Logical Embeddings for Argument Analysis

Neural networks can be trained to rank the choices made by logical reasoners, resulting in more efficient searches for answers. A key step in this process is creating useful embeddings, i.e., numeric representations of logical statements. This paper introduces and evaluates several approaches to creating embeddings that result in better downstream results. We train embeddings using triplet loss, which requires examples consisting of an anchor, a positive example, and a negative example. We introduce three ideas: generating anchors that are more likely to have repeated terms, generating positive and negative examples in a way that ensures a good balance between easy, medium, and hard examples, and periodically emphasizing the hardest examples during training. We conduct several experiments to evaluate this approach, including a comparison of different embeddings across different knowledge bases, in an attempt to identify what characteristics make an embedding well-suited to a particular reasoning task.

The logical reconstruction of argument graphs from natural language text is challenging because of the prevalence of enthymemes (i.e., arguments with implicit premises). There are natural language processing methods for identifying enthymemes in text, and there are symbolic methods based on abduction for identifying missing premises in a logical representation of enthymemes. However, there is a need for methods to generate implicit premises to logically show a known entailment or contradiction relationship between a pair of statements. To address this, we propose a neuro-symbolic pipeline that uses large language models (LLMs) to generate intermediate implicit premises that are translated into logical formulae and used with logical formulae representing explicit premises and explicit claims to show the logical relationships between them (entailment, contradiction, or neutrality). Our approach is evaluated on the Microtext Argumentative Corpus.

Argumentation is an important cognitive activity that involves the scrutiny of arguments and counterarguments. When given an argument, it is desirable that its premises entail its claim, and that the premises and claim are consistent, and when given a pair of arguments, it is desirable to check whether one argument supports or attacks another. If the arguments are in natural language, then we could use methods for natural language inference, also known as recognizing textual entailment (RTE). The state-of-the-art RTE methods use machine learning and deep learning, but these are not explainable. An alternative approach which we investigate in this paper is to translate text into an abstract meaning representation (AMR) graph. For this we use a pre-trained AMR parser. We then translate the AMR graph into propositional logic and use a SAT solver for automated reasoning. In text, often common sense suggests that an entailment (or contradiction) relationship holds between a premise and a claim, but because different wordings are used, this is not identified from their logical representations. To address this, we introduce relaxation methods to allow replacement or forgetting of some propositions. Our experimental results show our approach performs well on three RTE datasets. The benefit of our approach is that we have a logical representation of premises and claims, and of the relaxations that are used to identify the entailment and contradiction relations.