Annals of Mathematics and Artificial Intelligence最新文献

A strongly possible constraint is an intermediate concept between possible and certain constraints, based on the strongly possible world approach (a strongly possible world is obtained by replacing NULL’s by a value from the ones appearing in the corresponding attribute of the table). In the present paper, we introduce strongly possible versions of multivalued dependencies and cross joins, and we analyse the complexity of checking the validity of a given strongly possible cross joins. We also study two approximation measures, (g_3) and (g_5), of strongly possible keys (spKeys), functional dependencies (spFDs), multivalued dependencies (spMVDs) and cross joins (spCJs). For spKeys and spFDs, we show that the (g_3) value is always an upper bound of the (g_5) value for a given constraint in a table. However, there are tables of arbitrarily large number of tuples and a constant number of attributes that satisfy (g_3-g_5=frac{p}{q}) for any rational number (0le frac{p}{q}<1). On the other hand, we show that the values of measures (g_3) and (g_5) are independent of each other in the case of spMVDs and spCJs. We prove that checking whether a given strongly possible cross join holds in an incomplete table is NP-complete, in sharp contrast to the fact that checking a given cross join in a complete table is easily seen to be polynomially solvable. We also treat complexity questions of determination of the approximation values, namely we show that both, determining (g_3) and (g_5) for spCJs are NP-complete.

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.