  In standard first-order predicate logic, validity is defined as truth in all structures (sometimes called ‘models’) of a certain sort. In modal logic, validity is typically defined as truth at every world in every structure of a certain (different) sort. Kaplan similarly defines validity as truth at every context in every LD structure. (‘LD’ stands for ‘the Logic of Demonstratives’.) Each LD structure contains a set of contexts, a set of worlds, a set of individuals, a set of positions (common to all worlds), a set of times (common to all worlds), and a function that assigns to each predicate and individual constant an intension, which is a function from time-world pairs to extensions. (Thus Kaplan’s LD structures do not assign structured contents to expressions in contexts. LD structures use intensions to represent contents.) Each context has an associated agent, time, position, and world. Various stipulations about structures and contexts together ensure that, for every context \(c\) in every structure M: (i) the agent of \(c\) is a member of the extension of ‘Exist’ at the time and world of \(c\), and (ii) the ordered pair  \(\langle \text{the agent of } c, \text{the position of } c \rangle\)  is a member of the extension of ‘Located’ at the time and world of \(c\).