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Since S is an AnsProlog;not program, we will compute its answer set using the iterated xpoint approach. T 0S " 0 = . T 0 S " 1 = T 0 S (T 0 S " 0) = fbird(tweety) penguin(skippy)g. T 0 S " 2 = T 0 S (T 0 S " 1) = fbird(tweety) penguin(skippy) bird(skippy) ab(skippy) fly(tweety)g. T 0 S " 3 = T 0 S (T 0 S " 2) = T 0 S " 2 = S . Hence lfp(T 0 S ) = S , is the answer set of S . Thus, S is an answer set of . 2 De nition 4 de nes when an interpretation is an answer set. Hence, using it we can only verify if a particular interpretation is an answer set or not.

Possible(a) . possible(b) . possible(c) . The resulting program has the following answer sets: fpossible(a) possible(b) possible(c) chosen(a) :chosen(b) :chosen(c) someg fpossible(a) possible(b) possible(c) chosen(b) :chosen(c) :chosen(a) someg fpossible(a) possible(b) possible(c) chosen(c) :chosen(a) :chosen(b) someg fpossible(a) possible(b) possible(c) chosen(a) chosen(b) :chosen(c) someg fpossible(a) possible(b) possible(c) chosen(a) chosen(c) :chosen(b) someg fpossible(a) possible(b) possible(c) chosen(b) chosen(c) :chosen(a) someg fpossible(a) possible(b) possible(c) chosen(a) chosen(b) chosen(c) someg Note that neither fpossible(a) possible(b) possible(c) :chosen(a) :chosen(b) :chosen(c)g nor fpossible(a) possible(b) possible(c) :chosen(a) :chosen(b) :chosen(c) inconsistentg are answer sets of the above program.

Based on these criteria we will elaborate on the following notions: 1. Datalog and i-functions: In case of the `i-function' or inherent function corresponding to a Datalog or AnsProlog* program, the domain and co-domain are extracted from the program. Normally, predicates in the left hand side of non-fact rules are referred to as IDB (intensional database) or output predicates, and the other predicates are referred to as the EDB (extensional database) or input predicates. 2. l-functions: An l-function or literal function is a three-tuple h P Vi, where is an AnsProlog* program, P and V are sets of literals referred to as parameters and values, and the domain is extracted from and P .

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A Hacker's Revenge

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