Annals of Mathematics and Artificial Intelligence最新文献

In resource contribution games, a class of non-cooperative games, the players want to obtain a bundle of resources and are endowed with bags of bundles of resources that they can make available into a common for all to enjoy. Available resources can then be used towards their private goals. A player is potentially satisfied with a profile of contributed resources when his bundle could be extracted from the contributed resources. Resource contention occurs when the players who are potentially satisfied, cannot actually all obtain their bundle. The player’s preferences are always single-minded (they consider a profile good or they do not) and parsimonious (between two profiles that are equally good, they prefer the profile where they contribute less). What makes a profile of contributed resources good for a player depends on their attitude towards resource contention. We study the problem of deciding whether an outcome is a pure Nash equilibrium for three kinds of players’ attitudes towards resource contention: public contention-aversity, private contention-aversity, and contention-tolerance. In particular, we demonstrate that in the general case when the players are contention-averse, then the problem is harder than when they are contention-tolerant. We then identify a natural class of games where, in presence of contention-averse preferences, it becomes tractable, and where there is always a Nash equilibrium.

We introduce a novel framework for classification with a rejection option that consists of simultaneously learning two functions: a classifier along with a rejection function. We present a full theoretical analysis of this framework including new data-dependent learning bounds in terms of the Rademacher complexities of the classifier and rejection families as well as consistency and calibration results. These theoretical guarantees guide us in designing new algorithms that can exploit different kernel-based hypothesis sets for the classifier and rejection functions. We compare our general framework with the special case of confidence-based rejection for which we also devise alternative loss functions and algorithms. We report the results of several experiments showing that our kernel-based algorithms can yield a notable improvement over the best existing confidence-based rejection algorithm.

Given a Boolean relational specification (F(textbf{X}, textbf{Y})), where (textbf{X}) is a vector of inputs and (textbf{Y}) is a vector of outputs, Boolean functional synthesis requires us to compute a vector of (Skolem) functions (varvec{Psi }(textbf{X})), one for each output in (textbf{Y}), such that (F(textbf{X}, varvec{Psi }(textbf{X})) leftrightarrow exists textbf{Y},F(textbf{X},textbf{Y})) holds. This problem lies at the heart of many applications and has received significant attention in recent years. In this paper, we investigate the role of representation of (F(textbf{X}, textbf{Y})) and of (varvec{Psi }(textbf{X})) in determining the computational hardness of Boolean functional synthesis. We start by showing that an efficient way of existentially quantifying variables from a Boolean formula in a given order yields an efficient solution to Boolean functional synthesis and vice versa. We then propose a semantic normal form, called SynNNF, that guarantees polynomial-time synthesis and characterizes polynomial-time existential quantification for a given order of quantification of variables. We show that several syntactic and other semantic normal forms for Boolean formulas studied in the knowledge compilation literature are subsumed by SynNNF, and that SynNNF is exponentially more succinct than most of them. We also investigate how the representation of the synthesized (Skolem) functions (varvec{Psi }(textbf{X})) affects the complexity of Boolean functional synthesis, and present a map of complexity based on the representations of (F(textbf{X},textbf{Y})) and (varvec{Psi }(textbf{X})). Finally, we propose an algorithm to compile a specification represented as a NNF (including CNF) circuit to SynNNF. We present results of an extensive set of experiments conducted using an implementation of the above algorithm, and two other tools available in the public domain.

The Bdi model of rational agency has been studied for over three decades. Many robust multiagent systems have been developed, and a number of Bdi logics have been studied. Following this intensive development phase, the importance of integrating Bdi models with inconsistency handling and revision theory have been emphasized. There is also a demand for a tighter connection between Bdi-based implementations and Bdi logics. In this paper, we address these postulates by introducing a novel, paraconsistent logical Bdi model close to implementation, with building blocks that can be represented as Sql/rule-based databases. Importantly, tractability is achieved by reasoning as querying. This stands in a sharp contrast to the high complexity of known Bdi logics. We also extend belief shadowing, a shallow and lightweight alternative to deep and computationally demanding belief revision, to encompass agents’ motivational attitudes.

We investigate Tiered Coalition Formation Games (TCFGs), a cooperative game inspired by the stratification of Pokémon on the fan website, Smogon. It is known that, under match-up oriented preferences, Nash and core stability are equivalent. We previously introduced a notion of socially conscious stability for TCFGs, and introduced a game variant with fixed k-length tier lists. In this work we show that in tier lists under match-up oriented preferences, socially conscious stability is equivalent to Nash stability and to core stability, but in k-tier lists, the three stability notions are distinct. We also give a necessary condition for tier list stability in terms of robustness (the minimum in-tier utility of an agent). We introduce a notion of approximate Nash stability and approximately socially conscious stability, and provide experiments on the empirical run time of our k-tier local search algorithm, and the performance of our algorithms for generating approximately socially consciously stable tier lists.

Feature models are commonly used to specify the valid configurations of product lines. As industrial feature models are typically complex, researchers and practitioners employ various automated analyses to study the configuration spaces. Many of these automated analyses require that numerous complex computations are executed on the same feature model, for example by querying a SAT or #SATsolver. With knowledge compilation, feature models can be compiled in a one-time effort to a target language that enables polynomial-time queries for otherwise more complex problems. In this work, we elaborate on the potential of employing knowledge compilation on feature models. First, we gather various feature-model analyses and study their computational complexity with regard to the underlying computational problem and the number of solver queries required for the respective analysis. Second, we collect knowledge-compilation target languages and map feature-model analyses to the languages that make the analysis tractable. Third, we empirically evaluate publicly available knowledge compilers to further inspect the potential benefits of knowledge-compilation target languages.