Answer set programming is a logic programming paradigm based on the stable model semantics for extended logic programs (those that include both negation as failure and classical negation). An "answer set" is almost the same thing as a stable model but some of the atoms might be negated.
Disjunction and negation in rule heads is fine in ASP.
https://www.dbis.informatik.uni-goettingen.de/Teaching/DB/db-stable.pdf: on ASP in XSB