DATR is a declarative language for representing a restricted class of inheritance networks, permitting both multiple and default inheritance. The principal intended area of application is the representation of lexical entries for natural language processing, and we use examples from this domain throughout. In this paper we present the syntax and inferencemechanisms for the language. The goal of the DATRenterprise is the design of a simple language that (i) has the necessary expressive power to encode the lexical entries presupposed by contemporary work in the unification grammar tradition, (ii) can express all the evident generalizations about such entries, (iii) has an explicit theory of inference, (iv) is computationally tractable, and (v) has an explicit declarative semantics. The present paper is primarily concerned with (iii), though the examples used may hint at our strategy in respect of (i) and (ii).