The paper presents a decision rule forming a mathematical basis of earthquake forecasting problem. We develop an axiomatic approach to earthquake forecasting in terms of multicomponent random fields on a lattice. This approach provides a method for constructing point estimates and confidence intervals for conditional probabilities of strong earthquakes under conditions on the levels of precursors. Also, it provides an approach for setting a multilevel alarm system and hypothesis testing for binary alarms. We use a method of comparison for different algorithms of earthquake forecasts in terms of the increase of Shannon information. ‘Forecasting’ (the calculation of the probabilities) and ‘prediction’ (the alarm declaring) of earthquakes are equivalent in this approach.