#Python 3, 352 208 205 bytes

This is still very ungolfed, and I will try to add an explanation later. After some modifications, I managed to remove 144 147 bytes.

f=lambda x,l=len,r=range:'\n'.join(*x)if l(x)<2 else f([[x[i][j]+['0',''][j<=l(x[i])//2]for j in r(l(x[i]))]+[['?','?<'][l(x)<3]]+[x[i+1][j]+['1',''][j>=l(x[i])//2]for j in r(l(x[i]))]for i in r(0,l(x),2)])

A function f that takes input of the truth table values as a list of Booleans of the form ['1','1','1','0','0','1'...], where '1' is truthy and '0' is falsey, and returns a Stackylogic program.

Try it on Ideone

If you want to test a produced program, you can use GamrCorps's Convex interpreter here.

How it works

This is a recursive function and uses the inductive method described in the question.

At the zero-indexed recursion level a, the function creates n/2 a+1-input Stackylogic programs from the n a-input programs in the list. This is done by joining all adjacent pairs of two programs in the list with ?; since the cursor is always at the middle element of each constituent program, the required appending of 0 or 1 can be performed by iterating over each line of the programs being joined, and appending if the index of the current line is less than or equal to/greater than or equal to the middle index as appropriate. If the list contains only two programs, the next recursive call will give the final program; since this requires a cursor, joining instead occurs on ?<.

When the list has length 1, the list must contain just one element containing the full program. Hence, all lines in the program are joined on a newline, and then returned.

An example helps to illustrate this:

Take the input ['1', '1', '1', '0', '0', '1', '1', '1'].

Level  Return value

0  [['1', '?', '1'], ['1', '?', '0'], ['0', '?', '1'], ['1', '?', '1']]
1  [['1', '?', '10', '?', '11', '?', '0'], ['0', '?', '10', '?', '11', '?', '1']]
2  [['1', '?', '10', '?', '110', '?0', '00', '?<', '01', '?1', '101', '?', '11', '?', '1']]
3  '1\n?\n10\n?\n110\n?0\n00\n?<\n01\n?1\n101\n?\n11\n?\n1'

which when printed gives:

1
?
10
?
110
?0
00
?<
01
?1
101
?
11
?
1

Python 3, 352 208 205 bytes

This is still very ungolfed, and I will try to add an explanation later. After some modifications, I managed to remove 144 147 bytes.

f=lambda x,l=len,r=range:'\n'.join(*x)if l(x)<2 else f([[x[i][j]+['0',''][j<=l(x[i])//2]for j in r(l(x[i]))]+[['?','?<'][l(x)<3]]+[x[i+1][j]+['1',''][j>=l(x[i])//2]for j in r(l(x[i]))]for i in r(0,l(x),2)])

A function f that takes input of the truth table values as a list of Booleans of the form ['1','1','1','0','0','1'...], where '1' is truthy and '0' is falsey, and returns a Stackylogic program.

Try it on Ideone

If you want to test a produced program, you can use GamrCorps's Convex interpreter here.

How it works

This is a recursive function and uses the inductive method described in the question.

At the zero-indexed recursion level a, the function creates n/2 a+1-input Stackylogic programs from the n a-input programs in the list. This is done by joining all adjacent pairs of two programs in the list with ?; since the cursor is always at the middle element of each constituent program, the required appending of 0 or 1 can be performed by iterating over each line of the programs being joined, and appending if the index of the current line is less than or equal to/greater than or equal to the middle index as appropriate. If the list contains only two programs, the next recursive call will give the final program; since this requires a cursor, joining instead occurs on ?<.

When the list has length 1, the list must contain just one element containing the full program. Hence, all lines in the program are joined on a newline, and then returned.

An example helps to illustrate this:

Take the input ['1', '1', '1', '0', '0', '1', '1', '1'].

