Toward a Possibilistic Language Model: Grounding Large Language Model Uncertainty in Epistemic Support-Point Theory and Possibility Theory

Contemporary large language models (LLMs) generate text by sampling from probability distributions over vocabulary tokens, implicitly asserting that uncertainty about language is well-modeled by calibrated stochastic processes. This paper argues that such probabilistic closure is epistemically unjustified in the regime of language: meaning is bounded by admissible interpretation, not governed by frequentist statistics. The precise claim is not that probability cannot model language but that probabilistic closure is an epistemically overcommitted representation for token uncertainty under bounded admissibility—one that prevents the architecture from representing categorical inadmissibility and compels the assignment of positive probability mass to tokens that should not exist in the support at all. We propose the Possibilistic Language Model (PLM), a novel architecture grounding language generation in possibility theory and the Epistemic Support-Point Filter (ESPF) framework of Jah and Haslett (2025). The PLM replaces softmax probability distributions over tokens with possibilistic compatibility fields over vocabulary support sets; it replaces maximum-likelihood training with a Possibilistic Cramér–Rao regularized entropy-minimization objective; and it replaces standard scaled dot-product attention with Epistemic Possibilistic Attention (EPA), a falsification-driven attention operator that gates keys by admissible innovation geometry rather than by likelihood weighting. The PLM is not merely compatible with these foundations: it is the unique architecture forced by the TEAG axioms when instantiated over a discrete vocabulary manifold. The governing equation of token generation is a tropical Hamilton–Jacobi equation in the max-plus semiring, with the vocabulary surprisal field as Hamiltonian and the PCRB as minimum action per generation step. Epistemic Possibilistic Attention is the discretized Lax–Oleinik operator of this system. The minimax medoid commitment is proved to be the geodesic attractor of the surviving vocabulary well, not a heuristic selection rule. We define (not merely propose) the vocabulary possibility distribution and EPA operator; we derive the PCRB regularization from established ESPF theory inherited from Jah (2026a); we prove, conditionally on VFI maintenance, that the PLM produces non-degenerate generation from actual vocabulary tokens; and we prove that the PLM recovers a standard transformer in the Gaussian epistemic limit, which is the zero-temperature limit of the tropical Hamilton–Jacobi framework established in Jah (2026d). We are explicit throughout about what is fully self-contained here, what is inherited from prior TEAG works, and what remains as open proof obligations. The architecture naturally produces diagnostics—necessity, epistemic width, and surprisal—that quantify when a generation step is epistemically supported versus epistemically strained. We discuss initialization, training, inference, and multi-modal extensions, and identify open theoretical obligations alongside a concrete research agenda. The PLM is not presented as a drop-in replacement for probabilistic LLMs, but as a principled alternative for language tasks where epistemic humility, interpretability, and bounded admissibility matter more than distributional calibration.