The human brain possesses the remarkable capability of understanding, - terpreting, and producing human language, thereby relying mostly on the left hemisphere. The ability to acquire language is innate as can be seen from d- orders such as speci?c language impairment (SLI), which manifests itself in a missing sense for grammaticality. Language exhibits strong compositionality and structure. Hence biological neural networks are naturally connected to processing and generation of high-level symbolic structures. Unlike their biological counterparts, arti?cial neural networks and logic do not form such a close liason. Symbolic inference mechanisms and statistical machine learning constitute two major and very di?erent paradigms in ar- ?cial intelligence which both have their strengths and weaknesses: Statistical methods o?er ?exible and highly e?ective tools which are ideally suited for possibly corrupted or noisy data, high uncertainty and missing information as occur in everyday life such as sensor streams in robotics, measurements in medicine such as EEG and EKG, ?nancial and market indices, etc. The m- els, however, are often reduced to black box mechanisms which complicate the integration of prior high level knowledge or human inspection, and they lack theabilitytocopewitharichstructureofobjects,classes,andrelations. S- bolic mechanisms, on the other hand, are perfectly applicative for intuitive human-machine interaction, the integration of complex prior knowledge, and well founded recursive inference. Their capability of dealing with uncertainty andnoiseandtheire?ciencywhenaddressingcorruptedlargescalereal-world data sets, however, is limited. Thus, the inherent strengths and weaknesses of these two methods ideally complement each other.

The human brain possesses the remarkable capability of understanding, - terpreting, and producing human language, thereby relying mostly on the left hemisphere. The ability to acquire language is innate as can be seen from d- orders such as speci?c language impairment (SLI), which manifests itself in a missing sense for grammaticality. Language exhibits strong compositionality and structure. Hence biological neural networks are naturally connected to processing and generation of high-level symbolic structures. Unlike their biological counterparts, arti?cial neural networks and logic do not form such a close liason. Symbolic inference mechanisms and statistical machine learning constitute two major and very di?erent paradigms in ar- ?cial intelligence which both have their strengths and weaknesses: Statistical methods o?er ?exible and highly e?ective tools which are ideally suited for possibly corrupted or noisy data, high uncertainty and missing information as occur in everyday life such as sensor streams in robotics, measurements in medicine such as EEG and EKG, ?nancial and market indices, etc. The m- els, however, are often reduced to black box mechanisms which complicate the integration of prior high level knowledge or human inspection, and they lack theabilitytocopewitharichstructureofobjects,classes,andrelations. S- bolic mechanisms, on the other hand, are perfectly applicative for intuitive human-machine interaction, the integration of complex prior knowledge, and well founded recursive inference. Their capability of dealing with uncertainty andnoiseandtheire?ciencywhenaddressingcorruptedlargescalereal-world data sets, however, is limited. Thus, the inherent strengths and weaknesses of these two methods ideally complement each other.

The human brain possesses the remarkable capability of understanding, - terpreting, and producing human language, thereby relying mostly on the left hemisphere. The ability to acquire language is innate as can be seen from d- orders such as speci?c language impairment (SLI), which manifests itself in a missing sense for grammaticality. Language exhibits strong compositionality and structure. Hence biological neural networks are naturally connected to processing and generation of high-level symbolic structures. Unlike their biological counterparts, arti?cial neural networks and logic do not form such a close liason. Symbolic inference mechanisms and statistical machine learning constitute two major and very di?erent paradigms in ar- ?cial intelligence which both have their strengths and weaknesses: Statistical methods o?er ?exible and highly e?ective tools which are ideally suited for possibly corrupted or noisy data, high uncertainty and missing information as occur in everyday life such as sensor streams in robotics, measurements in medicine such as EEG and EKG, ?nancial and market indices, etc. The m- els, however, are often reduced to black box mechanisms which complicate the integration of prior high level knowledge or human inspection, and they lack theabilitytocopewitharichstructureofobjects,classes,andrelations. S- bolic mechanisms, on the other hand, are perfectly applicative for intuitive human-machine interaction, the integration of complex prior knowledge, and well founded recursive inference. Their capability of dealing with uncertainty andnoiseandtheire?ciencywhenaddressingcorruptedlargescalereal-world data sets, however, is limited. Thus, the inherent strengths and weaknesses of these two methods ideally complement each other.