Text as tautology: an exploration in inference, transitivity, and logical compression

Rhetorical structure theory (RST) and relational propositions have been shown useful in analyzing texts as expressions in propositional logic. Because these expressions are systematically derived, they may be expected to model discursive reasoning as articulated in the text. If this is the case, it would follow that logical operations performed on the expressions would be reflected in the texts. In this paper the logic of relational propositions is used to demonstrate the applicability of transitive inference to discourse. Starting with a selection of RST analyses from the research literature, analyses of the logic of relational propositions are performed to identify their corresponding logical expressions and within each expression to identify the inference path implicit within the text. By eliminating intermediary relational propositions, transitivity is then used to progressively compress the expression. The resulting compressions are applied to the corresponding texts and their compressed RST analyses. The application of transitive inference to logical expressions results in abridged texts that are intuitively coherent and logically compatible with their originals. This indicates an underlying isomorphism between the inferential structure of logical expressions and discursive coherence, and it confirms that these expressions function as logical models of the text. Potential areas for application include knowledge representation, logic and argumentation, and RST validation.

Low-rank Gallus gallus domesticus chicks are better at transitive inference reasoning

A form of deductive reasoning, transitive inference, is thought to allow animals to infer relationships between members of a social group without having to remember all the interactions that occur. Such an ability means that animals can avoid direct confrontations which could be costly. Here we show that chicks perform a transitive inference task differently according to sex and rank. In female chicks, low-ranking birds performed better than did the highest ranked. Male chicks, however, showed an inverted U-shape of ability across rank, with the middle ranked chicks best able to perform the task. These results are explained according to the roles the sexes take within the group. This research directly links the abilities of transitive inference learning and social hierarchy formation and prompts further investigation into the role of both sex and rank within the dynamics of group living.

The Role of the Ventromedial Prefrontal Cortex and Basal Forebrain in Relational Memory and Inference

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.

Asymmetric learning facilitates human inference of transitive relations

Humans and other animals are capable of inferring never-experienced relations (e.g., A>C) from other relational observations (e.g., A>B and B>C). The processes behind such transitive inference are subject to intense research. Here, we demonstrate a new aspect of relational learning, building on previous evidence that transitive inference can be accomplished through simple reinforcement learning mechanisms. We show in simulations that inference of novel relations benefits from an asymmetric learning policy, where observers update only their belief about the winner (or loser) in a pair. Across 4 experiments (n=145), we find substantial empirical support for such asymmetries in inferential learning. The learning policy favoured by our simulations and experiments gives rise to a compression of values which is routinely observed in psychophysics and behavioural economics. In other words, a seemingly biased learning strategy that yields well-known cognitive distortions can be beneficial for transitive inferential judgments.