The ventromedial prefrontal cortex (vmPFC) is involved in diverse cognitive operations, from inhibitory control to processing of semantic schemas. When accompanied by damage to the basal forebrain, vmPFC lesions can also impair relational memory, the ability to form and recall relations among items. Impairments in establishing direct relations among items (e.g., A is related to B, B is related to C) can also hinder the transitive processing of indirect relationships (e.g., inferring that A and C are related through direct relations that each contain B). Past work has found that transitive inference improves when the direct relations are organized within an existing knowledge structure, or schema. This type of semantic support is most effective for individuals whose relational memory deficits are mild (e.g., healthy age-related decline) rather than pronounced (e.g., hippocampal amnesia, amnestic mild cognitive impairment). Given that vmPFC damage can produce both relational memory and schema processing deficits, such damage may pose a particular challenge in establishing the type of relational structure required for transitive inference, even when supported by preexisting knowledge. To examine this idea, we tested individuals with lesions to the mPFC on multiple conditions that varied in pre-experimental semantic support and explored the extent to which they could identify both previously studied (direct) and novel transitive (indirect) relations. Most of the mPFC cases showed marked transitive inference deficits and even showed impaired knowledge of preexisting, direct, semantic relations, consistent with disruptions to schema-related processes. However, one case with more dorsal mPFC damage showed preserved ability to identify direct relations and make novel inferences, particularly when pre-experimental knowledge could be used to support performance. These results suggest that damage to the mPFC and basal forebrain can impede establishment of ad hoc relational schemas upon which transitive inference is based, but that appealing to prior knowledge may still be useful for those neurological cases that have some degree of preserved relational memory.