We introduce a simple inference system based on two primitive relations between terms, namely, inclusion and exclusion relations. We present a normalization theorem, and then provide a characterization of the structure of normal proofs. Based on this, inferences in a syllogistic fragment of natural language are reconstructed within our system. We also show that our system can be embedded into a fragment of propositional minimal logic.
This study reports an ecologic analysis of the relationship between mean birth weight (MBW) and nutritional, medical and social variables, using 1982 data for 47 prefectures in Japan.