# Week two 11:00 - 12:30

## Logic and Computation advanced course:Logics with Counting.

Teacher

Course material: pratt-hartmann.pdf

Abstract:

This course presents a survey of decidable fragments of first-order logic with counting quantifiers. Such fragments include: (i) the numerical syllogistic, (ii) the 1-variable fragment with counting, (iii) graded modal logic, (iv) the guarded two-variable fragment with counting and (v) the two-variable fragment with counting. Such logics present special difficulties for the student of computational logic, because their complexity-theoretic analysis often requires specialized techniques. This course will give a comprehensive treatment of these techniques, culminating in a proof that the satisfiability and finite satisfiability problems for the two-variable fragment with counting quantifiers are both NEXPTIME-complete.

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## Language and Logic introductory course:Event Semantics and Adverbial Modification.

Teachers
• Berit Gehrke ()
• Boban Arsenijevic ()

External page

Abstract:

The course gives a general overview of (Neo-)Davidsonian event semantics and its motivation from adverbial modification. It furthermore introduces the notion of event structure, both from a conceptual and a model-theoretic point of view. An important issue concerns how far event structure, aspectual structure and argument structure are mutually related and whether it is possible or even preferable to reduce them to one. To identify elements of the event structure, argument structure and/or aspectual structure, we focus on the (un-)availability of various adverbial modifiers, in particular manner, temporal, aspectual and spatial ones, as well as the relation of such modifiers to the overall structure, e.g. the issue of high (event-external) vs. low (event-internal) adverbs. The presentation of the cross-linguistic diversity in the marking of voice and argument and adjunct roles, and phenomena like serial verb constructions, lead to a general discussion of the nat ure of the verbal category.

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## Language and Logic advanced course:Proof-Theoretic Semantics.

Teacher

Course material: proof_theoretic_semantics.html

Abstract:

Proof-Theoretic Semantics (PTS) is an alternative to model-theoretic (or truth-condition) semantics. It is based on the idea that the central notion in terms of which meanings are assigned to expressions is that of proof rather than truth. In this sense PTS is inferential rather than denotational in spirit. Although the claim that meaning is use has been quite prominent in philosophy for more than half a century, the model-theoretic approach has always dominated formal semantics. However, within general proof theory several formal approaches to PTS have been developed which promise to provide an alternative to the model-theoretic approach. After recalling certain basics from proof theory of natural deduction, this tutorial presents traditional approaches to PTS in the spirit of Dummett, Prawitz and Martin-Löf as well as advanced conceptions based on "definitional reasoning" based on work of the author.

http://www-ls.informatik.uni-tuebingen.de/esslli/

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## Language and Computation foundational course:Case, Scrambling and Default Word Order.

Teachers
• Miriam Butt ()
• Heike Zinsmeister ()
Abstract:

Many of the world's languages are so-called "free word order" languages, whereby the major arguments of a clause can be scrambled quite freely. This scrambling generally goes hand-in-hand with a robust case marking system and some means of verb-argument agreement (usually verb-subject agreement, but not always), which allows the identification of the various arguments of the clause (i.e., which is the agent, the patient, the goal, etc.). Sometimes, however, the correct identification of which syntactic argument encodes which of the semantic participants of a verb/clause can only be achieved by world or contextual knowledge. Additionally, effects of so-called word order freezing can be observed, whereby suddenly the word order is not free, but is fixed if one wants a certain mapping of semantic participants to syntactic arguments. Finally, one generally also refers to a "default word order" exhibited by languages which in principle allow for the (more-or-less) free scrambling of syntactic arguments. The theoretical status of this default word order is not clear and this course will examine the topic of argument scrambling, word order freezing and default word order with respect to two main perspectives: 1) theoretical linguistics; 2) corpus linguistics.

With respect to the theoretical perspective, students will be introduced to current theories of case and word order so that we can examine what (if anything) these theories have to say about default word order and word order freezing in particular. With respect to the computational perspective, we will examine to what degree information from corpora can help guide the analysis and help us understand why things are scrambled when they are scrambled and what status the "default word order" actually has in terms of frequency and distribution. As part of the course (one day), we will also present psycholinguistic studies that identify (combinations of) features that determine word order preferences.

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## Language and Computation introductory course:Computational Lexical Semantics.

Teachers
• Gemma Boleda ()
• Stefan Evert ()
Abstract:

This course will provide students with an overview of current research in Computational Lexical Semantics, and with the necessary theoretical and methodological background to carry out their own research. Students will have an opportunity to work on practical examples, learning to tackle the difficulties mentioned above. Special emphasis will be put on the feedback between computational approaches and semantic theory.

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## Logic and Computation advanced course:Reasoning with Probabilities.

Teachers
• Eric Pacuit ()
• Joshua Sack ()

Course material: epprob-outline.pdf

Abstract:

Both logic and probability provide powerful tools for reasoning about uncertainty in a dynamic environment. Our goal in this course is to examine logical frameworks that incorporate probabilistic modeling of multiagent uncertainty. We will then see how merging these two perspectives on uncertainty can help clarify various conceptual issues and puzzles (such as the Monty Hall puzzle or the sleeping beauty problem). The primary objective is to explore the formal tools used by logicians, computer scientists, philosophers and game theorists for modeling uncertainty. We will focus on both the important conceptual issues (eg., Dutch book arguments, updating with probability zero events and higher-order probabilities) and the main technical results (eg., completeness and decidability of probabilistic modal logics).

Course Outline: The course will cover all of the following topics:

0. Background in dynamic epistemic logic and probabilistic models of uncertainty (including issues of measurability and Dutch book arguments)

1. Various puzzles about probability, beliefs and time (including the Monty Hall puzzle, the Sleeping Beauty problem and the Absent-Minded Driver problem)

2. Higher-order probability measures (including a definition of "common p-belief'' and uses of the concept in game theory)

3. Modal probabilistic logic (including proofs of completeness, decidability, and other standard results)

4. Uncertainty in a dynamic environment (including Bayesian/Jeffrey updates)

5. Updating with probability zero events (including lexicographic probability distributions, conditional probability distributions and relations with belief revision models) 6. Dynamic Epistemic Probabilistic Logic (including discussion of reduction axioms and temporal extensions)

Prerequisites: This is an advanced but self-contained course. Students will be expected to have had some exposure to (dynamic) epistemic logic and probabilistic logic. In particular, it will be assumed that students have already been introduced to epistemic logic and some of its dynamic extensions (i.e., public announcement logic); and although we will introduce many basic concepts of probabilistic theory (e.g., measure spaces), it will be expected that students have had previous exposure to probabilistic models of uncertainty.

http://ai.stanford.edu/~epacuit/classes/esslli/epprob.html

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