Mental World Model of Users

• Mental World Model of Users is a dynamic internal representation that encodes beliefs, intentions, and social relations.
• It uses graded modal operators based on the BDI framework to formally model cognitive and affective states.
• A hybrid reasoning approach integrates rule-based and simulation methods to enhance realistic, adaptable human-agent interactions.

A mental world model of users is an internal, dynamically updated representation constructed by an intelligent system or agent to encode, reason about, and anticipate a user’s beliefs, intentions, emotions, attitudes, and social relations. In formal human-agent interaction—such as virtual job interview simulations—such a model enables the agent to explicitly attribute and update both core cognitive and affective structures, allowing for more adaptive, transparent, and effective interactions.

1. Formal Representation of User Mental States

At the heart of the logical modeling framework is a modal logic calculus grounded in the Belief-Desire-Intention (BDI) paradigm. This approach models mental states as graded modal operators:

• Belief $(Bel_a^l(\varphi))$: Agent $a$ believes proposition $\varphi$ with certainty $l \in [0,1]$.
• Attitude $(Att_a^k(\varphi))$: Agent $a$ values (desires, approves) $\varphi$ to degree $k \in [-1,1]$.
• Intention $(Int_a(\varphi))$: Agent $a$ intends to realize/proceed with $\varphi$.
• Emotions $(Emo_{a,b}^i(\epsilon,\varphi))$: Agent $a$ experiences emotion $\epsilon$ (towards $b$ or in general) about $\varphi$, of intensity $i$.
• Social Relations: Liking and dominance levels $(Like_{a,b}^k, Dom_{a,b}^k)$ between agents.

The syntax (see equation 1 in the model) allows for recursive and nested attribution, enabling the system to reason about layered beliefs and meta-attitudes.

The overall logical form is: $$\begin{align*} Fml &: \varphi ::= \pi \;|\; Bel_a^l(\varphi) \;|\; Att_a^k(\varphi) \;|\; Int_a(\varphi) \;|\; Emo_{a,(b|\varnothing)}^i(\varepsilon,\varphi) \;| \; \ldots \end{align*}$$

Mental state reasoning—such as attributing “Mary knows John lost his dad, so she avoids mentioning fathers”—is realized by recursively applying these modal operators.

2. Hybrid Theory of Mind: Rule-based and Simulation-based Reasoning

The model employs a hybrid Theory of Mind architecture that fuses:

• Theory-Theory (TT): Commonsense psychological rules, e.g., “People desire positive outcomes”; specified as logical inference rules about affect and intention propagation.
• Simulation-Theory (ST): Attributional simulation, where the agent projects the user’s inferred mental state into its own reasoning engine (“What would I experience if I were in the user’s position?”).

This integration yields richer and more flexible user modeling: the system can reason both normatively (via rules and inference) and pragmatically (via simulation of situated affective reactions).

3. Modal Logic Semantics and Graded World Modeling

The modal logic framework extends classic logic to possible worlds, where each agent maintains a probability distribution (or accessibility relation) over possible worlds:

• Belief Semantics:

$$\mathcal{M}, w \models Bel_a^l(\varphi) \Leftrightarrow \frac{|\{v \in \mathcal{B}_a(w): \mathcal{M}, v \models \varphi\}|}{|\mathcal{B}_a(w)|} = l$$

This models graded confidence in beliefs.

Social relations, such as dominance or liking, are also coded as modal operators, thus affecting the agent’s inferences and subsequent action selection.

4. Appraisal-Based Inference for Emotions and Social Relations

Emotional attribution employs appraisal rules inspired by the OCC model of affect, realized as modal logic inference templates. For example: $$\begin{align*} Bel_a^l(\gamma) \wedge Att_a^{k>0}(\gamma) &\implies N(Joy_a^{i=f(l,k)}(\gamma))\ Bel_a^l(F(\gamma)) \wedge Des_a^{k<0}(\gamma) &\implies N(Fear_a^{i=f(l,k)}(\gamma))\ Bel_a^l(\gamma) \wedge Ideal_a^k(\gamma) \wedge Bel_a^{l'}(Rsp_b(\gamma)) &\implies N(Admiration_{a,b}^{i=f(l,l',k)}(\gamma)) \end{align*}$$

Intensity $i$ is a function of belief certainty and desirability, enabling nuanced, dynamically varying emotive responses.

Attitudes are further updated by propagating through social relation values: $$Bel_a^{l>thr}(\varphi) \wedge Att_a^k(F(\varphi)) \wedge Bel_a^{l'}(Att_b^{k'}(F(\varphi))) \wedge Like_{a,b}^h \wedge Dom_{a,b}^{h'} \implies Att_a^{f(k,k',h,h')}(\varphi)$$

Communication updates (via illocutionary acts, e.g., Assert, Request) further refine the agent’s world model, modulated by social relations.

5. Impact on Human-Agent Interaction: Empirical Evaluation

In a controlled job interview simulation, the logical Theory of Mind model was instantiated in a virtual recruiter with three different profiles (“supportive”, “neutral”, “challenging”). Outcomes demonstrate:

• Recruiter profile (ToM logic goals) significantly affected participants’ experienced emotions: embarrassment, concentration, stress, and uneasiness varied with agent affective reasoning.
• Statistical analysis (Kruskal-Wallis, Mann-Whitney) confirmed that ToM-driven behavior enhances the user’s emotional engagement—supportive and challenging (but not neutral) recruiters elicited stronger participant affect.
• The model’s ability to “mindread” and adapt to the user’s socio-affective state made interactions more realistic and effective.
• The logic-based ToM framework affords transparency (“white box” reasoning), extensibility (across domains), and explicit behavior justification.

6. Summary of Model Elements and Reasoning Patterns

Construct	Logic Form	Role in Inference
Belief	$Bel_a^l(\varphi)$	Quantifies confidence/state estimation
Attitude/Desire	$Att_a^k(\varphi),~Des_a^k(\varphi)$	Guides goal formation and emotion appraisal
Intention	$Int_a(\varphi)$	Immediate planning/actions
Emotion	$Emo_{a,b}^i(\epsilon,\varphi)$	Appraisal, intensity from belief/desire; social direction
Social Relation	$Like_{a,b}^k,~Dom_{a,b}^k$	Updates attitudes/emotions, adjusts communication impact
ToM Reasoning	Hybrid TT+ST	Combines general rules and simulation for mindreading

7. Domain Independence and Transferability

The framework’s explicit, graded, and modular design allows it to be ported to other application domains beyond interviews. The modal logic formalism admits explanations for agent decisions and opens the reasoning process to inspection or revision—crucial for both transparency and extensibility.

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This logical, hybrid Theory of Mind model establishes a rigorous, interpretable methodology for modeling user mental states in human-agent interaction, explicitly capturing beliefs, emotions, intentions, and social context with graded modal logic operators and appraisal-based inference. Empirical evaluation demonstrates its value in producing more affectively resonant and adaptive agent behavior, highlighting its relevance for any application demanding rich user modeling and naturalistic social interaction.