This study investigated the relationship between relational integration and semantic processing in numerical inductive reasoning using event-related potentials (ERPs). Participants were required to identify hidden rules in three-digit sequences and judged whether fourth probes were congruent with these rules. The experiment manipulated relational complexity: simple and hierarchical rules (e.g., ”12, 13, 14, 15” or ”12, 13, 15, 18”) shared identical first two numbers but differed in the third, in order to isolate the relational integration process. The type of cue was also manipulated: the no-cue condition presented only a fixation point, providing no rule information; the part-cue condition introduced operands (such as “+” or “–”) to ensure rules could be identified after presenting second numbers and confirmed after the onset of third numbers. Both the time domain and mass univariate ERP results locked to the third numbers revealed independent main effects of relational complexity and cue type on both the Late Negative Component (LNC) . The independent effects especially on the LNC implies that high-order numerical reasoning distinct from semantic processing.

This study investigated the relationship between relational integration and semantic processing in numerical inductive reasoning using event-related potentials (ERPs). Participants were required to identify hidden rules in three-digit sequences and judged whether fourth probes were congruent with these rules. The experiment manipulated relational complexity: simple and hierarchical rules (e.g., ”12, 13, 14, 15” or ”12, 13, 15, 18”) shared identical first two numbers but differed in the third, in order to isolate the relational integration process. The type of cue was also manipulated: the no-cue condition presented only a fixation point, providing no rule information; the part-cue condition introduced operands (such as “+” or “–”) to ensure rules could be identified after presenting second numbers and confirmed after the onset of third numbers. The mass univariate ERP results locked to the third numbers revealed independent main effects of relational complexity and cue type on both the Late Negative Component (LNC) and Late Positive Component (LPC). The independent effects especially on the LNC implies that high-order numerical reasoning distinct from semantic processing.

The Operational Momentum (OM) effect refers to the tendency to overestimate addition and underestimate subtraction outcomes during mental arithmetic, however, whether OM effect arises from multiple competing sources remains unclear. To explore the mechanism of OM effect, based on the theory of operand encoding in Triple Code Model (TCM), we divide operands into magnitude encoding and verbal encoding, and compare the differences of OM-congruent probe and OM-incongruent probe at behavioral and electrophysiological level under different encoding conditions. We found that in the magnitude encoding condition, participants exhibited a stable OM effect, and OM-congruent probes elicited a positive P3 component (250–350ms) in the parietal lobes, while OM-incongruent probes triggered a more negative N2 component (150–250ms) in the parietal lobes. In the verbal encoding condition, participants exhibited a reserved OM effect and OM-incongruent probes elicited a more negative N2 component (150–250ms) in the frontal lobes. These results indicate OM effect arises from multiple competing sources of bias in mental arithmetic, which is consistent with the assumptions of the AHAB model.