This paper outlines an implemented system called PROVERB that explains machine-found natural deduction proofs in natural language. Diierent from earlier works, we pursue a reconstructive approach. Based on the observation that natural deduction proofs are at a too low level of abstraction compared with proofs found in mathematical textbooks, we deene rst the concept of so-called assertion level...

Second order quantification is puzzling. The second order quantifiers have natural and compelling inference rules, and they also have natural models. These do not match: the inference rules are sound for the models, but not complete, so either the proof rules are too weak or the models are too strong. Some, such as Quine, take this to be no real problem, since they take “second order logic” to ...

background the use of dietary supplements is very common in sport gyms worldwide. however, their use in exercisers in lebanese gyms has never been investigated. conclusions these results indicate a lack of awareness among people who exercise regularly on the benefits and side-effects of dietary supplements. there is an urgent need for the implementation of campaigns that target gym users in leb...