Ensuring Inferential Reliability in Clinical LLMs: A Proof-Theoretic Approach via the ISA System

Large language models are increasingly being adopted in clinical education and decision support, yet their reasoning remains largely opaque and susceptible to hallucinations, limiting their reliability in high-stakes medical settings. This paper presents ISA (Informatore Scientifico Artificiale), a neuro-symbolic framework that constrains Gemini 3.5 to perform clinical reasoning within a propositional proof system based on sequent-style tableaux. The approach, which we term Logic-Constrained Prompt Learning, encodes the inference rules of the calculus through system instructions written in and restricts every derivation to a knowledge base extracted from official drug package leaflets. Since the underlying calculus is analytic, every inference is confined to the concepts explicitly contained in the premises, making unsupported reasoning immediately identifiable while producing derivations that are fully inspectable and formally verifiable. To assess the educational value of the approach, we conducted a randomized crossover pilot study involving twenty-six pharmacy students, comparing ISA with unconstrained conversational systems in the analysis of a clinical pharmacology case. Participants consistently rated the constrained system more highly with respect to inferential rigor, transparency, clinical reliability, and perceived safety. These findings suggest that proof-theoretic constraints can substantially improve the explainability of LLM-based clinical reasoning without sacrificing usability. Beyond the present implementation, the framework naturally extends to richer proof systems, including modal, default, and abductive logics, providing a general foundation for trustworthy neuro-symbolic reasoning in medical education and clinical decision support.