The Martin and Deutscher account of remembering is essentially this: S remembers (that) X iff X, S has observed (that) X in the past, S's current representation of X is appropriately causally related to S's earlier experience of (that) X via a memory trace.  It is not enough that S's current state be simply “causally dependent” on S's earlier state since there are deviant causal chain examples in which this condition is satisfied without their being instances of memory.  For instance, suppose Jones has an altercation with Smith that he then describes to Johnson.  Five years later, Jones has irretrievably forgotten about his disagreement with Smith but Johnson, who possesses a much better memory, remembers what Jones told him five years ago, and tells Jones everything he remembers about the incident.  Now Jones has a representation that is causally dependent upon his earlier representation of his altercation with Smith, but Jones still doesn't remember the relevant interaction with Smith. It should be noted that Martin and Deutscher have a fair amount to say about what the appropriate causal relation is (indeed, that phrase doesn't appear in their article), but their discussion is too long and complicated to reproduce here.