## Language and Logic Courses

### Foundational Courses

Bert Le Bruyn and Henriette de Swart. Cross-linguistic semantics: methodological advances

In this course, we present and discuss the methodologies that have been used in cross-linguistic semantics over the past two decades. One of the fundamental issues we are concerned with is the balance between data and theory: how much should we allow a theory based on one (set of) language(s) to guide our analysis of another (set of) language(s)? Up till recently, there was no other way to build a theory of language than by moving language by language and verifying/falsifying hypotheses based on previously studied languages. We argue that advances in parallel corpus analysis allow us to proceed in a more data-driven fashion and to question the status quo in how we make theoretical progress in cross-linguistic semantics.

Daniel Lassiter and Thomas Icard. Causal Models in Linguistics, Philosophy, and Psychology

This course explains and motivates formal models of causation built around Bayes nets and structural equation models, a topic of increasing interest across multiple cognitive science fields, and describes their application to select problems in psychology, philosophy, and linguistics.

Yoad Winter. Formal Semantics of Natural Language

This foundational course will introduce classical formal semantics of natural language, focusing on new directions and recent research. The first part of the course will cover semantic foundations including entailment, ambiguity, compositionality, types, models and basic lambda calculus. The second part will cover more advanced topics from recent work on presuppositions, plurals and events, focusing on empirical phenomena of foundational importance to compositionality: presupposition projection, distributive quantification, and modification across categories. The course is intended for students with basic mathematical and scientific background, but does not presuppose specific knowledge in logic or theoretical linguistics. For students who are new to formal semantics, the course will serve as a general overview which emphasizes the scientific value of analyzing semantic phenomena using elegant and rigorously defined mathematical methods. For students with previous background, the course will be useful as a pointer to current research of major importance for the foundations of formal semantics.

### Introductory Courses

Daniel Altshuler and Robert Truswell. Coordination: Syntax, Semantics, Discourse

Linguistics is full of boundary disputes. Empirical phenomena do not come neatly labeled as “syntax”, “semantics”, etc. The components of linguistic theory should interact to provide a complete account of the phenomena at hand, but often a syntactician will claim “this phenomenon is really semantics” (or ​vice versa​), without ensuring that a semantic analysis of the phenomenon is viable.

This course, based on our forthcoming OUP survey monograph, is an attempt to develop a complete analysis of coordination, a topic that spans syntax, formal semantics, and discourse semantics/pragmatics. We focus particularly on patterns of unbounded dependency formation in coordinate structures, which syntacticians claim require a partially semantic analysis, often without reference to current theories of the semantics of coordination. We explore the interactions between syntactic, semantic, and discourse theories, to develop an empirically rich holistic picture of the phenomenon at hand.

Patrick Blackburn and Antje Rumberg. Languages and Logics of Time: Priorean Perspectives

In this course we will introduce and motivate a variety of languages and logics of time from a historical and problem-oriented perspective. Our discussions will be grounded in the pioneering work of Arthur Prior, the founding father of tense logic, and we will explore the ways his ideas have been refined and reformed in later developments. The journey will take us from philosophical and linguistic questions concerning time and tense, temporal reference, the open future, change and aspectual categories, as well as the existence of individuals in time to contemporary formulations of basic tense logic, hybrid tense logic, branching time logic, event logic, description logic and first-order temporal logic. The course is interdisciplinary and only basic knowledge of elementary set theory, propositional and first-order logic is required.

David Boylan and Matthew Mandelkern. Conditionals and Information-Sensitivity

Recent research has converged on the idea that the semantics for conditionals is locally information-sensitive: roughly, the interpretation of a conditional depends, not just on its global context, but also on its local context. We will explore the theory of conditionals through this lens. We will thus introduce students to long-standing questions involving conditionals, as well as give them familiarity with the cutting-edge literature in this area. We will first consider how local information-sensitivity can illuminate the distinction between indicatives and subjunctives. We then will consider the logic of conditionals. Finally, we will consider the probability of conditionals. These topics have generally been explored in isolation from each other; we hope that, by bringing them together under the umbrella of local information-sensitivity, we will draw out inter-dependencies between these three issues and show how they can shed light on each other.

