Timeline for Questions from a new introduction to modal logic by Hughes and Cresswell
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 19, 2019 at 15:59 | comment | added | Rob | @Bumble. Also by your interpretation of the rules Player A would still have raised their hand for Mq. So you haven't explained how they could raise their hand for Lq but not Mq, which was the second assumption listed in the OP. | |
| May 19, 2019 at 15:51 | history | edited | Rob | CC BY-SA 4.0 |
deleted 132 characters in body
|
| May 19, 2019 at 15:50 | comment | added | Rob | @Bumble, I believe you are fundamentally mistaken. "If Mα is called raise your hand IF AT LEAST ONE OF THE PLAYERS you can see raised his or her hand" (p. 18). The language here seems to suggest that you must see at least one player. If you can see no one, you do not raise your hand. None does not equal some (sorry for the caps, it won't let me bold in a comment). | |
| May 17, 2019 at 12:56 | comment | added | Bumble | My comment is based exactly on the rules of the game. If the player can see nobody at all then they will raise their hand for every call of La, because trivially everybody they can see has raised their hand. This is why Lq -> Mq is not a theorem of K, and requires axiom D. | |
| May 17, 2019 at 7:40 | comment | added | Rob | The context of the question was the version of the game they propose, modified to account for modal operators. See p. 18. Your comment is a non-sequitur. You have NOT explained how based on the rules of the game (see my quote) how you could raise your hand for Lq but not Mq. | |
| May 16, 2019 at 23:47 | comment | added | Bumble | At this stage of their book (chapter 1), Hughes and Cresswell have only introduced axiom K. Without axiom D, Lq -> Mq is not a theorem, so it is not a contradiction for the player to raise their hand for La and not for Ma. It might be that the player can see nobody at all, in which case La is true and Ma is false. On the other hand, Mp -> (Lq -> Mq) is a theorem of K, because Mp requires some other player to be visible. | |
| May 16, 2019 at 23:23 | history | edited | Rob | CC BY-SA 4.0 |
added 39 characters in body
|
| May 16, 2019 at 18:07 | history | edited | Rob | CC BY-SA 4.0 |
added 12 characters in body
|
| May 16, 2019 at 14:50 | history | edited | Rob | CC BY-SA 4.0 |
added 127 characters in body
|
| May 16, 2019 at 14:41 | history | edited | Rob | CC BY-SA 4.0 |
added 248 characters in body
|
| May 16, 2019 at 14:30 | history | edited | Rob | CC BY-SA 4.0 |
deleted 22 characters in body
|
| May 16, 2019 at 14:19 | history | answered | Rob | CC BY-SA 4.0 |