AbstractA fragment of English featuring temporal prepositions and the order-denoting adjectives first and last is defined by means of a context-free grammar. The phrase-structures which this grammar assigns to the sentences it recognizes are viewed as formulas of an interval temporal logic, whose satisfaction-conditions faithfully represent the meanings of the corresponding English sentences. It is shown that the satisfiability problem for this logic is NEXPTIME-complete. The computational complexity of determining logical relationships between English sentences featuring the temporal constructions in question is thus established.