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We present two dialectic procedures for the sceptical ideal semantics for argumentation. The first procedure is defined in terms of dispute trees, for abstract argumentation frameworks. The second procedure is defined in dialectical terms, for assumption-based argumentation frameworks. The procedures are adapted from (variants of) corresponding procedures for computing the credulous admissible semantics for assumption-based argumentation, proposed in [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159]. We prove that the first procedure is sound and complete, and the second procedure is sound in general and complete for a special but natural class of assumption-based argumentation frameworks, that we refer to as p-acyclic. We also prove that in the case of p-acyclic assumption-based argumentation frameworks (a variant of) the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159] for the admissible semantics is complete. Finally, we present a variant of the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159] that is sound for the sceptical grounded semantics

We present a family of dialectic proof procedures for the admissibility semantics of assumption-based argumentation. These proof procedures are defined for any conventional logic formulated as a collection of inference rules and show how any such logic can be extended to a dialectic argumentation system. The proof procedures find a set of assumptions, to defend a given belief, by starting from an initial set of assumptions that supports an argument for the belief and adding defending assumptions incrementally to counterattack all attacks. The proof procedures share the same notion of winning strategy for a dispute and differ only in the search strategy they use for finding it. The novelty of our approach lies mainly in its use of backward reasoning to construct arguments and potential arguments, and the fact that the proponent and opponent can attack one another before an argument is completed. The definition of winning strategy can be implemented directly as a non-deterministic program, whose search strategy implements the search for defences.

We present updated results from the NOvA experiment for ν μ → ν μ and ν μ → ν e oscillations from an exposure of 8.85 × 10 20 protons on target, which represents an increase of 46% compared to our previous publication. The results utilize significant improvements in both the simulations and analysis of the data. A joint fit to the data for ν μ disappearance and ν e appearance gives the best-fit point as normal mass hierarchy, Δm 2 32 ¼ 2.44 × 10 −3 eV 2 =c 4 , sin 2 θ 23 ¼ 0.56, and δ CP ¼ 1.21π. The 68.3% confidence intervals in the normal mass hierarchy are Δm 2 32 ∈ ½2.37; 2.52 × 10 −3 eV 2 =c 4 , sin 2 θ 23 ∈ ½0.43; 0.51 ∪ ½0.52; 0.60, and δ CP ∈ ½0; 0.12π ∪ ½0.91π; 2π. The inverted mass hierarchy is disfavored at the 95% confidence level for all choices of the other oscillation parameters.