Abstract: Conditional reasoning is a basic inference in ordinary life and scientific research. For a conditional “if p, then q”, there are two kinds of certain semantic relations: p is sufficient for q, and q is necessary for p. There are three logically equivalent representations of semantic relations of the conditional: if p, then q; only if q, p; not p, or q. In the sufficient representation “if p, then q”, the sufficiency of p for q is explicit, and the necessity of q for p is implicit. In the necessary representation “only if q, p”, the sufficiency of p for q is implicit, and the necessity of q for p is explicit. In the disjunctive representation “not p, or q”, the sufficiency of p for q is implicit, and the necessity of q for p is implicit. The author supposed that the implicit-explicit representation of semantic relations in conditionals would affect people’s perception and understanding of semantic relations (sufficient or necessary relation) in conditionals, which would further affect people’s conditional inferences. The explicit representation of semantic relations would improve correspondent condition inferences, whereas the implicit representation of semantic relations would impair correspondent condition inferences. However, there is no previous study on the influence of representation of semantic relations of conditionals on conditional inferences.
The present experiment examined the possible influences of two between-subjects factors on conditional inferences for basic conditionals. One factor was the representation of semantic relations of the three logically equivalent conditionals which had three levels: the sufficient conditionals; the necessary conditionals; the disjunctive conditionals. The other factor concerning possibility judgment had two levels: the absence or presence of the task of possibility judgment in which participants judged whether the four cases (p and q; not p and q; not p and not q; p and not q) relevant to conditionals are possible given the conditionals. The task is to construct explicit mental models implicated in each conditional. The two between-subjects factors combined into six experimental conditions. In each experimental condition, there were two basic conditionals in a questionnaire on a sheet. For each conditional, there were four conditional inference questions (MP, MT, DA, and AC). In each inference question, participants were asked to judge whether a certain conclusion can be derived from a particular major premise and a minor premise. There were three answer options participants can choose from: Yes, No or Uncertain. In the three experimental conditions with the task of possibility judgment, the task of possibility judgment was arranged before the task of conditional inference. Participants were 254 college students which were randomly arranged into the six experimental conditions.
The results showed that for the three logically equivalent conditionals, there was a significant effect of the representation of semantic relations of conditionals on conditional inferences. Participants’ performances on conditional inferences corresponding to explicit semantic relations were better than those on conditional inferences corresponding to implicit semantic relations. There was no significant difference between conditional inferences in the task of possibility judgment and conditional inferences in the absence of task of possibility judgment. The task of possibility judgment as explicit mental model construction did not significantly improve participants’ performances on conditional inferences. There was dissociation between participants’ performances on conditional inferences and participants’ performances on possibility judgment. Participants’ performances on conditional inferences were significantly worse than participants’ performances on possibility judgment. These implied that participants did not completely base their conditional inferences on mental model construction.
In summary, the present study shows that people don’t completely base their conditional inferences on mental model construction; their conditional inferences are also affected by the representation of semantic relations of conditionals. For the three logically equivalent conditionals, people’s performances on conditional inferences improve as the representation of semantic relations of conditionals becomes the explicit form from the implicit form.

Key words: conditional inference, semantic relation, sufficiency, necessary, disjunctive, mental model