## Tuesday, September 28, 2010

### N goes to India

Jesse and I will be traveling to the 4th Indian Conference on Logic and its Applications to present our paper "A curious dialogical logic and its composition problem".

## Tuesday, September 14, 2010

### Returning to assumptions

In an earlier post I discussed how to handle reasoning from assumptions in the dialogic framework. My first proposal was:

**Reasoning from Assumptions Attempt #1 (Naive)**: Fix a set of formulas Γ. Γ\vDashφ iff P has a winning strategy for φ when he is allowed to assert any ψ\inΓ, either as an attack or as a defense. I quickly realized that this was not acceptable, since it doesn't work to capture reasoning from implication in CL; take the consequence (p&q)\vDash(p&q): If P asserts the right-hand side, then the material on the left won't help him at all when O attacks (p&q). This lead to:**Reasoning from Assumptions (Naive) Attempt #2**: Γ\vDashφ iff P has a winning strategy for φ when he is allowed to attack any &psi&\inΓ and to defend with anything in Γ. Now, if we think that any formula is a consequence of its own assumption in N (which may or may not be a reasonable thought), then this approach doesn't work since it fails to make (pVq)\vDash(pVq); if P asserts pVq (the right-hand side), and O attacks it, then if P counterattacks by attacking pVq (the left-hand side), this allows O to defend, and the dialogue will never end. This is only a problem if we think that this consequence should be valid in N. Assuming we do, let's get a bit more creative:**Reasoning from Assumptions Attempt #3**: Let a(Γ) be the set of atoms which are subformulas of elements of Γ. Then Γ\vDashφ iff P has a winning strategy for φ when he is allowed to assert anything in a(Γ) whenever he wants. This fails because then (pVq)\vDash(p&q). We should also consider:**Reasoning from Assumptions #4 (Jesse's proposal)**: Γ\vDashφ iff there is Γ'\subseteqΓ and \vDash\bigwedge Γ'\rightarrow φ. I dislike this suggestion because it builds in the validity of the deduction theorem, which begs the question against the possibility of reasoning from assumptions in N. I haven't come up with any other candidates yet.## Wednesday, September 8, 2010

### News and events

We have had two short papers accepted to the 17th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Yogyakarta, Indonesia, October 10-15, 2010:

- Jesse Alama & Sara L. Uckelman, "Playing Lorenzen dialogue games on the Web".
- Jesse Alama & Sara L. Uckelman, "Proof rules for the dialogical logic N".

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