Introduction

Attempts to formalize human preference, belief, and intention have given rise to robust epistemic and dynamic-logical frameworks. However, one domain remains resistant to logical analysis: romantic interaction.

This paper introduces Affective Predicate Logic (APL), a first-order modal framework designed to capture inferential patterns arising in digital romantic communication, specifically through participant observation of the Hinge dating platform between October 2024 and October 2025. While individual affective exchanges appear logically consistent, their aggregation leads to systematic model-theoretic failure. In particular, we demonstrate violations of completeness and compactness under classical semantics. Empirical data drawn from the case study shows persistent undecidability of propositions such as $\mathtt{TheyLikeMe}(a)$¹ and semantic collapse following interpretive divergence over “jazz.”

Methodology

The study was conducted primarily through participant observation, utilizing a single-agent experiential approach over an approximate twelve-month interval. Data was collected through naturalistic interaction via the Hinge platform, supplemented by asynchronous peer commentary (sample size: up to three group chats, nine individual consultations, and unstructured café discourse). Interactions were logged chronologically and retrospectively formalized into the language $\mathcal{L}_H$, with emotional state assessments calibrated using a semi-informal Likert scale ranging from “stable confidence” to “existential doubt”. Ambiguous textual and emoji-based communicative acts were analyzed under extended dynamic epistemic procedures, with updates categorized as either public announcements or implicit epistemic state revisions. No attempt was made to eliminate confounding variables such as self-presentation bias, algorithmic matchmaking unpredictability, or overinterpretation of punctuation. The methodology adheres to widely accepted standards of philosophical rigor, insofar as no alternative was available.

Syntax of Affective Predicate Logic

Definition (Language $\mathcal{L}_H$)
The language $\mathcal{L}_H$ consists of:

• Constants: $a_1, \dots, a_{81}$ representing interlocutors.
• Unary predicates:
  • $\texttt{Attractive}(x)$,
  • $\texttt{SuggestedCoffee}(x)$,
  • $\texttt{LikedMyPrompt}(x)$.
• Binary predicates:
  • $\texttt{Messaged}(x,y)$,
  • $\texttt{AmbiguousText}(x,y)$.
• Ternary predicate:
  • $\texttt{SemanticShift}(x,y,p)$ where $p$ is a formula or concept.
• Modal operators:
  • $\Box \varphi$ (affectively certain)
  • $\Diamond \varphi$ (romantically possible)
  • $\heartsuit\varphi$ (desirable but not confirmed)

We define:

• $\texttt{Interested}(x) := \heartsuit \texttt{TheyLikeMe}(x)$
• $\texttt{Ghosted}(x) := \lnot \exists \texttt{Messaged}(x,t) \land \lnot \Box \lnot \texttt{TheyLikeMe}(x)$

Semantics

Definition (Affective Model)
An Affective Model is a tuple:

$M = (W, R_\text{aff}, R_\text{text}, D, I)$

where:

• $W$ is a nonempty set of affective worlds;
• $R_{\text{aff}}$ models transitions in emotional state;
• $R_{\text{text}}$ models updates via message or emoji;
• $D$ is a nonempty domain of agents;
• $I$ assigns denotations to predicates at each world.

Evaluation is defined as usual. For example:

Importantly, truth values may update without explicit communication via silent belief revision, a phenomenon not permitted in classical epistemic frameworks.

Incompleteness of the Theory $T_H$

Definition (Completeness)
The theory $T_H$ is complete if for every closed formula $\varphi$,

Theorem (Indefinite Romantic Status)
There exists $a_{42}$ such that

even following conversational termination.

Proof (Sketch)
Post-conversational signals (delayed reply, ambiguous emoji, “haha”) support both $\varphi$ and $\neg \varphi$. Thus $\varphi$ remains undecidable.

Failure of Compactness

Definition (Local satisfiability)
A finite interaction set $\Delta \subseteq T_H$ is satisfiable iff

$\exists M,w \text{ such that } M,w \models Δ.$

Observation
Each individual encounter (finite set of interactions) is locally satisfiable. However,

Sources of contradiction include conflicting affective commitments, overlapping timeframes, non-reconciled emoji-based belief updates, and genre-based semantic divergence (penguin principle: all Sinatra is jazz).

Theorem (Global Incoherence)

is unsatisfiable in any Affective Model.

Update Logic of Ghosting

Ghosting operates as Silent Epistemic Collapse (SEC):

Before SEC: $\Diamond\heartsuit \texttt{TheyLikeMe}(a)$
After SEC: $\Box \lnot\heartsuit \texttt{TheyLikeMe}(a)$

with no explicit communicative act:

$\lnot \texttt{Messaged}(a,t)$ observed as sole indicator.

Conclusion

Phenomenon Logical Result

Single date interaction Satisfiable Silent update Non-public announcement Full affective history Inconsistent Definition of “jazz” Semantic collapse Long-term modeling Non-compact

Conjecture (Affective Incompleteness Hypothesis)
No recursively axiomatizable system captures reciprocity, mutual interest, and musical genre constraints within APL.

Future Work

Future research may involve the development of a paraconsistent logic of romance ($\mathcal{PL}^*$) to manage contradictory yet emotionally active states, the application of supervaluationist semantics to model borderline flirtation scenarios (particularly those involving ambiguous textual cues such as “haha” or ellipsis), and the formulation of a temporal logic of “vibes” to represent fluctuations in affective commitment over time. Additionally, further work may incorporate dynamic epistemic frameworks to capture cases of premature exclusivity assumptions, with particular attention to non-public announcements and silent state updates. Investigating the potential integration of probabilistic semantics or quantum-style superposition models for undecided interpersonal interest remains an open direction, as does the formal treatment of genre-based inference breakdowns (notably, but not limited to, the Sinatra incident).