The present paper deals with monotonic and dual monotonic language learning from positive as well as from positive and negative examples. The three notions of monotonicity re ect di erent formalizations of the requirement that the learner has to produce better and better generalizations when fed more and more data on the concept to be learned. The three versions of dual monotonicity describe th...

The present paper deals with monotonic and dual monotonic language learning from positive as well as from positive and negative examples. The three notions of monotonicity re ect di erent formalizations of the requirement that the learner has to always produce better and better generalizations when fed more and more data on the concept to be learnt. The three versions of dual monotonicity descr...

Monotonicity is a constraint which arises in many application domains. We present a machine learning model, the monotonic network, for which monotonicity can be enforced exactly, i.e., by virtue offunctional form . A straightforward method for implementing and training a monotonic network is described. Monotonic networks are proven to be universal approximators of continuous, differentiable mon...

In the article, a notion “logarithmically absolutely monotonic function” is introduced, an inclusion that a logarithmically absolutely monotonic function is also absolutely monotonic is revealed, the logarithmically complete monotonicity and the logarithmically absolute monotonicity of the function ` 1+ α x ́x+β are proved, where α and β are given real parameters, a new proof for the inclusion t...