The mathematical results of the paper are about formal languages, but they are meant to apply also to those fragments of natural language which can be formalized, much as the results of denotational semantics for formal languages are often applied to fragments of natural language. In addition to the language of predicate logic whose sense semantics are fairly simple, the theory also covers languages with description operators, arbitrary connectives and modal operators, generalized quantifiers, indirect reference and the ability to define their own truth predicate.