During the semicentenial history of Computer Science and Information Technologies, several thousands of computer languages have been created. Computer language universe includes languages for different purposes: programming languages, specification languages, modeling languages, languages for knowledge representation, etc. In each of these branches of computer languages it is possible to track several approaches (imperative, declarative, object-oriented, etc.), disciplines of processing (sequential, non-deterministic, parallel, distributed, etc.), formalized models (from Turing machines up to logic inference machines). Computer languages have a different potential to be integrated to different models of software process and information processing. The development of computer languages influences the development of new and evolution of existing programming systems and information technologies. On the contrary, the demand for new software and information technologies leads to design of new computer languages. Computer paradigms are the basis for classification of the computer languages. They are based on joint attributes which allow us to distinct and select a certain branch in the computer language universe. Currently the number of essentially different paradigms has reached several dozens. Study and precise specification of computer paradigms (including new ones) are called to improve the choice of appropriate computer languages for new software projects and information technologies. The paper presents a so-called “semantics and pragmatics view” – an approach to computer languages paradigms and classification, that is based on a unified formal semantics (Abstract State Machines) and an open ontology for pragmatists.