A rule-based model for Sisyphus-I

The constraints (or rules) below are a step toward a constraint satisfaction oriented (declarative) representation of the problem solving knowledge needed to solve the Sisyphus-I problem. They would thus be a replacement for our procedural approach. The ontology and the data set are the same as for the procedural approach.

However, here are additional declarations needed for representing the constraints.

Description > Goal_or_constraint;   Goal_or_constraint > Goal Constraint;
For the 1st kinds of solutions
  Thing > Value;   Value > Number;  Value(Goal_or_constraint,Value);
For the 2nd kinds of solutions
  Mandatory(Goal_or_constraint); Optional(Goal_or_constraint);






The head of group should rather be placed in a large central office
1st solution
[Goal: [Group_head]->(In)->[Large_central_office] ]->(Value)->[Value:10];
[Goal: [Group_head]->(In)->[Large_and_not_central_office] ]->(Value)->[Value:9];
[Goal: [Group_head]->(In)->[Small_central_office] ]->(Value)->[Value:8];
[Goal: [Group_head]->(In)->[Small_and_not_central_office] ]->(Value)->[Value:7];
    Example of representation in Formalised English:
    [A group_head is in a Large_central_office](Value 10).

2nd solution
[Constraint: [Group_head]->(In)->[Large_central_office] ]->(Mandatory);
    Example of representation in Formalised English:
    [A group_head is in a Large_central_office](Mandatory).



Secretaries should rather share an office near the head of group
1st solution
[Goal: [Office]- { <-(In)<-[Secretary: *x];
                   <-(In)<-[Secretary: *y!=*x]; 
                   (->(Near)->[Office]->)*N ->(Near)->[Office]<-(In)<-[Group_head];
                 } ]->(Value)->[Value:10-N];
    Three unusual notations are introduced here:
    1) "*y!=*x" meaning that the variables do not refer to the same individual,
    2) "(->(Near)->[Office]->)*N" which refers to a path composed of N sequences
       of the chain "->(Near)->[Office]",
    3) "10-N" which subtracts N to 10 so that the value of the goal is maximum
       when N is 0.

[Goal: [Office]- { <-(In)<-[Secretary: *x];
                   (->(Near)->[Office]->;)*N ->(Near)->[Office]<-(In)<-[Group_head];
                 } ]->(Value)->[Value:9-N];
    This goal has a lower value because the secretary is alone in the office.



A manager should rather be in a small central office near the head of group
1st solution
[Goal: [Small_central_office]- { <-(In)<-[Manager: *x];
                                 (->(Near)->[Office]->;)*N ->(Near)->[Office]<-(In)<-[Group_head];
                               } ]->(Value)->[Value:10-N];



An head of large project should rather be in a single office near the head of group
1st solution
[Goal: [Small_office]- { <-(In)<-[Large_project_head: *x];
                         (->(Near)->[Office]->;)*N ->(Near)->[Office]<-(In)<-[Group_head];
                       } ]->(Value)->[Value:10-N];



A smoker and a non-smoker should not share an office
1st solution
[Goal: [Large_office]- { <-(In)<-[Smoker: *x];
                         <-(In)<-[Smoker: *y!=*x];
                       } ]->(Value)->[Value:10];
[Goal: [Large_office]- { <-(In)<-[Non_smoker: *x];
                         <-(In)<-[Non_smoker: *y!=*x];
                       } ]->(Value)->[Value:9];
    For the sake of simplicity, the types Smoker and Non_smoker are
    used. Instead, according to our ontology, [Smoker: *x] should be replaced
    by "[Simple_researcher: *x]<-(Agent)<-[Smoke]" and [Non_smoker: *x] by
    [Simple_researcher: *x].

2nd solution
[Constraint: [Large_office]- { <-(In)<-[Smoker: *x];
                               <-(In)<-[Smoker: *y!=*x];
                             } ]->(Mandatory);
[Constraint: [Large_office]- { <-(In)<-[Non_smoker: *x];
                               <-(In)<-[Non_smoker: *y!=*x];
                             } ]->(Mandatory);

3rd solution
[Goal: [Large_office]- { <-(In)<-[Smoker: *x];
                         <-(In)<-[Non_smoker: *y!=*x];
                       } ]->(Value)->[Value:-10];



A hacker and a non-hacker should rather not share an office
1st solution
[Goal: [Large_office]- { <-(In)<-[Hacker: *x];
                         <-(In)<-[Hacker: *y!=*x];
                       } ]->(Value)->[Value:10];
[Goal: [Large_office]- { <-(In)<-[Non_hacker: *x];
                         <-(In)<-[Non_hacker: *y!=*x];
                       } ]->(Value)->[Value:10];
    As above, for the sake of simplicity, the types Hacker and Non_hacker
    are used.



Researchers of a same project should rather not share an office
1st solution
[Goal: [Large_office]- { <-(In)<-[Simple_researcher:*x]->(Project)->[Project:*p1];
                         <-(In)<-[Simple_researcher:*y!=*x]->(Project)->[Project:*p2!=*p1];
                       } ]->(Value)->[Value:10];
[Goal: [Large_office]- { <-(In)<-[Simple_researcher:*x]->(Project)->[Project:*p1];
                         <-(In)<-[Simple_researcher:*y!=*x]->(Project)->[Project:*p2==*p1];
                       } ]->(Value)->[Value:9];

2nd solution
[Constraint: [Large_office]- { <-(In)<-[Simple_researcher:*x]->(Project)->[Project:*p1];
                               <-(In)<-[Simple_researcher:*y!=*x]->(Project)->[Project:*p2!=*p1];
                             } ]->(Mandatory);