Consider the set 2Tof concepts aka subsets in the Thingspace T. A concept A is a specification of another concept B if A⊆B. This allows one to partially compare concepts by specificity, whether A is more specific than B, less specific, they are equal or incomparable.
In addition, for any two concepts B and C we find that B∩C is a subset both of B and C. Therefore, it is a specification of both. Similarly, any concept D which is a specification both of B and C is also a specification of B∩C. Additionally, B and C are specifications of B∪C, and any concept D, such that B and C are specifications of D, contains B and C. Therefore, D contains their union. Thus for any two concepts B and C we find a unique supremum of specification B∩C and a unique infimum of specification B∪C.
There also exist many other lattices. Consider, for example, the set Z2 where we declare that (a,b)≤(c,d) if a≤b,c≤d. Then for any pairs (a,b),(c,d),(e,f) s.t.(a,b)≤(e,f) and (c,d)≤(e,f) we also know that (max(a,c),max(b,d))≤(e,f), while (a,b)≤(max(a,c),max(b,d)) and (c,d)≤(max(a,c),max(b,d)). Therefore, (max(a,c),max(b,d)) is the unique supremum for (a,b) and (c,d). Similarly, (min(a,c),min(b,d)) is the unique infimum.
Consider the set 2Tof concepts aka subsets in the Thingspace T. A concept A is a specification of another concept B if A⊆B. This allows one to partially compare concepts by specificity, whether A is more specific than B, less specific, they are equal or incomparable.
In addition, for any two concepts B and C we find that B∩C is a subset both of B and C. Therefore, it is a specification of both. Similarly, any concept D which is a specification both of B and C is also a specification of B∩C.
Additionally, B and C are specifications of B∪C, and any concept D, such that B and C are specifications of D, contains B and C. Therefore, D contains their union.
Thus for any two concepts B and C we find a unique supremum of specification B∩C and a unique infimum of specification B∪C.
There also exist many other lattices. Consider, for example, the set Z2 where we declare that (a,b)≤(c,d) if a≤b,c≤d. Then for any pairs (a,b),(c,d),(e,f) s.t.(a,b)≤(e,f) and (c,d)≤(e,f) we also know that (max(a,c),max(b,d))≤(e,f), while (a,b)≤(max(a,c),max(b,d)) and (c,d)≤(max(a,c),max(b,d)). Therefore, (max(a,c),max(b,d)) is the unique supremum for (a,b) and (c,d). Similarly, (min(a,c),min(b,d)) is the unique infimum.
I hope that these examples help.