inc and dec I assume mean increment or decrement (I have no experience with CL) - racket/base includes (add1 .) and (sub1 .) for the same effect. If they didn't exist they would be trivial to add I think - if this isn't what inc and dec mean then I apologise.
In Scheme/Racket truth and falsity is really simple - #f is false and everything else is truthy. There's also already a null value for the empty list (which is 'true'). I don't know if nil would be useful.
In Common Lisp, unlike Scheme/Racket, nil is the null value AND the false value. In Scheme/Racket, 'nil is true unless you define it to be #f. If you wrote an if or cond expression to evaluate the 'nil in the link, I think that it would return true, whereas in CL nil is falsy (I think it is the only falsy value in CL, but I would still describe it as 'falsy' rather than false, possibly incorrectly).
e: Ah, I see why I'm not understanding you now - you're talking about the differences between Racket and SICP/Scheme whereas I made the assumption that we were talking about the difference between Common Lisp and Racket (from OP's comment). To further clarify, I believe this was my fault in comprehension, not yours in communication.
But it is how nil is defined in SICP:
'The value of nil, used to terminate the chain of pairs, can be thought of as a sequence of no elements, the empty list. The word nil is a contraction of the Latin word nihil, which means "nothing."' -- http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-15.html...
And then in a footnote to that paragraph:
"It's remarkable how much energy in the standardization of Lisp dialects has been dissipated in arguments that are literally over nothing: Should nil be an ordinary name? Should the value of nil be a symbol? Should it be a list? Should it be a pair? In Scheme, nil is an ordinary name, which we use in this section as a variable whose value is the end-of-list marker (just as true is an ordinary variable that has a true value). Other dialects of Lisp, including Common Lisp, treat nil as a special symbol. The authors of this book, who have endured too many language standardization brawls, would like to avoid the entire issue. Once we have introduced quotation in section 2.3, we will denote the empty list as '() and dispense with the variable nil entirely." -- http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-15.html...
Apologies for the confusion.
In that case, I don't think it's possible to define an exact equivalent of CL's nil in Scheme, as nil means both false and the empty list in CL -- the latter being falsy in CL and, as you point out, truthy in Scheme.