Compare cardinality of multiple sets and get specific value from member of greatest set












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I am using clingo to solve flood-it problems. I use the predicate frontier([CELL], [COLOR], [TIMESTEP]) to keep track of all cells that are neighbors of the flood. The set of frontiers could look something like this:



frontier(c(1,3),2,3) frontier(c(2,1),2,3) frontier(c(2,2),3,3) frontier(c(2,3),3,3) frontier(c(3,1),3,3) frontier(c(3,2),3,3) frontier(c(4,1),3,3)


We can split this set in two subsets. One where each color value is 2 or 3 respectively. What I need is basically two things:




  1. Determine which subset is bigger, i.e. if there are more cells with color value 2 or 3 (BTW the number of colors is not fixed, thus a solution has to be generic)

  2. Get the color value of a member of the biggest set


How can I compare the cardinalities of n (n>=2) sets in predicate logic?



Thank you in advance!






logic planning answer-set-programming clingo







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    I am using clingo to solve flood-it problems. I use the predicate frontier([CELL], [COLOR], [TIMESTEP]) to keep track of all cells that are neighbors of the flood. The set of frontiers could look something like this:



    frontier(c(1,3),2,3) frontier(c(2,1),2,3) frontier(c(2,2),3,3) frontier(c(2,3),3,3) frontier(c(3,1),3,3) frontier(c(3,2),3,3) frontier(c(4,1),3,3)


    We can split this set in two subsets. One where each color value is 2 or 3 respectively. What I need is basically two things:




    1. Determine which subset is bigger, i.e. if there are more cells with color value 2 or 3 (BTW the number of colors is not fixed, thus a solution has to be generic)

    2. Get the color value of a member of the biggest set


    How can I compare the cardinalities of n (n>=2) sets in predicate logic?



    Thank you in advance!






    logic planning answer-set-programming clingo







    share|improve this question

























      0












      0








      0







      I am using clingo to solve flood-it problems. I use the predicate frontier([CELL], [COLOR], [TIMESTEP]) to keep track of all cells that are neighbors of the flood. The set of frontiers could look something like this:



      frontier(c(1,3),2,3) frontier(c(2,1),2,3) frontier(c(2,2),3,3) frontier(c(2,3),3,3) frontier(c(3,1),3,3) frontier(c(3,2),3,3) frontier(c(4,1),3,3)


      We can split this set in two subsets. One where each color value is 2 or 3 respectively. What I need is basically two things:




      1. Determine which subset is bigger, i.e. if there are more cells with color value 2 or 3 (BTW the number of colors is not fixed, thus a solution has to be generic)

      2. Get the color value of a member of the biggest set


      How can I compare the cardinalities of n (n>=2) sets in predicate logic?



      Thank you in advance!






      logic planning answer-set-programming clingo







      share|improve this question













      I am using clingo to solve flood-it problems. I use the predicate frontier([CELL], [COLOR], [TIMESTEP]) to keep track of all cells that are neighbors of the flood. The set of frontiers could look something like this:



      frontier(c(1,3),2,3) frontier(c(2,1),2,3) frontier(c(2,2),3,3) frontier(c(2,3),3,3) frontier(c(3,1),3,3) frontier(c(3,2),3,3) frontier(c(4,1),3,3)


      We can split this set in two subsets. One where each color value is 2 or 3 respectively. What I need is basically two things:




      1. Determine which subset is bigger, i.e. if there are more cells with color value 2 or 3 (BTW the number of colors is not fixed, thus a solution has to be generic)

      2. Get the color value of a member of the biggest set


      How can I compare the cardinalities of n (n>=2) sets in predicate logic?



      Thank you in advance!






      logic planning answer-set-programming clingo




      logic planning answer-set-programming clingo






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      asked Nov 22 at 20:34









      Webastronaut

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          I found an answer which is more domain (i.e. clingo) specific than general.



          What I initially do is count the number of cells that are of color C:



          frontier_subset_size(C,N) :- color(C), N = #count{ X : frontier(X,C) }.


          Then I filter the biggest set(s) using the #max aggregate:



          max_subset_color(C) :- frontier_subset_size(C,N), N = #max{ M : frontier_subset_size(_,M) }.


          This works as desired for this specific problem.



          Yet I would like to know how to do that in pure predicate logic.






          share|improve this answer





















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            I found an answer which is more domain (i.e. clingo) specific than general.



            What I initially do is count the number of cells that are of color C:



            frontier_subset_size(C,N) :- color(C), N = #count{ X : frontier(X,C) }.


            Then I filter the biggest set(s) using the #max aggregate:



            max_subset_color(C) :- frontier_subset_size(C,N), N = #max{ M : frontier_subset_size(_,M) }.


            This works as desired for this specific problem.



            Yet I would like to know how to do that in pure predicate logic.






            share|improve this answer


























              0














              I found an answer which is more domain (i.e. clingo) specific than general.



              What I initially do is count the number of cells that are of color C:



              frontier_subset_size(C,N) :- color(C), N = #count{ X : frontier(X,C) }.


              Then I filter the biggest set(s) using the #max aggregate:



              max_subset_color(C) :- frontier_subset_size(C,N), N = #max{ M : frontier_subset_size(_,M) }.


              This works as desired for this specific problem.



              Yet I would like to know how to do that in pure predicate logic.






              share|improve this answer
























                0












                0








                0






                I found an answer which is more domain (i.e. clingo) specific than general.



                What I initially do is count the number of cells that are of color C:



                frontier_subset_size(C,N) :- color(C), N = #count{ X : frontier(X,C) }.


                Then I filter the biggest set(s) using the #max aggregate:



                max_subset_color(C) :- frontier_subset_size(C,N), N = #max{ M : frontier_subset_size(_,M) }.


                This works as desired for this specific problem.



                Yet I would like to know how to do that in pure predicate logic.






                share|improve this answer












                I found an answer which is more domain (i.e. clingo) specific than general.



                What I initially do is count the number of cells that are of color C:



                frontier_subset_size(C,N) :- color(C), N = #count{ X : frontier(X,C) }.


                Then I filter the biggest set(s) using the #max aggregate:



                max_subset_color(C) :- frontier_subset_size(C,N), N = #max{ M : frontier_subset_size(_,M) }.


                This works as desired for this specific problem.



                Yet I would like to know how to do that in pure predicate logic.







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered Dec 18 at 20:28









                Webastronaut

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