The book can be attributed to the field of philosophy of science, besides the last one is treated as a part of the foundations of science and its problems are treated in close connection with the problems of logical and modeling aspects of the foundations of science. It is designed ultimately to serve for preparation of a philosophic-methodological, modelling and logical basis of subsequent elaboration of the General Foundations of Science, providing the scientific knowledge with (1) strong substantiation and (2) unity of the (2.1) language, (2.2) basic principles and (2.3) methods of research of its various branches, which is especially urgent in the age of interdisciplinary investigations. The book consists of 8 articles treating various aspects of this topic - explication of the concepts "science", "foundations of science" and "interdisciplinary approach to foundations of science", the problems of core of scientific inquiry, of the limits of exact science, of mathematical proving as multi-agent spatio-temporal activity, of the significance of semantics of possible worlds for scientific reasoning, etc., outlining a new direction in the development of philosophy of science.