We adapt our light Dialectica interpretation to usual and light modal formulas (with universal quantification on boolean and natural variables) and prove it sound for a non-standard modal arithmetic based on Goedel's T and classical S_4. The range of this light modal Dialectica is the usual (non-modal) classical Arithmetic in all finite types (with booleans); the propositional kernel of its domain is Boolean and not S_4. The `heavy' modal Dialectica interpretation is a new technique; it cannot be simulated within our previous light Dialectica. The synthesized functionals are at least as good as before; the translation process is much improved and could be more suitable for the human operators.

翻译：我们把我们的光对立体解释适应于常规和光模式公式(对布林和自然变量进行普遍量化),并证明它对于基于戈德尔T和古典S_4的非标准模式计算是合情合理的。这种光模式对立体的广度是所有有限类型(有布林)的常规(非现代)古老的亚理学(有布林);其域的标语内核是布林而非S_4。“重度”模式对立体解释是一种新技术;它不能在我们以前的光中模拟。合成功能至少和以前一样好;翻译过程大为改善,可能更适合人类操作者。