From Natural Logic to Natural Reasoning

This paper starts with a brief history of Natural Logic from its origins to the most recent work on implicatives. It then describes on-going attempts to represent the meanings of so-called ‘evaluative adjectives’ in these terms based on what linguists have traditionally assumed about constructions such as NP was stupid to VP, NP was not lucky to VP that have been described as factive. It turns out that the account cannot be based solely on lexical classification as the existing framework of Natural Logic assumes. The conclusion we draw from this ongoing work is that Natural Logic of the classical type must be grounded in a more inclusive theory of Natural Reasoning that takes into account pragmatic factors in the context of use such as the assumed relation between the evaluative adjective and even the perceived communicative intent of the speaker. 1 What Is Natural Logic? Natural Logic attempts to do formal reasoning in natural language making use of syntactic structure and the semantic properties of lexical items and constructions. It contrasts with approaches that involve a translation from a natural to a formal language such as predicate calculus or a higher-order logic. Figure 1 sketches the history of Natural Logic as told by Johan van Benthem in [3] and in lectures. The short version goes as follows. Natural Logic has been around over 2000 years. It started out pretty well with Aristotle and the Greeks who invented syllogisms, some two dozen valid patterns of inference in ancient Greek. In the medieval times all of this was ported into Latin and extended by people like William of Ockham and Buridan. With the waning of the Middle Ages began a decline in logic that bottoms out in the works of De Morgan in the middle of the 19th century. But soon came the rise of modern logic first with Gottlob Frege in the 1890s and on the Natural Logic side with Charles Sanders Peirce about the same time. The current revival in Natural Logic was started by Johan van Benthem [2] and his student Vı́ctor Sánchez-Valencia [26] in the 1990s. Among the latest advances is the work by Jan van Eijck [8], Bill MacCartney [20] and the recent papers by Thomas Icard [10] and Larry Moss [11] that build on the work of MacCartney and Christopher Manning [21]. The original work reported in this paper is part of a joint project with Cleo Condoravdi, Stanley Peters, and Annie Zaenen at the Center for the Study of Language and Information. Special thanks to Annie Zaenen for the content and form of this paper. c © Springer International Publishing Switzerland 2015 A. Gelbukh (Ed.): CICLing 2015, Part I, LNCS 9041, pp. 295–309, 2015. DOI: 10.1007/978-3-319-18111-0_23