Abstract

We describe specific fragments of the immune system using relational systems (Kripke frames) that represent the semantics of the novel logic _EŁ_$$_{P}$$-Modal Epistemic Łukasiewicz logic. The language of _EŁ_$$_{P}$$ extends the infinitely valued Łukasiewicz logic Ł by introducing a unary connective, interpreted as a modal epistemic operator that denotes knowledge and quasi-knowledge. This paper demonstrates that theorems within this logic hold for the immune system model. Furthermore, we propose conjectures related to the model that are unresolved by immune scientists, striving to prove or refute these conjectures as theorems. Additionally, we investigate the decidability and unification problems of the corresponding logic and its admissible rules.