Abstract

Chapman's paper, "Planning for Conjunctive Goals," has been widely acknowledged for its contribution toward understanding the nature of partial-order planning, and it has been one of the bases of later work by others---but it is not free of problems. This paper addresses some problems involving modal truth and the Modal Truth Criterion (MTC). Our results are as follows: (i) Even though modal duality is a fundamental property of classical modal logics, it does not hold for modal truth in Chapman's plans; i.e., "necessarily p" is not equivalent to "not possibly :p." (ii) Although the MTC for necessary truth is correct, the MTC for possible truth is incorrect: it provides necessary but insufficient conditions for ensuring possible truth. Furthermore, even though necessary truth can be determined in polynomial time, possible truth is NP-hard. (iii) If we rewrite the MTC to talk about modal conditional truth (i.e., modal truth conditional on executability) rather than modal truth, then bot...

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