LYRICS: a General Interface Layer to Integrate Logic Inference and Deep Learning

Abstract

In spite of the amazing results obtained by deep learning in many applications, a real intelligent behavior of an agent acting in a complex environment is likely to require some kind of higher-level symbolic inference. Therefore, there is a clear need for the definition of a general and tight integration between low-level tasks, processing sensorial data that can be effectively elaborated using deep learning techniques, and the logic reasoning that allows humans to take decisions in complex environments. This paper presents LYRICS, a generic interface layer for AI, which is implemented in TersorFlow (TF). LYRICS provides an input language that allows to define arbitrary First Order Logic (FOL) background knowledge. The predicates and functions of the FOL knowledge can be bound to any TF computational graph, and the formulas are converted into a set of real-valued constraints, which participate to the overall optimization problem. This allows to learn the weights of the learners, under the constraints imposed by the prior knowledge. The framework is extremely general as it imposes no restrictions in terms of which models or knowledge can be integrated. In this paper, we show the generality of the approach showing some use cases of the presented language, including model checking, supervised learning and collective classification.

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“…Hybrid methods for XAI Integration Logic & Numeric Knowledge-Based Artificial Neural Networks (KBANN) [14] Hu et al [15] Logic Tensor Networks (LTN) [16,17,18,19] Semantic Loss Function (SLF) [20] Lyrics [21] Logic & Numeric & Statistic Markov Logic Networks (MLN) [22] CILP++ [23] Differentiable Inductive Logic Programming (∂ILP) [24] Neural Theorem Prover [25] DeepProbLog [26] Lifted Relational Neural Networks (LRNN) [27] Composition Extraction Rules Pedagogical Saito et al [28] RxREN [29] ALPA [30] Decompositional RuleNet [31] MofN [32] Giles et al [33] KT [34] VI-Analysis [35] RX [36] Núñez et al [37] (SVM-specific) Trees TREPAN [38] Krishnan et al [39] Schetinin et al [40] Injection Knowledge Graph Embedding RESCAL + TRESCAL [41] INS [42] Low-rank Logic Embeddings [43] KALE [44] OSCAR [45] Fig. 1.…”