Consider:
He #believed# that (the dog was alive).
He #said# that (the dog was alive).
He #said# that (the dog was alive).
The stuff in parentheses is a sentence that's an argument to the verb - i.e. a sentential complement - and the word "that" is a relativizer or complementizer that quotes the relative sentential complement. What other verbs can go between the hashes? I tried to make a little taxonomy. Certainly not complete, but I think it's a good start:
• Believe: anticipate assume believe envision expect feel gather guess imagine judge know presume reckon recollect remember repute suppose surmise suspect think
• Believe not: doubt disbelieve forget question
• Perceive: appreciate ascertain deduce detect determine discover discern infer figure find glean hear learn memorize notice observe overhear perceive read realize recognize relearn savor see sense smell taste witness
• Show: elucidate demonstrate establish explain explicate prove reveal show
• Say: announce articulate communicate convey claim ejaculate express indicate mention narrate note present recount recite reiterate relate relay remark repeat report say specify state tell warn
• Say not: denounce deny disavow reject
• Say (manner of sound production): babble bark bellow blab bleat blurt boom bray burble cackle chatter chirp cluck coo croak croon crow cry groan growl grumble grunt hiss holler hoot howl moan mumble murmur mutter purr roar scream screech shout shriek snap snarl squawk squeak squeal stammer stutter thunder tsk wail warble wheeze whimper whine whisper whistle whoop yammer yap yell yelp yodel
• Say definitely: assert avow charge certify confirm declare decree diagnose guarantee hold maintain ordain preach proclaim promise pronounce teach warrant
• Say indefinitely: hint imply mean suggest
• Say finally: accept acknowledge admit allow begrudge cede concede conclude confess confide consider credit grant profess surrender
• Say provisionally: advance allege bet conjecture contribute extend offer pose posit proffer propose submit supply wager predict
• Send message (medium specific): broadcast chant dictate illustrate post radio sign signal sing telegraph telephone write
• Positive Evaluation: adore delight gladden like love
• Negative Evaluation: anguish care hate regret revile rue
• Negative Prospective evaluation: despair dread fear panic worry
• Positive Prospective evaluation: desire fancy hope pray will wish
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Let me know if I missed a good one and I'll add it!