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% Space Syntax with Prolog % Pedro Afonso Fernandes (paf@ucp.pt) % August 2022 % Knowledge base: Gulbenkian public housing estate (Odivelas, near Lisbon, Portugal) % Non-topological costs: 3 - stairs, 2 - ramps, 1 - otherwise connected(outside,hotelcar,3). connected(outside,rua_carlos_reis_E,3). connected(outside,rua_bordalo_pinheiro_E,2). connected(outside,rua_bordalo_pinheiro_S,2). connected(outside,logradouro_W,3). connected(outside,confraria,1). connected(outside,pavilhao,1). connected(outside,rua_helena_aragao_S,1). connected(outside,rua_helena_aragao_N,3). connected(outside,rua_helena_aragao_E,1). connected(outside,rua_jose_regio,3). connected(outside,pcta_jose_regio,2). connected(outside,cc_girassol,1). connected(hotelcar,casinha,1). connected(hotelcar,rua_carlos_reis_E,1). connected(hotelcar,rua_bordalo_pinheiro_S,1). connected(rua_carlos_reis_E,rua_bordalo_pinheiro_S,1). connected(rua_carlos_reis_E,rua_carlos_reis_S,1). connected(casinha,rua_bordalo_pinheiro_S,1). connected(casinha,rua_carlos_reis_S,1). connected(casinha,pcta_grao_vasco,1). connected(casinha,pcta_jose_regio,2). connected(casinha,cc_girassol,3). connected(rua_bordalo_pinheiro_E,rua_bordalo_pinheiro_S,1). connected(rua_bordalo_pinheiro_E,rua_carlos_reis_S,1). connected(rua_bordalo_pinheiro_E,pcta_grao_vasco,1). connected(rua_bordalo_pinheiro_E,logradouro_S,1). connected(rua_bordalo_pinheiro_E,pavilhao,3). connected(logradouro_S,rua_bordalo_pinheiro_S,1). connected(logradouro_S,pcta_grao_vasco,1). connected(logradouro_S,pavilhao,3). connected(pcta_grao_vasco,pavilhao,3). connected(pcta_grao_vasco,pcta_jose_regio,2). connected(cc_girassol,pcta_jose_regio,3). connected(rua_jose_regio,pcta_jose_regio,2). connected(logradouro_N,pcta_jose_regio,1). connected(logradouro_N,rua_jose_regio,1). connected(talude,rua_jose_regio,2). connected(talude,pavilhao,3). connected(talude,logradouro_W,1). connected(talude,confraria,3). connected(confraria,rua_bordalo_pinheiro_S,3). connected(confraria,logradouro_W,3). connected(rua_helena_aragao_E,pavilhao,1). connected(rua_helena_aragao_E,rua_helena_aragao_S,1). connected(rua_helena_aragao_E,rua_helena_aragao_N,1). % Space Syntax measures with non-topological costs: adjacent1(X,Y,1):-connected(X,Y,1). adjacent1(X,Y,1):-connected(Y,X,1). adjacent2(X,Y,1):-connected(X,Y,2). adjacent2(X,Y,1):-connected(Y,X,2). adjacent3(X,Y,1):-connected(X,Y,3). adjacent3(X,Y,1):-connected(Y,X,3). adjacent(X,Y,1):-adjacent1(X,Y,1). adjacent(X,Y,1):-adjacent2(X,Y,1). adjacent(X,Y,1):-adjacent3(X,Y,1). connectivity(X,Y,AC):-aggregate_all(count,adjacent(X,Y,1),AC). control(X,Y,E):-aggregate_all(sum(G),(adjacent(X,Z,1),connectivity(Z,Y,AC),G is 