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Abstract. A new kind of labeled transition systems, program specic transition systems, is proposed. These systems are used to formalize and unify some aspects of program handling. Such aspects as the development of program operational semantics and proof of safety properties of programs are considered, and the appropriate classes of program specic transition systems are dened. Ontological transition systems and operational ontological semantics are dened in terms of program specic transition systems.

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A new formalism for description of ontologies of systems and their changes -conceptual transition systems -is presented. The basic definitions of the theory of conceptual transition systems are given. These systems were demonstrated to allow to specify both typical and new kinds of ontological elements constituting ontologies. The classification of ontological elements based on such systems is described.Keywords: transition systems, conceptual structures, ontologies, ontological elements, conceptual transition systems, conceptuals IntroductionDevelopment of formalisms, languages and tools for describing the conceptual structure of various systems is an important problem of the modern knowledge industry. Description of changes of the conceptual structure of the system when it functions is an another important problem.Conceptual transition systems (CTSs) are a formalism of description (specification) of systems that solves these problems. This formalism is based on the following requirements:1. It describes the conceptual structure of the specified system. 2. It describes the content of the conceptual structure of the specified system, i. e. it describes the specified system in the context of the conceptual structure.3. It describes the change of the conceptual structure of the specified system. 4. It describes the change of the content of the conceptual structure of the specified system, i. e. it describes the change of the specified system in the context of the conceptual structure.5. It is quite universal to specify typical ontological elements (concepts, attributes, concept instances, relations, relation instances, individuals, types, domains, and so on.).6. It provides a quite complete classification of ontological elements, including the determination of their new kinds and subkinds.7. It is based on the conception 'state -transition' of the usual transition systems, keeping their simplicity and universality and adding a conceptual 'filling'. This requirement is * Partially supported by RFBR under grants 15-01-05974 and 15-07-04144. 2Anureev I.S. Conceptual transition systems important since the simplicity of determination of transition systems makes them an universal formalism to describe the behavior of various systems (algorithms, programs, software models, computer systems, and so on.).8. It supports reflection of any order, i. e. allows to specify: the system (reflection of the order 0), the specification of the system (reflection of the order 1), the specification of the specification of the system (reflection of the order 2) and so on. Specifications of the higher order (with reflection of the higher order) impose restrictions on the specifications of the lower order (with reflection of the lower order).To our knowledge, there is no formalism that meets all the above requirements. Comparison of CTSs with the formalisms which partially meet these requirements is given in section 9.The paper has the following structure. The preliminary concepts and notation are given in section 2. The basic definitions ...