The research is focused on definitions of discourse relations, a topic that is currently little-studied. The paper gives a brief overview of existing solutions for discourse relations definitions: Rhetorical Structure Theory (RST), Segmented Discourse Representation Theory (SDRT), Penn Discourse Treebank (PDTB), and Cognitive approach to Coherence Relations. The author shows criteria used to define a discourse relation, or, in case of a narrower definition, a logical-semantic relation, in these approaches and outlines the shortcomings of the described definitions. The author also describes the principles used to build the classification and the definitions of logical-semantic relations (LSR) in the Supracorpora Database of connectives (SDB). The classification is based on four basic semantic operations upon which rests every LSR's definition: implication, location on the chronological scale, comparison, correlation between specific and general or an element and a set. The classification consistently distinguishes the levels at which the LSR can be established: propositional, illocutionary, and metalinguistic. Each LSR is defined on the basis of these two criteria. Thus, for example, for the LSR of alternative based on the comparison operation, one has the choice between the LSR of propositional, illocutionary and metalinguistic alternative (We will go to the mountains or to the sea vs. Put the gun away, or are you scared? vs. The symbol of the year or, simply speaking, cutie-pie). In case of LSRs based on implication or comparison, the polarity criterion is added, distinguishing whether the LSR is established between p and q or their negative correlates p and q are also to be taken into account in order to obtain a correct interpretation (cf. well-known descriptions of how the Russian conjunction no 'but' functions). In addition, semantic and pragmatic characteristics of the context are also considered in the classification. For example, in the case of the LSR of specification and generalization, the semantic correlation between p and q (together with their intensional and extensional interpretations) is taken heed of. Several definitions of LSR and corresponding examples are provided. Thus, the LSR of extensional specification is defined as follows: based on the operation of correlation between the general and the particular; established at the propositional level; X contains a generalized notion or state of things p; Y contains a more particular q-notion, limiting p-extensional. And the LSR of intensional specification is defined as follows: based on the operation of correlation between the general and the particular; established at the metalinguistic level; X contains a generalized concept or state of things p; Y contains a more particular q-notion, limiting p-intensional. The definitions used in the SDB definitions make it possible to evaluate, on the basis of the proposed criteria, the semantic closeness of relations and increase the level of consistency in the work of experts and annotators. That in turn increases the value of the annotated material, and therefore its reliability.