a\), formula \(\varphi\)), drawing on 2D semantics to simultaneously capture information along both the world dimension and the agent dimension, so that the semantics of \(R\) and \(D\) can naturally quantify over an agent's cross-world existence and property-holding respectively
    • Design Motivation: The binary satisfaction relation of standard Kripke semantics cannot simultaneously track "which agent is perceived" and "in which world it is perceived." The two-dimensional structure of 2D semantics precisely matches the requirements of the de re/de dicto distinction

  3. Axiomatic System and Completeness:

    • Function: Provides a sound and complete deductive system for the three-modality epistemic logic
    • Mechanism: The system comprises 8 axioms and 4 inference rules. Core axioms include: \(K\varphi \to \varphi\) (Truth); \(\varphi \to R\varphi\) and \(K\varphi \to D\varphi\) (Self-Awareness, connecting the three operators); \(D\varphi \to KD\varphi\) (introspection of de dicto awareness); \(R(\varphi \lor \psi) \to R\varphi \lor R\psi\) (disjunctivity of de re, reflecting its "directed at a concrete object" character); \(D(R\varphi \lor D\varphi) \to D\varphi\) (General Awareness, unifying the two forms of awareness). Inference rules include Modus Ponens, Necessitation (\(\varphi \vdash K\varphi\)), and Monotonicity rules for \(D\) and \(R\)
    • Design Motivation: The axioms characterize the hierarchical relationships among \(K\), \(R\), and \(D\) — \(K\) entails \(D\), self-instantiated properties entail \(R\) — while de re is disjunctive and de dicto is not, precisely reflecting the structural asymmetry between the two forms of awareness

Loss & Training

This paper is a purely theoretical/formal verification work involving no loss functions or training strategies. The core technical contribution is the completeness proof, which employs an enhanced "matrix" technique:

  • Frame Construction: Frames are defined as partially constructed models containing an explicit awareness relation ↝
  • λ-assured Sets: The notion of λ-assured is introduced to handle the "ghost spy" phenomenon in model construction — only agents that are absolutely undetectable are consistent with a dataset
  • Complete Frames: Finite frames are incrementally extended (by adding new worlds/agents) to satisfy five categories of completeness requirements
  • Canonical Model: A canonical model is constructed from complete frames, and the Truth Lemma is proved (\(\varphi \in X^a_w \iff w, a \Vdash \varphi\))

Key Experimental Results

This paper is purely theoretical; the main results are two theorems:

Theorem Statement Significance
Theorem 1 (Soundness) If \(\vdash\varphi\), then \(w, a \Vdash \varphi\) for all worlds \(w\) and agents \(a\) in every epistemic model The axiomatic system derives no false conclusions
Theorem 2 (Strong Completeness) If \(X \nvdash \varphi\), then there exists an epistemic model in which all formulas in \(X\) are true but \(\varphi\) is false The axiomatic system suffices to derive all semantically valid formulas

Ablation Study

As a theoretical work, the paper validates the necessity of each axiom through the following observations:

  • The justification for the Self-Awareness axiom follows from the model design: every agent necessarily exists in all worlds in which it appears
  • Introspection of Awareness holds only for \(D\) (de dicto) and not in general for \(R\) (de re) — a significant asymmetry
  • Disjunctivity holds only for \(R\) (guaranteed by the existential quantifier structure of its semantics) and not for \(D\)
  • The General Awareness axiom connects \(R\) and \(D\), named after the "general awareness" abbreviation \(A\varphi = R\varphi \lor D\varphi\)

Highlights & Insights

  1. Conceptual Innovation: This is the first work to recast awareness from an independent concept into a subtype of knowledge — a philosophically more elegant and practically more operational perspective
  2. Precise Formalization of De Re/De Dicto: The paper captures a distinction that inherently requires quantification using a quantifier-free modal logic rather than first-order epistemic logic
  3. Well-Crafted Running Example: The scenario involving Ann, WeRide, and the police car renders abstract logical concepts intuitive
  4. Introduction of λ-assured Sets: Elegantly addresses the technical difficulty of "loss of awareness when new worlds are added" during frame construction
  5. Innovation in the Matrix Technique for Completeness: Extends existing techniques by incorporating the awareness relation and row labels, resolving the "decoupling" of worlds and agents inherent in 2D semantics

Limitations & Future Work

  1. Absence of Computational Complexity Analysis: The paper does not discuss the complexity of the modal satisfiability problem or model checking
  2. Static Logic: Dynamic updates are not considered (e.g., dynamic logic extensions for changes in awareness due to information acquisition or forgetting)
  3. Transworld Identity Assumption: The paper assumes transworld identity, which is itself a contested topic in the philosophy of language
  4. Single-Agent Perspective: Although the model contains multiple agents, the modalities \(K\), \(R\), and \(D\) all pertain to properties of the "current agent," without directly characterizing multi-agent interaction reasoning
  5. Lack of Applied Validation: The paper does not demonstrate the application of this logical system in real AI systems (e.g., autonomous driving decisions) or a model checking implementation
  6. Integration with Probability/Uncertainty: In practice, awareness is often gradual rather than binary, which two-valued logic cannot fully capture
Work Focus Distinction from This Paper
Fagin & Halpern (1987) Conceptual awareness (awareness of concepts) This paper concerns agent awareness (awareness of other agents)
Board & Chung (2021, 2022) Object-based unawareness Does not distinguish de re/de dicto
Epstein, Naumov & Tao (2023) De re/de dicto "know who" Uses quantifiers; cannot express awareness
Epistemic Logic with Assignments (Wang & Seligman 2018) General epistemic logic with assignments More general but not specific to awareness
Jiang & Naumov (2025) De re/de dicto in data anonymization Focuses on dataset property inference, not awareness
Naumov & Tao (2023) Completeness of "telling apart" modality No awareness modality; this paper builds on their matrix technique with significant extensions

The unique contributions of this paper are: (1) the first proposal of quantifier-free awareness modalities \(R\) and \(D\); and (2) the introduction of the awareness relation and λ-assured conditions in the completeness proof.

The work carries several broader implications: 1. AI Safety: Provides a formal verification framework for the "perception–decision" pipeline in systems such as autonomous driving — precisely specifying "under what awareness conditions should the system take what action" 2. Multi-Agent Systems: Extendable to awareness reasoning in multi-agent cooperation/game settings, e.g., higher-order awareness such as "I know that you know I am here" 3. LLM-Based Agents: Current LLM-based agent awareness mechanisms (e.g., tool use, environment perception) lack formal guarantees; the logical framework proposed here can provide a theoretical foundation 4. Model Checking Tool Development: The axiomatic system can serve as the basis for automated verification tools that check whether the awareness properties of AI systems satisfy safety specifications

Rating

  • Novelty: ★★★★☆ — The perspective of treating awareness as a form of knowledge is novel; the formalization of de re/de dicto within awareness is an original contribution
  • Theoretical Depth: ★★★★★ — Complete soundness and strong completeness proofs with high technical rigor
  • Practical Utility: ★★☆☆☆ — Purely theoretical work; considerable distance remains to practical application
  • Clarity of Presentation: ★★★★☆ — Running examples effectively aid comprehension, though the proof sections are technically demanding
  • Overall: ★★★★☆