Penta-State Probabilistic Model (PSPM)

Abstract

Probability is usually represented either as a binary truth value or as a fuzzy extension of it, and neither form describes well how people hold a partial belief, such as “probably yes” or “probably no”. We ask whether this kind of human belief and decision making can be written as a probabilistic model. We introduce the theoretical foundation of the Penta-State Probabilistic Model (PSPM), a five-valued probabilistic scoring and readout model for directional confidence estimation in AI reasoning, inspired by the human decision making process. PSPM describes a probability with five understandable states: True, False, Partial-True, Partial-False, and Undecided. It is designed for short evidence checklists (roughly 5–10 major evidences) and turns evidence counts into an evidence ratio in [0, 1] through two stages. The Major stage chooses the positive, negative or neutral pole and how strong it is, while the Minor stage only breaks exact ties between major evidences, so partial evidence alone can never reach True or False. Unanswered evidence can only lower the strength of the result, which stops PSPM from overclaiming. We prove the structural properties of the score (state partition, closure, mirror symmetry, exact state thresholds, and monotonicity in a restricted case) and state clearly where they do not hold.