Constructing responses in task-oriented dialogue systems typically relies on information sources such the current dialogue state or external databases. This paper presents a novel approach to knowledge-grounded response generation that combines retrieval-augmented language models with logical reasoning. The approach revolves around a knowledge graph representing the current dialogue state and background information, and proceeds in three steps. The knowledge graph is first enriched with logically derived facts inferred using probabilistic logical programming. A neural model is then employed at each turn to score the conversational relevance of each node and edge of this extended graph. Finally, the elements with highest relevance scores are converted to a natural language form, and are integrated into the prompt for the neural conversational model employed to generate the system response. We investigate the benefits of the proposed approach on two datasets (KVRET and GraphWOZ) along with a human evaluation. Experimental results show that the combination of (probabilistic) logical reasoning with conversational relevance scoring does increase both the factuality and fluency of the responses.
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