• Novel logic-based approach to data bias in machine learning predictions for defining and quantifying fairness based on the Ulam game. • New perspectives on the rule of constrained monotonicity valid in the play process of the Ulam game and its generalisation to weighted evidence. • Connection between the notion of correctability and levels of monotonicity satisfied by machine learning algorithms. • Novel game-theoretic framework of algorithmic fairness. In the present work, we develop a novel information-theoretic and logic-based approach to data bias in Machine Learning predictions and show its relevance in the specific context of fairness evaluation. We frame predictions made on biased data as Ulam games, which formalise key aspects of data-driven inference, and from which a variation of the rational non-monotonic consequence relation can be defined. We investigate this framework to model how differential levels of noise in input features impact Machine Learning predictions. To the best of our knowledge, this is the first game-theoretic formalisation of ML unfairness.

Abstract We investigate the relations between bipolar logical argumentation frames and the three main t-norm-based fuzzy logics: Łukasiewicz ( Ł ), Gödel ( $${\textbf {G}}$$ ) and product logic ( $$\varvec{\Pi }$$ ). The arguments that we consider are complex entities, and the inference relation between the support and the claim is instantiated with the standard consequence relation of one specific fuzzy logic. We introduce several argumentative principles defined in terms of the attack and the support relation that refine the existence of such relations whenever the involved arguments share some propositional formulas. Through the notion of argumentative immunity introduced in Corsi and Fermüller (2018a) we finally recover complete semantics for Ł , $${\textbf {G}}$$ and $$\varvec{\Pi }.$$

Abstract Attack principles have been introduced in semi-abstract argumentation frameworks and, in the present work, we interpret them in sequent-based argumentation frameworks. Thus, we investigate the role of minimality and consistency of the support set of an argument. Through the notion of preservation of strength, we introduce a formal criterion to sort out the attack principles; isolate the more “acceptable” ones, i.e. those easier to justify; and recover a new argumentative semantics for the non-classical logic that arises from dropping the rules $(\neg , r)$, $(\land , r)$ and $(\supset , l)$ from Gentzen’s classical sequent calculus for classical logic $\textsf{LK}$.

We investigate the notion of coherence for (non-)additive uncertainty measures from a logico-geometric point of view. Our main result is to the effect that distinct criteria for coherence are not always matched by axiomatically distinct measures of uncertainty. In addition we introduce a metalogic within which this kind of result can be captured formally.

This article continues the investigation started in [19] on the role of possibilistic mixed strategies in strategic-form games. In this earlier work we assumed, as standard in possibility theory, that joint possibility distributions were computed by combining possibilistic mixed strategies with the minimum t-norm. In this paper, we investigate the consequences of defining joint possibility distributions by using any continuous t-norm, with players' expected utilities based on the Choquet integral. We characterise under which conditions a pair of possibilistic mixed strategies is an equilibrium, generalising the results first presented in [19], and also show that the set of equilibria in possibilistic mixed strategies depends on the set of idempotent elements of a t-norm and not just on the chosen t-norm.

We explore systematic connections between weighted (semi-abstract) argumentation frames and t-norm-based fuzzy logics. To this aim we introduce the concept of argumentative immunity, as well as corresponding notions of argumentative soundness and completeness with respect to given sets of logical attack principles. For Gödel logic, a detailed proof of argumentative soundness and completeness with respect to appropriate principles is presented. For Łukasiewicz and product logic this is indicated more briefly, but with some hints on corresponding interpretations of the attack relation between (claims of) arguments. Moreover, the central axiom of prelinearity is analyzed from our argumentation-based perspective.