Drafts of lecture slides

My first lecture was an introduction to the topic as a whole.

Then came a lecture on basic syllogistic logics, and then one on logics with relations. This set covers logics with verbs, relative clauses, and comparative adjectives.

After this, we turn to the study of logics beyond the Aristotle boundary, that is, to logics with restricted notions of variables.

The final topic of the course is the monotonicity calculus.

Some of these sets are not complete, so please check back for more definitive versions.

Welcome to the ESSLLI course Logics for natural language inference

The course will study logical systems which are relevant to semantics and also logical systems which try to use surface forms directly. It also will cover in detail how various standard logical systems work, including natural deduction systems, and others; the typed lambda calculus; and first-order logic and its decidable fragments. It will also present detailed studies of logical systems which are closer to natural language, such as extended syllogistic logics. These topics will be taught from the point of view of representing natural language inference.

More specifically, the course is divided into a general introduction and four more content-full parts.

Introduction: a list of test problems for natural logic, a summary of the results that we'll see in the course, and general history of the area. I also will present some background on decidable fragments of first-order logic.

Syllogistic proof systems: I'll summarize what is known about complete logical systems which can be called 'syllogistic' in the sense that they do not use variables or other devices besides the surface forms. It might be surprising that one can do any sort of linguistic reasoning this way. I will try to present a fair number of the completeness proofs themselves in this part of the course.

Logics with relations: Moving on to logics with verbs and relative clauses brings a set of extra problems and opportunities. For example, there is an Aristotle boundary between the logics which can be handled syllogistically and those which cannot.

Logic beyond the Aristotle boundary: This part of the course presents natural deduction-style systems which can handle interesting linguistic phenomena and at the same time remain decidable. In addition, I'll discuss comparative adjectives.

Monotonicity and Polarity: The best-known work in the area of natural logic is based on the monotonicity calculus first identified and studied by Johan van Benthem. This part of the course will present much of what has been done in the area As part of the course, I'll present the needed background on categorial grammars and polarity phenomena in language.

Current Plan

Although I have mentioned an Introduction and four units, I don't see these five items as each taking one lecture day at ESSLLI. At this point, my plan is to do the Introduction and syllogistic logic work on the first day, and to do the other three sections in four days, as time permits.