Certain conditionals have something other than a clause as their consequent: their antecedent if-clauses are ‘adverbial clauses’ without a verb. We argue that they function in a way already seen for those with clausal consequents, despite lacking the content we might expect for the formation of a conditional. The use of the if-clause with sub-clausal consequents is feasible thanks to the fact that this function does not depend on the consequent content, and so is not impeded when the consequent does not provide a proposition, question or imperative. To support this we provide meaning rules for conditionals in terms of information state updates, letting the same construction play out in different ways depending on context and content.

To model conditionals in a way that reflects their acceptability, we must include some means of making judgements about whether antecedent and consequent are meaningfully related or not. Enthymemes are non-logical arguments which do not hold up by themselves, but are acceptable through their relation to a topos, an already-known general principle or pattern for reasoning. This paper uses enthymemes and topoi as a way to model the world-knowledge behind these judgements. In doing so, it provides a reformalisation (in TTR) of enthymemes and topoi as networks rather than functions, and information state update rules for conditionals.