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Deep Adaptive Semantic Logic (DASL)
Harnessing formalized expert knowledge to construct sophisticated deep learning architectures
Deep Adaptive Semantic Logic (DASL) is a novel and deeply principled approach to full integration of knowledge representation and reasoning (KRR) with statistical machine learning (SML). The DASL project aims to ultimately facilitate “discussions” between scientists and data by transforming reasoning in terms of a logical language into reasoning in terms of a soft semantic representation.
DASL replaces the set-theoretic semantics of model theory with semantics based on real-valued functions. Model theory underlies the formal inference behind current formal systems, expert systems, and machine reasoning systems. Such systems build up set-theoretic interpretations of the formal language by relying on subject matter expertise expressed in formal logic, frequently first-order logic. These systems perform syntactic manipulations that are capable of recognizing when two expressions match exactly, but they cannot make approximate matches.
DASL applies deep learning techniques to supplement data with knowledge framed over widely varying levels of formality. This approach enables the system to perform logically deep reasoning without brittleness, provide explanations, and incorporate existing models based, for example, on physical laws or economic theories. Scientists provide complex background knowledge and hypotheses in familiar but formal language, and the DASL model generalizes the available data in ways best fit to the theory. The scientist continues the “discussion” by querying the model for any properties expressed in the theory.
The deep learning techniques are used to simultaneously learn mappings from object names (constants) of the language to points in a high-dimensional real-number space and from higher level symbols in the language to functions on that space. DASL uses both empirical data and the logical rules asserted as expert knowledge to serve as training data. The resulting semantic representations approximate the empirical data and asserted knowledge as closely as possible, and they are always self-consistent even if the given axioms are not.
When the rules and data can all be fit with minimal loss, the resulting system can be queried and will produce any assertion logically entailed by the given axioms. This condition can be accomplished even when no empirical data is available. At the other extreme, when data is available and axioms representing prior knowledge are not available, DASL generates a conventional neural network.
This material is based upon work supported by the Defense Advanced Research Projects Agency (DARPA) under Contract No. HR001118C0023. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of DARPA.