need or importance of a reasonable answer. A physician cannot delay for a long time a treatment of a patient just because he or she is not yet certain about the final diagnosis. Travelers reaching a crossroads would not just stay there even if they are not sure which way leads to their destination.

Mark Twain wrote, “The trouble with the world is not that people know too little, but that they know so many things that ain’t so.” Even given an extensive knowledge of the world, its incompleteness makes erroneous judgment inevitable. In the present state of the world a formula $F$ has a certain value although this value may be uncertain from the standpoint of $S$. If the information about $F$ contained in $S$ is incomplete (briefly, $F$ is incomplete in $S$), we have to find a way of reasoning producing a *belief* regarding $F$ which is *credible* in the sense that it stands a good chance of being true in the reality. So a system of automated reasoning must be able to answer the following query:

> Given a formula $F$ and a system $S$ describing faithfully a world, what is a most credible belief regarding the 