Automatic extraction and reasoning over temporal properties in natural language discourse has not had wide use in practical systems due to its demand for a rich and compositional, yet inference-friendly, representation of time. Motivated by our study of temporal expressions from the Penn Treebank corpora, we address the problem by proposing a two-level constraint-based framework for processing and reasoning over temporal information in natural language. Within this framework, temporal expressions are viewed as partial assignments to the variables of an underlying calendar constraint system, and multiple expressions together describe a temporal constraint-satisfaction problem (TCSP). To support this framework, we designed a typed formal language for encoding natural language expressions. The language can cope with phenomena such as under-specification and granularity change. The constraint problems can be solved using various constraint propagation and search methods, and the solutions can then be used to answer a wide range of time-related queries.