We devote this paper to the axiomatization and the computability of ${\mathbf{PDL}}_0^{\mathrm{\Delta }}$, a variant of iteration-free PDL with fork. Concerning the axiomatization, our results are based on the following: although the program operation of fork is not modally definable in the ordinary language of PDL, it becomes definable in a modal language strengthened by the introduction of propositional quantifiers. Instead of using axioms to define the program operation of fork in the language of PDL enlarged with propositional quantifiers, we add an unorthodox rule of proof that makes the canonical model standard for the program operation of fork and we use large programs for the proof of the Truth Lemma. Concerning the computability, we prove by a selection procedure that ${\mathbf{PDL}}_0^{\mathrm{\Delta }}$ has a strong finite property, hence is decidable.

我们致力于这篇论文的公理化和可计算性 ${\mathbf{客运专线}}_0^{\mathrm{\Delta }}$，是带有fork的无迭代PDL的变体。关于公理化，我们的结果基于以下内容：尽管fork的程序操作不是用PDL的普通语言模态定义的，但是它可以通过引入命题量词而得到增强的模态语言来定义。我们没有使用公理来定义以命题量词扩大的PDL语言来定义fork的程序操作，而是添加了一个非正统的证明规则，该规则使fork的程序操作成为规范的模型标准，而使用大型程序来证明fork的程序操作。真相引理。关于可计算性，我们通过选择程序证明${\mathbf{客运专线}}_0^{\mathrm{\Delta }}$ 具有很强的有限属性，因此是可判定的。