Critical exponents of the 3d Ising and related models from Conformal Bootstrap

Latex, 19 pages, 9 figures, v4: updated literature resultsThe constraints of conformal bootstrap are applied to investigate a set of conformal field theories in various dimensions. The prescriptions can be applied to both unitary and non unitary theories allowing for the study of the spectrum of low-lying primary operators of the theory. We evaluate the lowest scaling dimensions of the local operators associated with the Yang-Lee edge singularity for $2 \le D \le 6$. Likewise we obtain the scaling dimensions of six scalars and four spinning operators for the 3d critical Ising model. Our findings are in agreement with existing results to a per mill precision and estimate several new exponents

Quantitative Argumentation Debates with Votes for Opinion Polling

Opinion polls are used in a variety of settings to assess the opinions of a population, but they mostly conceal the reasoning behind these opinions. Argumentation, as understood in AI, can be used to evaluate opinions in dialectical exchanges, transparently articulating the reasoning behind the opinions. We give a method integrating argumentation within opinion polling to empower voters to add new statements that render their opinions in the polls individually rational while at the same time justifying them. We then show how these poll results can be amalgamated to give a collectively rational set of voters in an argumentation framework. Our method relies upon Quantitative Argumentation Debate for Voting (QuAD-V) frameworks, which extend QuAD frameworks (a form of bipolar argumentation frameworks in which arguments have an intrinsic strength) with votes expressing individuals’ opinions on arguments

ArguCast: a system for online multi-forecasting with gradual argumentation

Judgmental forecasting is a form of forecasting which employs (human) users to make predictions about specied future events. Judgmental forecasting has been shown to perform better than quantitative methods for forecasting, e.g. when historical data is unavailable or causal reasoning is needed. However, it has a number of limitations, arising from users’ irrationality and cognitive biases. To mitigate against these phenomena, we leverage on computational argumentation, a eld which excels in the representation and resolution of conicting knowledge and human-like reasoning, and propose novel ArguCast frameworks (ACFs) and the novel online system ArguCast, integrating ACFs. ACFs and ArguCast accommodate multi-forecasting, by allowing multiple users to debate on multiple forecasting predictions simultaneously, each potentially admitting multiple outcomes. Finally, we propose a novel notion of user rationality in ACFs based on votes on arguments in ACFs, allowing the ltering out of irrational opinions before obtaining group forecasting predictions by means commonly used in judgmental forecasting

Adapting the DF-QuAD algorithm to bipolar argumentation

We define a quantitative semantics for evaluating the strength of arguments in Bipolar Argumentation frameworks (BAFs) by adapting the Discontinuity-Free QuAD (DF-QuAD) algorithm previously used for evaluating the strength of arguments in Quantitative Argumentation Debates (QuAD) frameworks. We study the relationship between the new semantics and some existing semantics for other argumentation frameworks, as well as some properties of the semantics

Argumentation-based recommendations: fantastic explanations and how to find them

A significant problem of recommender systems is their inability to explain recommendations, resulting in turn in ineffective feedback from users and the inability to adapt to users’ preferences. We propose a hybrid method for calculating predicted ratings, built upon an item/aspect-based graph with users’ partially given ratings, that can be naturally used to provide explanations for recommendations, extracted from user-tailored Tripolar Argumentation Frameworks (TFs). We show that our method can be understood as a gradual semantics for TFs, exhibiting a desirable, albeit weak, property of balance. We also show experimentally that our method is competitive in generating correct predictions, compared with state-of-the-art methods, and illustrate how users can interact with the generated explanations to improve quality of recommendations

Boundary and Interface CFTs from the Conformal Bootstrap

40 pages, many figures v2: new results on 3d O(N) bulk spectrum added, one appendix eliminated, typos corrected, references updated. v3: two references to high precision Monte Carlo data added; they nicely agree with our bootstrap calculations. Matches published version. v4: results for the extraordinary transition for N=2,3 removed: see added noteWe explore some consequences of the crossing symmetry for defect conformal field theories, focusing on codimension one defects like flat boundaries or interfaces. We study surface transitions of the 3d Ising and other O(N) models through numerical solutions to the crossing equations with the method of determinants. In the extraordinary transition, where the low-lying spectrum of the surface operators is known, we use the bootstrap equations to obtain information on the bulk spectrum of the theory. In the ordinary transition the knowledge of the low-lying bulk spectrum allows to calculate the scale dimension of the relevant surface operator, which compares well with known results of two-loop calculations in 3d. Estimates of various OPE coefficients are also obtained. We also analyze in 4-epsilon dimensions the renormalization group interface between the O(N) model and the free theory and check numerically the results in 3d

Renormalization constants of the lattice energy momentum tensor using the gradient flow

We employ a new strategy for a non perturbative determination of the renormalized energy momentum tensor. The strategy is based on the definition of suitable lattice Ward identities probed by observables computed along the gradient flow. The new set of identities exhibits many interesting qualities, arising from the UV finiteness of flowed composite operators. In this paper we show how this method can be used to non perturbatively renormalize the energy momentum tensor for a SU(3) Yang-Mills theory, and report our numerical results

Explaining classifiers’ outputs with causal models and argumentation

We introduce a conceptualisation for generating argumentation frameworks (AFs) from causal models for the purpose of forging explanations for mod-els’ outputs. The conceptualisation is based on reinterpreting properties of semantics of AFs as explanation moulds, which are means for characterising argumentative relations. We demonstrate our methodology by reinterpreting the property of bi-variate reinforcement in bipolar AFs, showing how the ex-tracted bipolar AFs may be used as relation-based explanations for the outputs of causal models. We then evaluate our method empirically when the causal models represent (Bayesian and neural network) machine learning models for classification. The results show advantages over a popular approach from the literature, both in highlighting specific relationships between feature and classification variables and in generating counterfactual explanations with respect to a commonly used metric

The "Games of Argumentation" web platform

This demo presents the web system “Games of Argumentation”, which allows users to build argumentation graphs and examine them in a game-theoretical manner using up to three different evaluation techniques. The concurrent evaluations of arguments using different techniques, which may be qualitative or quantitative, provides a significant aid to users in both understanding game-theoretical argumentation semantics and pinpointing their differences from alternative semantics, traditional or otherwise, to differentiate between them