In 1952 P. F. Strawson proposed a logic of presuppositions. It is an interpretation of Aristotelian logic, i.e. of the logic of the traditional syllogism. In 1981 Richard Diaz published a monograph in which he presented truth-relevant logic. This paper shows that truth-relevant logic is but a propositional version of the logic of presuppositions. A semantics of the logic of presuppositions is developed using truth-relevant logic. The semantics is then further extended to polyadic logic and some consequences discussed.

翻译：1952年，P. F. 斯特劳森提出了一种预设逻辑，这是对亚里士多德逻辑（即传统三段论逻辑）的一种解释。1981年，理查德·迪亚兹出版了一部专著，在其中提出了真值相关逻辑。本文表明，真值相关逻辑不过是预设逻辑的一个命题版本。利用真值相关逻辑，本文发展了一种预设逻辑的语义学，并将该语义学进一步扩展至多元逻辑，同时讨论了若干推论。