1/AC),E). depth(X,Y,1):-adjacent1(X,Y,1). depth(X,Y,2):-adjacent1(X,Z,1),depth(Z,Y,1),dif(X,Y). depth(X,Y,2):-adjacent2(X,Y,1). depth(X,Y,3):-adjacent1(X,Z,1),depth(Z,Y,2),dif(X,Y). depth(X,Y,3):-adjacent2(X,Z,1),depth(Z,Y,1),dif(X,Y). depth(X,Y,3):-adjacent3(X,Y,1). depth(X,Y,4):-adjacent1(X,Z,1),depth(Z,Y,3),dif(X,Y). depth(X,Y,4):-adjacent2(X,Z,1),depth(Z,Y,2),dif(X,Y). depth(X,Y,4):-adjacent3(X,Z,1),depth(Z,Y,1),dif(X,Y). depth(X,Y,5):-adjacent1(X,Z,1),depth(Z,Y,4),dif(X,Y). depth(X,Y,5):-adjacent2(X,Z,1),depth(Z,Y,3),dif(X,Y). depth(X,Y,5):-adjacent3(X,Z,1),depth(Z,Y,2),dif(X,Y). depth(X,Y,6):-adjacent1(X,Z,1),depth(Z,Y,5),dif(X,Y). depth(X,Y,6):-adjacent2(X,Z,1),depth(Z,Y,4),dif(X,Y). depth(X,Y,6):-adjacent3(X,Z,1),depth(Z,Y,3),dif(X,Y). depth(X,Y,7):-adjacent1(X,Z,1),depth(Z,Y,6),dif(X,Y). depth(X,Y,7):-adjacent2(X,Z,1),depth(Z,Y,5),dif(X,Y). depth(X,Y,7):-adjacent3(X,Z,1),depth(Z,Y,4),dif(X,Y). depth(X,Y,8):-adjacent1(X,Z,1),depth(Z,Y,7),dif(X,Y). depth(X,Y,8):-adjacent2(X,Z,1),depth(Z,Y,6),dif(X,Y). depth(X,Y,8):-adjacent3(X,Z,1),depth(Z,Y,5),dif(X,Y). depth(X,Y,9):-adjacent1(X,Z,1),depth(Z,Y,8),dif(X,Y). depth(X,Y,9):-adjacent2(X,Z,1),depth(Z,Y,7),dif(X,Y). depth(X,Y,9):-adjacent3(X,Z,1),depth(Z,Y,6),dif(X,Y). graph(X,Y,D):-distinct([Y],depth(X,Y,D)). controllability(X,Y,Z,F):-connectivity(X,Y,AC),aggregate_all(count,graph(X,Z,2),D2),F is AC/(AC+D2). totdepth(X,Y,TD):-aggregate_all(sum(D),graph(X,Y,D),TD). nodes(X,Y,D,N):-aggregate_all(count,graph(X,Y,D),N). meandepth(X,Y,D,MD):-totdepth(X,Y,TD),nodes(X,Y,D,N), MD is TD/N. integration(X,Y,D,I):-meandepth(X,Y,D,MD), I is 1/MD. asymmetry(X,Y,D,RA):-totdepth(X,Y,TD),nodes(X,Y,D,N), RA is 2*(TD/N-1)/(N-1). dvalue(K,DV):-DV is 2*(K*(log((K+2)/3)/log(2)-1)+1)/((K-1)*(K-2)). rra(X,Y,D,RRA):-asymmetry(X,Y,D,RA),nodes(X,Y,D,N),dvalue(N+1,DV), RRA is RA/DV. integrationHH(X,Y,D,IHH):-rra(X,Y,D,RRA), IHH is 1/RRA. % Local measures for radius R: rdepth(X,Y,D,R):-depth(X,Y,D), D =< R. rgraph(X,Y,D,R):-distinct([Y],rdepth(X,Y,D,R)). rtotdepth(X,Y,TD,R):-aggregate_all(sum(D),rgraph(X,Y,D,R),TD). rnodes(X,Y,D,N,R):-aggregate_all(count,rgraph(X,Y,D,R),N). rmeandepth(X,Y,D,MD,R):-rtotdepth(X,Y,TD,R),rnodes(X,Y,D,N,R), MD is TD/N. rintegration(X,Y,D,I,R):-rmeandepth(X,Y,D,MD,R), I is 1/MD. rasymmetry(X,Y,D,RA,R):-rtotdepth(X,Y,TD,R),rnodes(X,Y,D,N,R), RA is 2*(TD/N-1)/(N-1). rrra(X,Y,D,RRA,R):-rasymmetry(X,Y,D,RA,R),rnodes(X,Y,D,N,R),dvalue(N+1,DV), RRA is RA/DV. rintegrationHH(X,Y,D,IHH,R):-rrra(X,Y,D,RRA,R), IHH is 1/RRA. % Rings: graph2(X,Y,D):-distinct([Y],(depth(X,Y,D),D>1)). ring(X,Y,Z,D):-adjacent(X,Y,1),graph2(Y,X,D),connectivity(X,Z,AC), AC > 1. rings(X,Y,Z,D,R):-aggregate_all(count,(ring(X,Y,Z,D)),C), R is max(C-1,0). ringiness(X,Y,Z,RR):-rings(X,Y,Z,D,R),nodes(X,Y,D,N), RR is R/N. % Queries (examples): % adjacent(outside,Y,1). % connectivity(outside,Y,AC). % graph(outside,Y,D). % control(outside,Y,E). % controllability(outside,Y,Z,F). % totdepth(outside,Y,TD). % meandepth(outside,Y,D,MD). % integration(outside,Y,D,I). % asymmetry(outside,Y,D,RA). % rra(outside,Y,D,RRA). % integrationHH(outside,Y,D,IHH). % rgraph(outside,Y,D,3). % rintegration(outside,Y,D,I,3). % rasymmetry(outside,Y,D,RA,3). % ringiness(outside,Y,Z,RR). % Multi-condition query: % X=outside, % connectivity(X,Y,AC), control(X,Y,E), meandepth(X,Y,D,MD), % asymmetry(X,Y,D,RA), integrationHH(X,Y,D,IHH).