Natural Logic in AI and Cognitive Science

This paper presents an ongoing research project called “natural logic” and makes the case that it is relevant to AI, Computational Linguistics, and Cognitive Science. We propose to add some of the natural logic modules which have already been developed to existing NLP systems. We see our approach as complementing and augmenting data-driven approaches exemplified by IBM’s Watson. We give a brief introduction to natural logic and present examples of proofs that can be given in a working system. We furthermore introduce monotonic logic, another promising approach for extracting information from sentences that contain quantifiers. We finish the paper by presenting some early work that integrates syllogistic reasoning into exsiting NLP systems. Introduction The history of logic and AI is a checkered one. Starting with huge optimism, the idea of applying logic in AI and NLP is very much a minority one today. The 2015 report of the One Hundred Year Study on Artificial Intelligence states that ”The resounding success of the data-driven paradigm has displaced the traditional paradigms of AI. Procedures such as theorem proving and logic-based knowledge representation and reasoning are receiving reduced attention, in part because of the ongoing challenge of connecting with real world groundings.” (Stone et al. 2016). At the same time, there were important contributions in previous parts of the AI literature on the topic of reasoning with fragments of natural language. Important for our story are (Nishihara et al. 1990; McAllester and Givan 1992; Purdy 2006). We propose to add syllogistic reasoning to NLP systems. The sort of system we have in mind is exemplified by IBM’s Watson system. Jim Hendler and his research group (Hendler and Ellis 2014) proposed that Watson’s accomplishments are due to a combination of natural language processing, search technologies, semantic typing, scoring heuristics and machine learning. Conspicuously absent from this list are reasoning and logic. We know that several kinds of reasoning took place behind the scenes, such as in the context of semantic typing and in the context of reasoning about time and place (Kalyanpur et al. 2012; Ferrucci 2012; c Copyright retained by the authors. Gliozzo et al. 2013). While some of the reasoning in Watson was in support of finding answers to questions and to establish the confidence of potential answers, the geospatial and temporal reasoning were designed to make explicit some of the information that was implicitly contained in the given information. In this context, our project is aimed at adding addition reasoning components to NLP systems such as Watson. We see our project as a support system that is designed to extract yet more information from natural language texts. It is decidedly not a free standing reasoner. As such, we see our project as part of a research agenda implicitly defined by IBM Watson, i.e. to do better than the Jeopardy! system. Watson used some fairly off-the-shelf IR techniques, including passage term matching, textual alignment and skip bigrams (Murdock et al. 2012). The designers of Watson additionally extracted information from sources that they knew would be valuable, such as anchor tag links and the contents of title tags in the HTML sources of Wikipedia pages. We believe that by adding syllogistic reasoning, NLP systems will be able to extract further information from documents or will be able to find further evidence for given information. In this context, we see our approach as supporting a datadriven approach through reasoning. We believe that reasoning adds additional, valuable resources to processing natural language texts. Natural Logic: Extended Syllogistic Reasoning We describe here the research program of extended syllogistic reasoning as it appears in papers such as (van Benthem 1986; Sánchez-Valencia 1991; van Eijck 2007; Fyodorov et al. 2003; Moss 2015; van Benthem 2008; Pratt-Hartmann and Moss 2009). The basic idea is to take very small fragments of language, fragments where one can find “reasoning”’ of some kind, and to find complete logical systems for those fragments. Ideally, the logical systems would not use “extra syntax” of any kind, and thus not involve translation into first-order logic. Even more, they should be efficiently decidable. That means that there should be algorithms that carry out the decision procedure (unlike what we see for very strong logical systems), and these algorithms should be very fast for the very simplest fragments. Here is a summary of the field. There are many sound and complete logical systems for small fragments of language. Lawrence S. Moss and Michael Wollowski MAICS 2017 pp. 41–46