Crispin Wright in his 1982 paper argues for strict finitism, a constructive standpoint that is more restrictive than intuitionism. In its appendix, he proposes models of strict finitistic arithmetic. They are tree-like structures, formed in his strict finitistic metatheory, of equations between numerals on which concrete arithmetical sentences are evaluated. As a first step towards classical formalisation of strict finitism, we propose their counterparts in the classical metatheory with one additional assumption, and then extract the propositional part of ‘strict finitistic logic’ from it and investigate. We will provide a sound and complete pair of a Kripke-style semantics and a sequent calculus, and compare with other logics. The logic lacks the law of excluded middle and Modus Ponens and is weaker than classical logic, but stronger than any proper intermediate logics in terms of theoremhood. In fact, all the other well-known classical theorems are found to be theorems. Finally, we will make an observation that models of this semantics can be seen as nodes of an intuitionistic model.

克里斯平赖特在他 1982 年的论文中主张严格的有限主义，这是一种比直觉主义更具限制性的建设性观点。在其附录中，他提出了严格的有限算术模型。它们是树状结构，在他严格的有限元理论中形成，是数字之间的方程式，在这些方程式上计算具体的算术语句。作为严格有限论的经典形式化的第一步，我们提出了它们在经典元理论中的对应物和一个额外的假设，然后从中提取“严格有限论逻辑”的命题部分并进行研究。我们将提供一对健全且完整的 Kripke 式语义和相继演算，并与其他逻辑进行比较。该逻辑缺乏排中律和前件法，弱于经典逻辑，但在定理方面比任何适当的中间逻辑都强。事实上，所有其他众所周知的经典定理都被发现是定理。最后，我们将观察到这种语义的模型可以看作是直觉模型的节点。