Reformulation & Clarification (δηλαδή / με άλλα λόγια)

The reformulation family RESTATES what you just said, more clearly - the second clause does not add a NEW fact, it CLARIFIES the first. δηλαδή (“that is / i.e. / meaning / in other words”) is the everyday workhorse, extremely common in speech (a lone «Δηλαδή;» = “What do you mean?”): «Δεν τον καταλαβαίνω· δηλαδή, μιλάει πολύ γρήγορα». με άλλα λόγια (“in other words”, literally “with other words”) is the more explicit, slightly more formal equivalent: «Το εισιτήριο είναι ακριβό· με άλλα λόγια, δεν το παίρνω». The crucial contrast is with the CONSEQUENCE family: επομένως / άρα draw a NEW conclusion that follows; δηλαδή / με άλλα λόγια re-express the SAME point. Test: if “I mean…” fits, it is reformulation; if “and therefore…” fits, it is consequence. δηλαδή does three related jobs - restating, clarifying a vague word, and spelling out an implication - all on the SAME idea, always with the plain indicative.