tag:blogger.com,1999:blog-5371132400241072988.post5253653644115551577..comments2012-10-16T02:22:45.319-07:00Comments on TONIGHT: Proponent v. Opponent: returning to the role of EJesse Alamahttp://www.blogger.com/profile/18300729364134604326noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-5371132400241072988.post-71534630481329843712011-07-01T08:17:24.816-07:002011-07-01T08:17:24.816-07:00I think I also have a (certainly similar and perha...I think I also have a (certainly similar and perhaps equivalent result):<br /><br />Let CL'= {D10 + D3,1,∞ + D4,1,∞}. P has a winning CL'-strategy for φ iff he has a winning CL-strategy for φ.<br /><br />Proof.<br />(⇐) E implies D13, which is equivalent to D4,1,∞, and E implies D3,1,∞. Thus, any CL-strategy will also be a CL'-strategy.<br />(⇒) Proved analogously to the proofs of the bold conjectures for IL.Sara L. Uckelmanhttps://www.blogger.com/profile/14716054827293611237noreply@blogger.comtag:blogger.com,1999:blog-5371132400241072988.post-67110626532787059372011-07-01T01:18:31.652-07:002011-07-01T01:18:31.652-07:00For (2), how do you prove the N+D14+E -> N+D14 ...For (2), how do you prove the N+D14+E -> N+D14 direction?Sara L. Uckelmanhttps://www.blogger.com/profile/14716054827293611237noreply@blogger.comtag:blogger.com,1999:blog-5371132400241072988.post-37689226621863710722011-07-01T01:15:37.903-07:002011-07-01T01:15:37.903-07:00Cool. Exactly in line with what we expected.Cool. Exactly in line with what we expected.Sara L. Uckelmanhttps://www.blogger.com/profile/14716054827293611237noreply@blogger.comtag:blogger.com,1999:blog-5371132400241072988.post-4284199669657015572011-07-01T01:05:31.843-07:002011-07-01T01:05:31.843-07:00I believe I've found a proof that the N rules ...I believe I've found a proof that the N rules plus D14 gives us CL and that the E rule is redundant for this ruleset. That is, I believe have proofs for:<br /><br />(1) there exists a winning N+D14 strategy for A iff A is a tautology<br /><br />(2) there exists a winning N+D14+E strategy for A iff there exists a winning N+D14 strategy for A.<br /><br />The proof of (1) is a modification of the proof that we used for the Ei ruleset in our "Dialogue games for classical logic".<br /><br />I believe I also have proofs that deal with classical logic in the context of the ruleset N+No-Repetitions, and proofs that E is redundant for this ruleset as well.Jesse Alamahttps://www.blogger.com/profile/18300729364134604326noreply@blogger.com