Annals of Mathematics and Artificial Intelligence最新文献

The main purpose of this article is to develop a lattice point of view for the study of argumentation framework extensions. We first characterize self-defending sets of an argumentation framework by the closed sets of an implicational system that can be computed in polynomial time from the argumentation framework. On the other hand, for any implicational system (Sigma ) over the set of arguments, we associate an argumentation framework whose admissible sets are in bijection with closed sets of (Sigma ). Second, we propose conflict-closed sets reduction rules, based on implicational system, to find out minimal subsets of vertex cover closed while maintaining all potential admissible extensions as well as preferred extensions. This leads to a polynomial delay and space algorithm to enumerate admissible sets of argumentation frameworks without even cycles. Finally, based on the implicational system, a new decomposition of the argumentation framework is defined and leads to a polynomial delay and space algorithm to enumerate admissible sets for a bipartite argumentation framework. The proposed algorithm improves the exponential space complexity of previous algorithms.

We describe a system for automated ruler and compass triangle constructions in hyperbolic geometry. We discuss key differences between constructions in Euclidean and hyperbolic setting, compile a list of primitive constructions and lemmas used for constructions in hyperbolic geometry, build an automated system for solving construction problems, and test it on a corpus of triangle-construction problems. We extend the list of primitive constructions for hyperbolic geometry by several constructions that cannot be done by ruler and compass, but can be done by using algebraic calculations and show that such extended system solves more problems. We also use a dynamic geometry library to build an online compendium containing construction descriptions, illustrations, and step-by-step animations.

Bayesian Learning is an inference method designed to tackle exploration-exploitation trade-off as a function of the uncertainty of a given probability model from observations within the Reinforcement Learning (RL) paradigm. It allows the incorporation of prior knowledge, as probabilistic distributions, into the algorithms. Finding the resulting Bayes-optimal policies is notorious problem. We focus our attention on RL of a special kind of ergodic and controllable Markov games. We propose a new framework for computing the near-optimal policies for each agent, where it is assumed that the Markov chains are regular and the inverse of the behavior strategy is well defined. A fundamental result of this paper is the development of a theoretical method that, based on the formulation of a non-linear problem, computes the near-optimal adaptive-behavior strategies and policies of the game under some restrictions that maximize the expected reward. We prove that such behavior strategies and the policies satisfy the Bayesian-Nash equilibrium. Another important result is that the RL process learn a model through the interaction of the agents with the environment, and shows how the proposed method can finitely approximate and estimate the elements of the transition matrices and utilities maintaining an efficient long-term learning performance measure. We develop the algorithm for implementing this model. A numerical empirical example shows how to deploy the estimation process as a function of agent experiences.

We investigated the relationship between various design approaches of AgentSpeak code for Jason Beliefs-Desires-Intentions (BDI) agents and their performance in a simulated automotive collision avoidance scenario. Also explored was how the approaches affected software maintainability, assessed through coupling, cohesion, and cyclomatic complexity. We then compared each agent’s performance, specifically their reasoning cycle duration and their responsiveness. Our findings revealed that agents with looser coupling and higher cohesion are more responsive to stimuli, implying that more maintainable AgentSpeak code can result in better performing agents. Performance was inversely related to cyclomatic complexity.

The Geometry Automated-Theorem-Provers (GATP) based on the deductive database method use a data-based search strategy to improve the efficiency of forward chaining. An implementation of such a method is expected to be able to efficiently prove a large set of geometric conjectures, producing readable proofs. The number of conjectures a given implementation can prove will depend on the set of inference rules chosen, the deductive database method is not a decision procedure. Using an approach based in an SQL database library and using an in-memory database, the implementation described in this paper tries to achieve the following goals. Efficiency in the management of the inference rules, the set of already known facts and the new facts discovered, by the use of the efficient data manipulation techniques of the SQL library. Flexibility, by transforming the inference rules in SQL data manipulation language queries, will open the possibility of meta-development of GATP based on a provided set of rules. Natural language and visual renderings, possible by the use of a synthetic forward chaining method. Implemented as an open source library, that will open its use by third-party programs, e.g. the dynamic geometry systems.