The paper studies some cases in physics such as Galilean inertia motion and etc., and presents a logical schema of recursive abduction, from which we can derive the universality of physical laws in an effective logical path without requiring infinite inductions. Recursive abduction provides an effective logical framework to connect a universal physical law with finite empirical observations based on both quasi-law tautologies and suitable recursive dimensions, two new concepts introduced in this paper. Under the viewpoint of recursive abduction, the historical difficulty from Hume’s problem naturally vanishes. In Hume’s problem one always misunderstood a time-recursive issue as an infinitely inductive problem and, thus, sank into an inescapable quagmire. With this new effective logical schema, the paper gives a concluding discussion to Hume’s problem and justifies the validity of probability argument for natural laws.

Grain shape and chalkiness are important appearance quality traits of rice, which also affect the yield and milling quality. In this study, 190 F2 families derived from the cross between Hua 5178S and Hua 611 were sequenced to construct a genetic linkage map. Combined with F2 and F2:3 generations grain shape and chalkiness phenotype, a total of 15 QTL were detected. There are 8 grain shape QTL distributed on chromosomes 2, 5, 6, 8, and 10; 7 chalkiness QTL distributed on chromosomes 2, 3, and 6. A QTL cluster affecting multiple chalkiness traits was found on chromosome 6, qWBR6.1, qWCR6 and qCR6 were selected for genetic effect verification. It was found that qWBR6.1, qWCR6 and qCR6 explained 13% and 24%, and 29% of the phenotypic variations respectively, and qWCR6 and qCR6 were co-mapped. This study laid a foundation for further cloning of rice appearance quality genes.