Level  Return value

0  [['1', '?', '1'], ['1', '?', '0'], ['0', '?', '1'], ['1', '?', '1']]
1  [['1', '?', '10', '?', '11', '?', '0'], ['0', '?', '10', '?', '11', '?', '1']]
2  [['1', '?', '10', '?', '110', '?0', '00', '?<', '01', '?1', '101', '?', '11', '?', '1']]
3  '1\n?\n10\n?\n110\n?0\n00\n?<\n01\n?1\n101\n?\n11\n?\n1'

which when printed gives:

1
?
10
?
110
?0
00
?<
01
?1
101
?
11
?
1

#Python 3, 352 208 205 bytes

This is still very ungolfed, and I will try to add an explanation later. After some modifications, I managed to remove 144 147 bytes.

f=lambda x,l=len,r=range:'\n'.join(*x)if l(x)<2 else f([[x[i][j]+['0',''][j<=l(x[i])//2]for j in r(l(x[i]))]+[['?','?<'][l(x)<3]]+[x[i+1][j]+['1',''][j>=l(x[i])//2]for j in r(l(x[i]))]for i in r(0,l(x),2)])

A function f that takes input of the truth table values as a list of Booleans of the form ['1','1','1','0','0','1'...], where '1' is truthy and '0' is falsey, and returns a Stackylogic program.

Try it on Ideone

If you want to test a produced program, you can use GamrCorps's Convex interpreter here.

How it works

This is a recursive function and uses the inductive method described in the question.

At the zero-indexed recursion level a, the function creates n/2 a+1-input Stackylogic programs from the n a-input programs in the list. This is done by joining all adjacent pairs of two programs in the list with ?; since the cursor is always at the middle element of each constituent program, the required appending of 0 or 1 can be performed by iterating over each line of the programs being joined, and appending if the index of the current line is less than or equal to/greater than or equal to the middle index as appropriate. If the list contains only two programs, the next recursive call will give the final program; since this requires a cursor, joining instead occurs on ?<.

When the list has length 1, the list must contain just one element containing the full program. Hence, all lines in the program are joined on a newline, and then returned.

An example helps to illustrate this:

Take the input ['1', '1', '1', '0', '0', '1', '1', '1'].

Level  Return value

0  [['1', '?', '1'], ['1', '?', '0'], ['0', '?', '1'], ['1', '?', '1']]
1  [['1', '?', '10', '?', '11', '?', '0'], ['0', '?', '10', '?', '11', '?', '1']]
2  [['1', '?', '10', '?', '110', '?0', '00', '?<', '01', '?1', '101', '?', '11', '?', '1']]
3  '1\n?\n10\n?\n110\n?0\n00\n?<\n01\n?1\n101\n?\n11\n?\n1'

which when printed gives:

1
?
10
?
110
?0
00
?<
01
?1
101
?
11
?
1

#Python 3, 352 208 205 bytes

This is still very ungolfed, and I will try to add an explanation later. After some modifications, I managed to remove 144 147 bytes.

f=lambda x,l=len,r=range:'\n'.join(*x)if l(x)<2 else f([[x[i][j]+['0',''][j<=l(x[i])//2]for j in r(l(x[i]))]+[['?','?<'][l(x)<3]]+[x[i+1][j]+['1',''][j>=l(x[i])//2]for j in r(l(x[i]))]for i in r(0,l(x),2)])

A function f that takes input of the truth table values as a list of Booleans of the form ['1','1','1','0','0','1'...], where '1' is truthy and '0' is falsey, and returns a Stackylogic program.

Try it on Ideone

If you want to test a produced program, you can use GamrCorps's Convex interpreter here.

How it works

This is a recursive function and uses the inductive method described in the question.

At the zero-indexed recursion level a, the function creates n/2 a+1-input Stackylogic programs from the n a-input programs in the list. This is done by joining all adjacent pairs of two programs in the list with ?; since the cursor is always at the middle element of each constituent program, the required appending of 0 or 1 can be performed by iterating over each line of the programs being joined, and appending if the index of the current line is less than or equal to/greater than or equal to the middle index as appropriate. If the list contains only two programs, the next recursive call will give the final program; since this requires a cursor, joining instead occurs on ?<.

When the list has length 1, the list must contain just one element containing the full program. Hence, all lines in the program are joined on a newline, and then returned.

An example helps to illustrate this:

Take the input ['1', '1', '1', '0', '0', '1', '1', '1'].

