grammar.subjunctive.doubt-denial
Doubt and denial: no creo que, dudo que
Negated belief and doubt flip to the subjunctive: creo que viene (indicative) vs no creo que venga. Dudar que, negar que, no es cierto que.
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Explanation
Expressions of doubt, denial, or disbelief trigger the subjunctive in the clause that follows. The clearest case is the polarity switch on belief verbs: creo que viene takes the indicative (you assert it), but no creo que venga takes the subjunctive (you withhold the assertion). Same with pensar, parecer, es verdad que: no pienso que sea buena idea, no es verdad que cueste tanto.
Verbs that mean doubt or denial outright are subjunctive even without a negative: dudo que sea así, niego que haya pasado, no estoy seguro de que llegue. The subjunctive marks the event as unasserted.
Restoring certainty flips it back: no dudo que es buen profesional ('I don't doubt it, so I'm asserting it'). Questions with creer can go either way, and the mood signals the asker's leaning: ¿crees que venga? (doubtful) vs ¿crees que viene? (neutral).
Examples
I don't think he'll arrive on time.
Region: global
I don't doubt he's a good professional.
Region: global
I don't think it's that expensive, but I doubt they have it in stock.