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** Josh Dever (University of Texas at Austin) **

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This is a crash course in some of the central tools and results from the metatheory of quantified first-order logic and propositional modal logic. Only minimal prior exposure to logic is required -- preferably, familiarity with the syntax of first-order logic and with the determination of truth values of sentences in models.

**Session 1: Saturday, June 16, 1:00 to 5:00pm, UTC 1.102**

This session will begin with an introduction to proof by mathematical induction, and its role in proving central metatheoretic results about logical systems. We will then prove the soundness and completeness of standard proof systems for first-order logic, and extract the compactness theorem as a corollary. Some consequences of compactness for first-order model theory will be considered. We will then turn to the basics of recursion theory, considering various alternative definitions of computability and establishing their equivalence.

**Session 2: Sunday, June 17, 9:30 am to 12:30 pm, UTC 1.102**

This session will cover more advanced topics in first-order metatheory. We will begin by establishing the connections between computability and the Godel incompleteness theorems, and then use the tools developed so far to examine the difference in expressive power between first-order logic and infinitary or second-order logics.

**Session 3 Sunday, June 17, 1:30 to 5:30pm, UTC 1.102**

This session will center on propositional modal logic. We will develop the standard Kripkean model theory for modal logics, and then turn to canonical model methods for frame completeness theorems. We will then consider the expressive relationship between modal and first-order logics by examining bisimulations, and by proving the van Benthem characterization theorem.

**Liz Coppock (University of Düsseldorf)John Beavers (University of Texas at Austin)**

Slides:

This course is a chance for linguists of all subfields, philosophers, and computer scientists to get their basic formal semantics chops in fighting shape. The materials will be drawn mainly from Heim and Kratzer's ubiquitous 1998 textbook "Semantics in Generative Grammar", and supplemented by Dowty, Wall and Peters's 1981 classic "Introduction to Montague Semantics".

**Session 1: Saturday, June 16, 1:00 to 5:00pm, UTC 1.116**

On the first day, we will cover fundamental (but sometimes confusing) issues concerning object language and metalanguage, some useful type-driven semantic composition rules, the semantics of verbs, common nouns, intersective modifiers, proper names, and non-quantificational determiners, and practical ways of writing out compositional semantic derivations. The particular topics that will be covered include:

- Syntax and semantics of predicate calculus
- Interpretation with respect to a model; semantic types
- Montague's program: English as a formal language
- Heim and Kratzer's style using (lambdified) English as a meta-language
- Frege's conjecture, functions, lambda notation (à la Heim and Kratzer), the composition rule of Functional Application
- Type-driven interpretation vs. syntax-driven interpretation
- Semantics of intransitive verbs: characteristic functions vs. sets
- Semantics of transitive verbs, Schönfinkelization
- Argument linking
- The composition rule of Predicate Modification
- Semantics of "the" and partial functions
- Top-down and bottom-up computation of semantic values

**Session 2: Sunday, June 17, 9:30 am to 12:30 pm, UTC 1.116**

On the second day, we will start getting fancy with variable assignments, and talk about the semantics of pronouns, quantificational determiners, and relative clauses. Particular topics include:

- Syntax and semantics of predicate calculus with variables and quantifiers
- Semantics of quantifiers, variables, and relative clauses à la Heim & Kratzer
- Heim and Kratzer's composition rule of Predicate Abstraction, and the Traces and Pronouns rule
- The problem of quantifiers in object position, QR vs. in-situ approaches
- Free and bound variable anaphora
- Strict and sloppy readings in ellipsis

**Dan Lassiter (Stanford University)**

Links:

Why should linguists and philosophers care about probability? Is probability the "faithful guardian of common sense" or just number-crunching? Is statistical inference a philosophically motivated enterprise that can lead to deep insights, or a bunch of cookie-cutter techniques that you have to memorize and apply in order to get papers published?

The use of probabilistic models is growing rapidly in all of the core NASSLLI areas, and understanding them is both theoretically useful and practically important for students. This course is an introduction with a focus on philosophical and conceptual understanding and NASSLLI-relevant applications. The mathematics used in the course will be kept to a minimum: high-school algebra, basic logic and set theory, and some ideas from possible-worlds semantics that will be introduced along the way. We will build intuitions by comparing mathematical definitions with properties of data sets generated using the free statistical software R (students are encouraged to bring laptop computers with R installed).

**Session 1: Saturday, June 16, 1:00 to 5:00pm, UTC 1.104**

- Motivations: the importance of uncertain inference in scientific practice and in cognitive science
- Chance, evidence, and belief: Philosophical interpretations of probability
- Formal semantics of probability
- Ways to derive probability from more basic assumptions about frequency, belief, language, or choice

**Session 2: Sunday, June 17, 9:30am to 12:30pm, 1.104**

- More on semantic foundations and mathematical features of probability and random variables
- Simulation in R for intuition-building and sanity-checking (no programming background assumed)
- Statistical inference: Frequentist and Bayesian approaches
- Using R for model-building and statistical inference

Note: Our planned bootcamp class on Textual Inference has been canceled. (6/6/2012)