Generating Predicate Logic Expressions from Natural Language

Formal logic expressions are commonly written in standardized mathematical notation. Learning this notation typically requires many years of experience and is not an explicit part of undergraduate academic curricula. Constructing and comprehending logical predicates can feel difficult and unintuitive. We hypothesized that this process can be automated using neural machine translation. Most machine translation techniques involve word-based segmentation as a preprocessing step. Given the nature of our custom dataset, hosts first-order-logic (FOL) semantics primarily in unigram tokens, the word-based approach does not seem applicable. The proposed solution was to automate the translation of short English sentences into FOL expressions using character-level prediction in a recurrent neural network model. We trained four encoder-decoder models (LSTM, Bidirectional GRU with Attention, and two variants of Bi-directional LSTM with Attention). Our experimental results showed that several established neural translation techniques can be implemented to produce highly accurate machine translators of English sentences to FOL formalisms, given only characters as markers of semantics. We also demonstrated that attention-based enhancement to the encoder-decoder architecture can vastly improve translation accuracy. Most machine translation techniques involve word-based segmentation as a preprocessing step. Given the nature of our custom dataset, hosts first-order-logic (FOL) semantics primarily in unigram tokens, the word-based approach does not seem applicable. The proposed solution was to automate the translation of short English sentences into FOL expressions using character-level prediction in a recurrent neural network model. We trained four encoder-decoder models (LSTM, Bidirectional GRU with Attention, and two variants of Bi-directional LSTM with Attention). Our experimental results showed that several established neural translation techniques can be implemented to produce highly accurate machine translators of English sentences to FOL formalisms, given only characters as markers of semantics. We also demonstrated that attention-based enhancement to the encoder-decoder architecture can vastly improve translation accuracy. We trained four encoder-decoder models (LSTM, Bidirectional GRU with Attention, and two variants of Bi-directional LSTM with Attention). Our experimental results showed that several established neural translation techniques can be implemented to produce highly accurate machine translators of English sentences to FOL formalisms, given only characters as markers of semantics. We also demonstrated that attention-based enhancement to the encoder-decoder architecture can vastly improve translation accuracy.