In Fallout 3 and New Vegas, players had the option to direct how events play out by selecting dialogue options that were based on skills. If one had sufficient points in skills such as Medicine and Speech, they could complete a quest in an optional manner by healing troops to increase the amount of people willing to fight, or use convincing words to prevent violent conflict. Skills having an effect on how one carries on with dialogue made situations unique for each player and character build.

In Fallout 4, the skill system has been merged into a SPECIAL system that combines stats, perks, and skills into one package. Instead of the traditional system, skills such as Explosives and Sneak have been reformed into perks with ranks instead of points. With this, I would hope that selecting these "skill perks" will still have an influence on how the world reacts when engaging in dialogue. This is what I believe promotes the creation multiple builds to increase replay value.

Do you hope that these perks will have an influence in how dialogue forwards quests and the story?

S.P.E.C.I.A.L.S will probably have influence on dialogue, maybe perks like Black Widow and Lady Killer are now just bound to the six you choose, so you get unique dialogue based on your gender (that would be neat). Other than that i am pretty sure that the perk that represents skills will be featured in dialogue and effect the course of it, its a trademark of the franchise after all and Bethesda followed it in Fallout 3, why would they exclude it now?

Yes perks will influence dialogue, i can guarantee you that at-least Confirmed Bachelor/Black Widow, Cannibal and Intimidation will be in the dialogue.

But probably there will be much more perks then these three.

Off-topic here, but I wonder if they'll get a little more "authentic" with the cannibalization animations this time around, they seem to be really ramping up the little details, like being able to see our legs in FP (according to speculation at least!).

I wouldn't doubt it. I liked the way perk-related dialogue was implemented in Fallout 3; there were occasions where perks like Entomologist or Robotics Expert gave you an extra dialog option.