Level  Return value

0  [['1', '?', '1'], ['1', '?', '0'], ['0', '?', '1'], ['1', '?', '1']]
1  [['1', '?', '10', '?', '11', '?', '0'], ['0', '?', '10', '?', '11', '?', '1']]
2  [['1', '?', '10', '?', '110', '?0', '00', '?<', '01', '?1', '101', '?', '11', '?', '1']]
3  '1\n?\n10\n?\n110\n?0\n00\n?<\n01\n?1\n101\n?\n11\n?\n1'

which when printed gives:

1
?
10
?
110
?0
00
?<
01
?1
101
?
11
?
1

#Python 3, 352 208 bytes

This is still very ungolfed, and I will try to add an explanation later. After some modifications, I managed to remove 144 bytes.

f=lambda x,l=len,r=range:'\n'.join(*x)if l(x)<2 else f([[x[i*2][j]+['0',''][j<=l(x[i])//2]for j in r(l(x[i]))]+[['?','?<'][l(x)<3]]+[x[i*2+1][j]+['1',''][j>=l(x[i])//2]for j in r(l(x[i]))]for i in r(l(x)//2)])

A function f that takes input of the truth table values as a list of Booleans of the form ['1','1','1','0','0','1'...], where '1' is truthy and '0' is falsey, and returns a Stackylogic program.

Try it on Ideone

If you want to test a produced program, you can use GamrCorps's Convex interpreter here.

How it works

This is a recursive function and uses the inductive method described in the question.

At the zero-indexed recursion level a, the function creates n/2 a+1-input Stackylogic programs from the n a-input programs in the list. This is done by joining all adjacent pairs of two programs in the list with ?; since the cursor is always at the middle element of each constituent program, the required appending of 0 or 1 can be performed by iterating over each line of the programs being joined, and appending if the index of the current line is less than or equal to/greater than or equal to the middle index as appropriate. If the list contains only two programs, the next recursive call will give the final program; since this requires a cursor, joining instead occurs on ?<.

When the list has length 1, the list must contain just one element containing the full program. Hence, all lines in the program are joined on a newline, and then returned.

An example helps to illustrate this:

Take the input `['1', '1', '1', '0', '0', '1', '1', '1']`.

Level  Return value

0  [['1', '?', '1'], ['1', '?', '0'], ['0', '?', '1'], ['1', '?', '1']]
1  [['1', '?', '10', '?', '11', '?', '0'], ['0', '?', '10', '?', '11', '?', '1']]
2  [['1', '?', '10', '?', '110', '?0', '00', '?<', '01', '?1', '101', '?', '11', '?', '1']]
3  '1\n?\n10\n?\n110\n?0\n00\n?<\n01\n?1\n101\n?\n11\n?\n1'

which when printed gives:

1
?
10
?
110
?0
00
?<
01
?1
101
?
11
?
1

#Python 3, 352 208 205 bytes

This is still very ungolfed, and I will try to add an explanation later. After some modifications, I managed to remove 144 147 bytes.

f=lambda x,l=len,r=range:'\n'.join(*x)if l(x)<2 else f([[x[i][j]+['0',''][j<=l(x[i])//2]for j in r(l(x[i]))]+[['?','?<'][l(x)<3]]+[x[i+1][j]+['1',''][j>=l(x[i])//2]for j in r(l(x[i]))]for i in r(0,l(x),2)])

A function f that takes input of the truth table values as a list of Booleans of the form ['1','1','1','0','0','1'...], where '1' is truthy and '0' is falsey, and returns a Stackylogic program.

Try it on Ideone

If you want to test a produced program, you can use GamrCorps's Convex interpreter here.

How it works

This is a recursive function and uses the inductive method described in the question.

At the zero-indexed recursion level a, the function creates n/2 a+1-input Stackylogic programs from the n a-input programs in the list. This is done by joining all adjacent pairs of two programs in the list with ?; since the cursor is always at the middle element of each constituent program, the required appending of 0 or 1 can be performed by iterating over each line of the programs being joined, and appending if the index of the current line is less than or equal to/greater than or equal to the middle index as appropriate. If the list contains only two programs, the next recursive call will give the final program; since this requires a cursor, joining instead occurs on ?<.

When the list has length 1, the list must contain just one element containing the full program. Hence, all lines in the program are joined on a newline, and then returned.

An example helps to illustrate this:

Take the input ['1', '1', '1', '0', '0', '1', '1', '1'].

Level  Return value

0  [['1', '?', '1'], ['1', '?', '0'], ['0', '?', '1'], ['1', '?', '1']]
1  [['1', '?', '10', '?', '11', '?', '0'], ['0', '?', '10', '?', '11', '?', '1']]
2  [['1', '?', '10', '?', '110', '?0', '00', '?<', '01', '?1', '101', '?', '11', '?', '1']]
3  '1\n?\n10\n?\n110\n?0\n00\n?<\n01\n?1\n101\n?\n11\n?\n1'

which when printed gives:

1
?
10
?
110
?0
00
?<
01
?1
101
?
11
?
1