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Dempster-Shafer evidence theory has been widely used in various fields of applications, because of the flexibility and effectiveness in modeling uncertainties without prior information. However, the existing evidence theory is insufficient…
The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…
We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…
Geoffrion's theorem is a fundamental result from mathematical programming assessing the quality of Lagrangian relaxation, a standard technique to get bounds for integer programs. An often implicit condition is that the set of feasible…
We provide some examples showing how game-theoretic arguments can be used in computability theory and algorithmic information theory: unique numbering theorem (Friedberg), the gap between conditional complexity and total conditional…
Game theory has been one of the most successful quantitative concepts to describe social interactions, their strategical aspects, and outcomes. Among the payoff matrix quantifying the result of a social interaction, the interaction…
In this article we will propose a completely new point of view for solving one of the most important paradoxes concerning game theory. The solution develop shifts the focus from the result to the strategy s ability to operate in a cognitive…
Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through…
A formula $\phi$ is called \emph{$n$-provable} in a formal arithmetical theory $S$ if $\phi$ is provable in $S$ together with all true arithmetical $\Pi_{n}$-sentences taken as additional axioms. While in general the set of all $n$-provable…
It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We…
We look at substructural calculi from a game semantic point of view, guided by certain intuitions about resource conscious and, more specifically, cost conscious reasoning. To this aim, we start with a game, where player I defends a claim…
According to one of its founders, game theory would soon be a little over a hundred years old . A well-known theory in the academic and strategic fields, it is often the subject of criticism and, for many, seems too simplistic to be truly…
There is a long history in game theory on the topic of Bayesian or "rational" learning, in which each player maintains beliefs over a set of alternative behaviours, or types, for the other players. This idea has gained increasing interest…
The conditioning in the Dempster-Shafer Theory of Evidence has been defined (by Shafer \cite{Shafer:90} as combination of a belief function and of an "event" via Dempster rule. On the other hand Shafer \cite{Shafer:90} gives a…
Dempster/Shafer (D/S) theory has been advocated as a way of representing incompleteness of evidence in a system's knowledge base. Methods now exist for propagating beliefs through chains of inference. This paper discusses how rules with…
We introduce a game-theoretic framework to study the hypothesis testing problem, in the presence of an adversary aiming at preventing a correct decision. Specifically, the paper considers a scenario in which an analyst has to decide whether…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
Number games play a central role in alternating normal play combinatorial game theory due to their real-number-like properties (Conway 1976). Here we undertake a critical re-examination: we begin with integer and dyadic games and identify…
Explaining why aggregated measures change is a critical challenge in data analytics that existing systems struggle to address. While current attribution methods exist, they lack a unified solution that is simultaneously general for…