In many practical situations, we only know the bounds on the distances. A natural question is: knowing these bounds, can we check whether there exists a metric whose distance always lie within these bounds – or such a metric is not possible and thus, the bounds are inconsistent. In this paper, we provide an answer to this question. We also describe possible applications of this result to a desc...

Abstract Although the work of G.F.C. Griss is commonly understood as a program negationless mathematics, close examination Griss’s suggests more fundamental feature its executability , requirement that mental constructions are possible only if corresponding activity can be actively carried out. Emphasizing reveals arguments against negation leave open several types negation—including D. Nelson’...

Negation is both an operation in formal logic and natural language by which a proposition replaced one stating the opposite, as addition of "not" or another negation cue. Treating adequate way required for cognitive reasoning, aims at modeling human ability to draw meaningful conclusions despite incomplete inconsistent knowledge. One task reasoning answering questions given sentences language. ...

In the last few years negation and speculation scope classification systems have been developed successfully, most of them using machine–learning approaches. In this paper we present a competitive system that finds the scope of negation and speculation in sentences for English by means of syntactic dependency analysis without using machine–learning. A greedy algorithm first detects the cues (le...