1. something you consider to be true which you base other ideas and actions on
based/founded/established on the premise
A premise is a piece of information that you hold to be true, upon which you make other decisions. It can be something which forms the basis of an argument or viewpoint: "My premise is, if we invest in Education now, we will have better-qualified workers in the future." You can use the word 'premise' as a way of stating that you have taken a piece of information to be true: "If our premise is that the Earth is not warming up - how can we explain the following natural phenomenon?" This is a formal phrase you will usually hear in Educational, Scientific or other professional contexts.