Natural Logic
Lawrence S. Moss · 2015
This chapter aims to presents logical systems that deal with inference in natural language, or something close to it. The first wave of activity concerns logical systems based on the syllogism, or extensions of it. Syllogistic reasoning deals with very simple sentences; to a linguist its subject matter would not count as syntax in any serious sense. The chapter presents proof systems that are syllogistic in the sense that all sentences involved in a formal proof are themselves in the same fragment as the hypotheses and the conclusion. It shows how to formulate proof systems incorporating variables for fragments of language. It then sketches very simple calculus of monotonicity and polarity, along the lines of the primary sources. The chapter talks about Van Benthem's seminal idea, which proposes a systematic account of polarity, an account which works on something closer to real sentences than to logical representations.