  There are important problems in physics related to the concept of
probability. One of these problems is related to negative probabilities used in
physics from 1930s. In spite of many demonstrations of usefulness of negative
probabilities, physicists looked at them with suspicion trying to avoid this
new concept in their theories. The main question that has bothered physicists
is mathematical grounding and interpretation of negative probabilities. In this
paper, we introduce extended probability as a probability function, which can
take both positive and negative values. Defining extended probabilities in an
axiomatic way, we show that classical probability is a positive section of
extended probability.
