A model for context-dependent natural language semantics is proposed and formalized in terms of possible worlds. The meaning of a sentence depends on context and at the same time affects that context representing the knowledge about the world collected from a discourse. The model fits well with a "flat" semantic representation as first proposed by Hobbs (1985), consisting basically of a conjunction of atomic predications in which all variables are existentially quantified with the widest possible scope; in our framework, this provides very concise semantic terms as compared with other representations. There is a natural correspondence between the possible world semantics and a constraint solver, and it is shown how such a semantics can be defined using the programming language of Constraint Handling Rules (Frühwirth, 1995). Discourse analysis is clearly a process of abduction in this framework, and it is shown that the mentioned constraint solvers serve as effective and efficient abductive engines for the purpose.