Annals of Mathematics and Artificial Intelligence最新文献

The AGM paradigm, introduced by Alchourrón, Gärdenfors and Makinson, is a well-established formal framework that identifies the postulates (principles) governing any rational revision operator on belief sets. A central pillar in the study of belief revision is Katsuno and Mendelzon’s representation result, which, based on previous work by Grove, ties together the class of revision operators defined within the AGM paradigm and a special type of total preorder over consistent complete theories (commonly called possible worlds or models). In this article, we lift Katsuno and Mendelzon’s representation result into the realm of the mathematical notion of filters, which are special subsets of partially ordered sets. In particular, we develop a framework for filters revision, by formulating a collection of postulates that constrain the behaviour of revision operators on filters, and establishing a representation result that connects the proposed postulates and a certain type of total preorder over ultrafilters. Overall, we show that AGM-style revision of filters can be obtained with extremely weak assumptions; in fact, significantly weaker than those of the AGM paradigm. This outcome, together with the broad applicability and interdisciplinarity of filters, lends a high level of abstraction to the introduced filters-based framework, which, as we demonstrate, generalizes the AGM paradigm.

Many modern-day systems rely on information that is constantly arriving, and they need to make decisions based on it – a problem known as continuous query answering. In many situations, these systems can benefit from identifying possible outcomes that are consistent with the data available so far. Such scenarios are called hypothetical answers, and previous work has defined them precisely and shown how they can be updated in step with the arrival of additional input. Most existing formalisms assume that data always arrives instantaneously, which is not realistic. In this work, we relax this problem by allowing data to arrive later, and potentially out of order. By revisiting the underlying intuitions in previous work, we develop a more general framework that supports communication delays. The interaction between communication delays and negation poses some challenging problems, which we address using fixpoint theory. We show that the relevant fixpoints can be computed in finite time by a carefully designed algorithm.

We propose a formal model of a knowledge graph (abbr. KG) that classifies the ground triples into sets that correspond to the triple types. The triple types are partially ordered by the sub-type relation. Consequently, the sets of ground triples that are the interpretations of triple types are partially ordered by the subsumption relation. The types of triple patterns restrict the sets of ground triples, which need to be addressed in the evaluation of triple patterns, to the interpretation of the types of triple patterns. Therefore, a schema graph of a KG should include all triple types that are likely to be determined as the types of triple patterns. The stored schema graph consists of the selected triple types that are stored in a KG and the complete schema graph includes all valid triple types of KG. We propose choosing the schema graph, which consists of the triple types from a strip around the stored schema graph, i.e., the triple types from the stored schema graph and some adjacent levels of triple types with respect to the sub-type relation. Given a selected schema graph, the statistics are updated for each ground triple t from a KG. First, we determine the set of triple types stt from the schema graph that are affected by adding a triple t to an RDF store. Finally, the statistics of triple types from the set stt are updated.

An attack graph is a concise portrayal of the various paths within an open system that enable an attacker to reach a prohibited state (such as gaining access to a restricted resource), despite the system’s preventive measures. The assessment of system vulnerability involves examining the presence of such paths. In this work, we analyze attack graphs using a game-theoretic approach. Specifically, we introduce a well-suited game model that represents the dynamics between the system and the attacker, and propose an automata-based solution to demonstrate the absence of vulnerability.

At the ADG 2023 a protocol, implemented on an extension of Larus automated theorem prover, to automatically complete statements and proofs in Euclidean geometry, was presented by S. T. Gonzalez, P. Janičić, and J. Narboux. The approach is logic-based, in contrast to algebraic methods, and its performance was tested on five high-school level geometry problems. In our contribution we address the same five issues with the automated reasoning, algebraic-based, tools of GeoGebra Discovery. The results allow us to reflect on the pros and cons of these two diverse approaches, showing, in particular, the opportunities that GeoGebra Discovery brings to improve human reasoning in geometry.

In this paper, a novel method is presented to increase the developability of the quasi-developable Bézier surface from two design curves using the Simulated Annealing-based Shape Parameter Search (SASPS) algorithm based on the shape parameters of the cubic Bézier design curves. In addition, another new method for determining the number of sampling points is given to increase the developability degree. It allows perturbing the design curves within the limits allowed by the user based on the shape parameters. We also defined a multi-objective function for the optimal quasi-developable Bézier surface. Example models show that the proposed method is efficient and effective in achieving optimal developability.

Robustness is a crucial requirement for the deployment of AI systems in real-world scenarios. In the context of AI planning, the concept of action reversibility, i.e., the ability to undo the effects of an action using a reverse plan, is a promising direction for achieving robust plans. Plans composed exclusively of reversible actions exhibit resilience against goal changes during the execution of the plan. However, the evaluation of action reversibility systems in STRIPS planning presents a challenge, given that standard planning benchmarks are often not suitable. Early experiments using a naive implementation of an action reversibility algorithm show that the available domain generation approach is susceptible to bias. Building on this existing domain generator, we introduce two slight variations that exhibit entirely different search space characteristics. We assess these domain generators using the naive action reversibility implementation and existing ASP implementations, and demonstrate that different generators indeed favor different implementations. As a follow-up to this line of research, we present a generalized domain generator facilitating the creation of domains with diverse search space characteristics. To finally reduce the utilization of contrived generation patterns, we propose another domain generator based on the Barabási-Albert model yielding less rigid domains. Our experiments demonstrate that these new domain generators can produce a variety of domains with diverse search space characteristics, enabling a less biased evaluation of action reversibility systems.

This paper presents a performance evaluation of several heuristic search algorithms in the context of pathfinding. Our objective is to assess the performance of these algorithms in various grid-based environments to present how specific domain features influence their efficiency. Additionally, we extend our experiments by incorporating Multi-Agent Path Finding (MAPF) benchmarks, using handcrafted features and features extracted with Convolutional Neural Network (CNN) to characterize the maps. The results of our evaluation were later used to train machine learning models capable of predicting the efficient algorithm for a given pathfinding task based on performance criteria. This multi-algorithm pathfinding method enhances the selection of the best algorithm for different pathfinding problems. Furthermore, we revealed the most important features that impact the selection of the efficient algorithm. We identify the most important characteristics of the grid that affect the selection and performance of the algorithms.