In cater the need of Beyond 5G communications, large numbers of data driven artificial intelligence based fiber models has been put forward as to utilize artificial intelligence's regression ability to predict pulse evolution in fiber transmission at a much faster speed compared with the traditional split step Fourier method. In order to increase the physical interpretabiliy, principle driven fiber models have been proposed which inserts the Nonlinear Schodinger Equation into their loss functions. However, regardless of either principle driven or data driven models, they need to be re-trained the whole model under different transmission conditions. Unfortunately, this situation can be unavoidable when conducting the fiber communication optimization work. If the scale of different transmission conditions is large, then the whole model needs to be retrained large numbers of time with relatively large scale of parameters which may consume higher time costs. Computing efficiency will be dragged down as well. In order to address this problem, we propose the principle driven parameterized fiber model in this manuscript. This model breaks down the predicted NLSE solution with respect to one set of transmission condition into the linear combination of several eigen solutions which were outputted by each pre-trained principle driven fiber model via the reduced basis method. Therefore, the model can greatly alleviate the heavy burden of re-training since only the linear combination coefficients need to be found when changing the transmission condition. Not only strong physical interpretability can the model posses, but also higher computing efficiency can be obtained. Under the demonstration, the model's computational complexity is 0.0113% of split step Fourier method and 1% of the previously proposed principle driven fiber model.

Databases are often assumed to have definite content. The reality, though, is the database at hand may be deficient due to missing, invalid, or uncertain information. As a simple illustration, the primary address of a person may be missing, or it may conflict with another primary address, or it may be improbable given the presence of nearby businesses. A common practice to address this challenge is to rectify the database by fixing the gaps, as done in data imputation, entity resolution, and data cleaning. The process of rectifying the database, however, may involve arbitrary choices due to computational limitations, such as errors in statistical or machine-learning models, or mere lack of information that even humans cannot cope with in full confidence. In turn, answers to queries over the deficient database may depend on the choices made to rectify it; thus, the answers to queries may vary from one choice to choice, even though both choices may be equally legitimate. In the pursuit of principled solutions, there has been a continuous research effort to develop fundamental approaches for handling database deficiency with no (or with less) arbitrariness. The purpose of this review article is to highlight some of the ways in which the possible world semantics has been deployed as a principled approach to overcome database deficiency in different contexts. In this approach, we acknowledge that we need to rectify the deficiency: fill in missing information, delete wrong records (hereafter tuples or facts), correct erroneous values, and so on. Yet, since many rectifications may exist and since we do not know which is the correct one, we do not commit to a specific one. Instead, we view our deficient database as a representation of the results of all conceivable rectifications, each such rectification giving rise to a legitimate candidate of a valid database that we call a possible world. Since the possible worlds differ from each other, a query may produce different collections of answers (which are also tuples) when applied to different possible worlds. Therefore, query answering requires the use of an aggregation method to combine the query results over the possible worlds.

Knowledge base exchange is an important problem in the area of data exchange and knowledge representation, where one is interested in exchanging information between a source and a target knowledge base connected through a mapping. In this paper, we study this fundamental problem for knowledge bases and mappings expressed in OWL 2 QL, the profile of OWL 2 based on the description logic DL-Lite_R. More specifically, we consider the problem of computing universal solutions, identified as one of the most desirable translations to be materialized, and the problem of computing UCQ-representations, which optimally capture in a target TBox the information that can be extracted from a source TBox and a mapping by means of unions of conjunctive queries. For the former we provide a novel automata-theoretic technique, and complexity results that range from NP to EXPTIME, while for the latter we show NLOGSPACE-completeness.

In this paper, we study the problem of exchanging knowledge between a source and a target knowledge base (KB), connected through mappings. Differently from the traditional database exchange setting, which considers only the exchange of data, we are interested in exchanging implicit knowledge. As representation formalism we use Description Logics (DLs), thus assuming that the source and target KBs are given as a DL TBox+ABox, while the mappings have the form of DL TBox assertions. We study the problem of translating the knowledge in the source KB according to these mappings. We define a general framework of KB exchange, and address the problems of representing implicit source information in the target, and of computing different kinds of solutions, i.e., target KBs with specified properties, given a source KB and a mapping. We develop first results and study the complexity of KB exchange for DL-Lite_RDFS, a DL corresponding to the FOL fragment of RDFS, and for DL-Lite_R.