By "soft validity" I mean this: The formal definition of validity is that if the premises are true, the conclusion must be true. I will call this "hard validity." "Soft validity" means the premises do indeed support the argument to some degree, but not to the degree that the conclusion must be true.
An example of a "softly valid" argument would be something like, "Five witnesses at the scene testified that the suspect was present." Obviously it doesn't entail that the suspect was there; all five might be deluded, or lying, or saw someone that looks the same. But it is a premise that supports the conclusion that the suspect was present, and would be considered that way in a court of law.
By comparison the premise "five people who weren't at the scene think he was probably there" does not support the conclusion, and the argument isn't even softly valid. If five witnesses who were there were sure the suspect wasn't there, that could be called "softly contradictory."
The reason I ask is I am teaching a class I call Argument & Logic in which we analyze arguments and consider fallacies. When I state an argument doesn't have a fallacy and the premises do support the conclusion (but that it doesn't actually entail), I want to say it's a "valid argument" but that's technically incorrect. However the term is used that way in day to day conversation.