New predicates and relations we may want to take into consideration would be ordering/location of different blocks. Splitting the table into different "columns" may also make referring to different blocks easier in certain cases. Having a reference to the blocks to the left and right of the block in focus may also make certain types of manipulation easier.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |   

A rough idea of what such a table may look like, where each 'slot' of the table columns is approximately one large block wide.
Which may make things like heuristic planning easier if we are trying to produce more intricate stacks of blocks, or have rules in which we cannot stack small blocks on large blocks or can only stack block towers so high.
A breakdown like this could also potentially make referring to blocks to the left or right of a selected area easier, especially in Prolog while using pattern matching to find spaces that are 'greater' or 'lesser' in value than the current positioning we're interested in.

Considering the addition of cones also makes the problem more interesting in that there are suddenly somewhat fewer actions that we can inherently take since cones can only stack onto blocks. Removing capabilities for these blocks such as the ability to stack onto them should be a matter of only having to check the reference and know the block is conical. Keeping this in mind allows us to think about asking the system questions about possible moves by adding reasonable rules to the program.Knowing that adding a cone to the top of the stack makes any further interaction with the stack impossible without first unstacking the cone is important for the problem to note and be able to work around.

             
 C    C      C
 b    y   Y  b
 R    g   C  G        B
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 

An invalid representation of the world, such that capital letters denote Large Blocks in colors red, blue, yellow, green, lowercase letters denote Small Blocks in the same colors and capital C denotes Cone Blocks. Because we are attempting to stack Large Block Yellow on a Cone Block, we are breaking the rules of the world and we would want our program to give reasonable output as to why this is. We may want to ask the program about reasonable next steps we could take, and would want an output that explores valid states to the right of our current location.