Which of these 128 combinations are satisfiable in Carmo and Jones style deontic logic? (1=true, 0=false) (Here 5(c) is the strong version.)
Some possibilities are ruled out by Observation 5.1.2 that says 5(bcde) imply 5(g); and Lemma II.2.2 that says 5(abcd) imply 5(f), formalized by RJ Reiff.
| 5(abcdefg) | Model |
|---|---|
| 0000000 | ? |
| 0000001 | ? |
| 0000010 | ? |
| 0000011 | ? |
| 0000100 | ? |
| 0000101 | ? |
| 0000110 | ? |
| 0000111 | ? |
| 0001000 | ? |
| 0001001 | ? |
| 0001010 | ? |
| 0001011 | ? |
| 0001100 | ? |
| 0001101 | ? |
| 0001110 | ? |
| 0001111 | ? |
| 0010000 | ? |
| 0010001 | ? |
| 0010010 | ? |
| 0010011 | ? |
| 0010100 | ? |
| 0010101 | ? |
| 0010110 | ? |
| 0010111 | ? |
| 0011000 | ? |
| 0011001 | ? |
| 0011010 | ? |
| 0011011 | ? |
| 0011100 | ? |
| 0011101 | ? |
| 0011110 | ? |
| 0011111 | ? |
| 0100000 | ? |
| 0100001 | ? |
| 0100010 | ? |
| 0100011 | ? |
| 0100100 | ? |
| 0100101 | ? |
| 0100110 | ? |
| 0100111 | ? |
| 0101000 | ? |
| 0101001 | ? |
| 0101010 | ? |
| 0101011 | ? |
| 0101100 | ? |
| 0101101 | ? |
| 0101110 | ? |
| 0101111 | ? |
| 0110000 | ? |
| 0110001 | ? |
| 0110010 | ? |
| 0110011 | ? |
| 0110100 | ? |
| 0110101 | ? |
| 0110110 | ? |
| 0110111 | ? |
| 0111000 | ? |
| 0111001 | ? |
| 0111010 | ? |
| 0111011 | ? |
| 0111100 | none; Obs. 5.1.2 |
| 0111101 | ? |
| 0111110 | none; Obs. 5.1.2 |
| 0111111 | see: A5_not_implied |
| 1000000 | ? |
| 1000001 | ? |
| 1000010 | ? |
| 1000011 | ? |
| 1000100 | ? |
| 1000101 | ? |
| 1000110 | ? |
| 1000111 | ? |
| 1001000 | ? |
| 1001001 | ? |
| 1001010 | ? |
| 1001011 | ? |
| 1001100 | ? |
| 1001101 | ? |
| 1001110 | ? |
| 1001111 | ? |
| 1010000 | ? |
| 1010001 | ? |
| 1010010 | ? |
| 1010011 | ? |
| 1010100 | ? |
| 1010101 | ? |
| 1010110 | ? |
| 1010111 | ? |
| 1011000 | ? |
| 1011001 | ? |
| 1011010 | ? |
| 1011011 | ? |
| 1011100 | ? |
| 1011101 | ? |
| 1011110 | ? |
| 1011111 | see: B5_not_implied’ |
| 1100000 | ? |
| 1100001 | ? |
| 1100010 | ? |
| 1100011 | ? |
| 1100100 | ? |
| 1100101 | ? |
| 1100110 | ? |
| 1100111 | ? |
| 1101000 | ? |
| 1101001 | ? |
| 1101010 | ? |
| 1101011 | ? |
| 1101100 | see: C5_not_implied’ |
| 1101101 | ? |
| 1101110 | ? |
| 1101111 | ? |
| 1110000 | ? |
| 1110001 | ? |
| 1110010 | ? |
| 1110011 | ? |
| 1110100 | ? |
| 1110101 | see theorem: strong_do_not_imply_5d_or_5f |
| 1110110 | ? |
| 1110111 | ? |
| 1111000 | none; see II.2.2 |
| 1111001 | none; see II.2.2 |
| 1111010 | ? |
| 1111011 | see theorem: do_not_imply_5e |
| 1111100 | impossible as 5(fg) follow from 5(abcde) |
| 1111101 | impossible as 5(fg) follow from 5(abcde) |
| 1111110 | impossible as 5(fg) follow from 5(abcde) |
| 1111111 | stayAlive, alive, noObligations |