
| A Knowledge-Representation Language with Social Features   | 49                                                                                                            |
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| ρ(s), g(s)                                                 | Atoms and predicates associated with the social condition s                                                   |
| n (P)                                                      | The translation of a COLP program P into a SOLP program                                                       |
| σ A()                                                      | The autonomous reduction operator                                                                             |
| AFP(P)                                                     | The set of all autonomous fixpoints of P                                                                      |
| C(P1, · · · ,Pn)                                           | The LPA program resulting from the translation of all the SCs included in the SOLP collection {P1, · · · ,Pn} |
| FP(P)                                                      | The set of all fixpoints of P                                                                                 |
| IC-SOSn                                                    | The decision problem "individually credulous reasoning"                                                       |
| IS-SOSn                                                    | The decision problem "individually skeptical reasoning"                                                       |
| JFP(P1, · · · ,Pn)                                         | The set of the joint fixpoints of the COLP programs P1, · · · ,Pn                                             |
| MSC P                                                      | The set of all the SCs (with depth 0) occurring in P                                                          |
| MSChP,r,ni                                                 | The set of all the SCs having a given depth n and occurring in a social rule r of a SOLP program P            |
| ′ u                                                        | The traditional program resulting from the translation of all the                                             |
| P                                                          | SOLP programs in a SOLP collection, where the SCs are replaced by ρ-atoms                                                                                                               |
| SAT                                                        | A set of ρ-atoms and g-predicates associated with the social conditions true for a given SOLP program w.r.t. a social interpretation                                                                                                               |
| SC-SOSn                                                    | The decision problem "socially credulous reasoning"                                                           |
| SM (P)                                                     | The set of all the stable models of P                                                                         |
| SOSn                                                       | The decision problem "social model existence"                                                                 |
| SS-SOSn                                                    | The decision problem "socially skeptical reasoning"                                                           |
| STC ()                                                     | The social immediate consequence operator, applied to the SOLP collection C                                   |
| T P (r )                                                   | The translation of the SCs included in a social rule r of P                                                   |
| TP ()                                                      | The immediate consequence operator, applied to the program P                                                  |
| TR(P)                                                      | The set of tolerance rules in the program P                                                                   |
| USC P                                                      | The set of all the SCs (at any nesting depth) in P                                                            |
| Var (P)                                                    | The set of atoms appearing in P                                                                               |
| W P                                                        | The translation of the SCs included in P                                                                      |
| (n-)SC                                                     | (n-)Social Condition                                                                                          |
| COLP                                                       | COmpromise Logic Programming                                                                                  |
| JFP                                                        | Joint Fixpoint Semantics                                                                                      |
| NAF                                                        | Negation As Failure                                                                                           |
| SOLP                                                       | SOcial Logic Programming                                                                                      |
