Calendar Logic

A propositional temporal logic is introduced whose operators quantify over intervals of a reference time line. The intervals are specified symbolically, for example ‘next week’s weekend’. The specification language for the intervals takes into account all the features of real calendar systems. A simple statement which can be expressed in this language is for example: ‘yesterday I worked for eight hours with one hour lunch break at noon’. Calendar Logic can be translated into propositional logic. Satisfiability is therefore decidable. Since the translation is exponential, a tableau decision procedure for checking decidability is presented as an alternative.