Ivano Ciardelli. Questions in Logic

Logic is concerned with relations between sentences that hold in virtue of their logical form, such as entailment and consistency. Traditionally, however, logic has focused on a special class of sentences, namely, statements---sentences which can be true or false. The course makes a case for extending logic beyond statements to encompass also questions, and describes how such an extension can be achieved in the framework of inquisitive logic. We will see that once logic is generalized to questions, interesting logical notions such as answerhood and dependency emerge as facets of the fundamental notion of entailment, and can thereby be analyzed by using the logician's toolkit of model-theoretic constructions and proof systems. In addition to motivating the enterprise and laying out the conceptual framework in detail, we will also see how classical propositional and predicate logic can be made inquisitive, i.e., enriched with questions, and what the resulting logics look like in terms of meta-theoretic properties and proof systems.

Itamar Kastner. The logical form of lexical semantics

It is common to say that the lexicon is the store of idiosyncratic information. This is true to some extent —- dog(x) is a different primitive than cat(x) -- but such a view sidesteps the many generalizations that work on lexical semantics has unearthed. Many verbs, in particular, differ not only in conceptual meaning but also in grammatical requirements: for example, we can "eat and eat all day" but not "??devour and devour all day". Building on a recent surge in empirical and formal work, this course will introduce students to a number of generalizations, discuss how they should be formalized, and make concrete a number of open questions, including:

- What are the most robust crosslinguistic generalizations regarding the interaction between lexicon and grammar?

- What formal tools can account for these?

- Is it possible to reach a constrained inventory of lexical semantic primitives?

• How can these claims be tested experimentally and modeled computationally?

Timothée Bernard and Justin Bledin. Negative events and truthmaker semantics

This course introduces the conceptual and logical foundations of negative events. We review the arguments raised in the linguistics and philosophy literature for and against them. We contrast events and situations, and relate them to exact and inexact verifiers in truthmaker semantics. We present the model-theoretic properties of a family of negation-like operations based on the notion of incompatibility, and then develop a formalization of negative events compatible with standard treatments of time and modality. Applications to negative perception reports and other phenomena are considered. This course together with Negative individuals and truthmaker semantics'' forms a unit on negative ontology in formal semantics, though each course can be taken independently of the other.

Ilaria Canavotto and Eric Pacuit. Conditionals in Decision and Game Theory

Reasoning about conditionals, such as "If I do action a, the outcome will be c", plays an important role when studying the foundations of decision and game theory. There are two objectives for this course. The first objective is to introduce the most prominent semantics for conditionals from the logic, philosophy and formal semantics literatures. The second objective is to introduce decision and game theory with a special emphasis on the puzzles and paradoxes that involve reasoning about conditionals (such as Newcomb's paradox, certain analyses of the Prisoner's Dilemma, and the Aumann-Stalnaker debate about backward induction). This course will provide a solid foundation for students interested in studying the semantics of conditionals and for students interested in using ideas from decision and game theory in their own field of study.

Simon Charlow and Dylan Bumford. Effectful composition in natural language semantics

Computer programs are often factored into pure components -- simple, total functions from inputs to outputs -- and components that may have side effects -- errors, changes to memory, parallel threads, abortion of the current command, etc. In this course, we'll make the case that human languages are similarly organized around the give and pull of pure and effectful processes, and we'll aim to show how denotational techniques from computer science can be leveraged to support elegant and illuminating semantic analyses of natural language phenomena.

Paul Dekker. Outline of a Theory of Interpretation

The course formally elaborates the idea of a theory of interpretation by translation, mostly in the spirit of Frege, Quine, Davidson and Kamp. The course provides some minimal formal tools required for presenting our extensional understanding of actual discourse, including intensional discourse, and a more or less philosophical motivation for presenting it this way.

While most of the developed formalism will be by and large similar to the relatively common semantics architectures, the proposed approach distinguishes itself in that it tries and accomplish all this with no, or the least possible, ontological and representational commitments. We make no assumptions about what meanings are, or possibilities, or representations---or objects, for that matter, nor about how one could go about modeling them. The course might be very adequately characterized as a training in a logical, Fregean, understanding of {\em DRT\/}, and related formalisms.

Melissa Fusco and Jacopo Romoli. Free choice: theoretical and experimental perspectives (revision)

Disjunctions in the scope of possibility modals give rise to a conjunctive inference, generally referred to as Free choice.' For example, (1) suggests that Angie can take Spanish and can take Calculus (and hence that she can choose' between the two). This inference is problematic, since it is not validated by a classical semantics for modals, in combination with a Boolean analysis of disjunction. To complicate things further, free choice tends to disappear under negation: (2) doesn't merely suggest that Angie can't choose, but rather that she can take neither Spanish nor Calculus. This second effect is sometimes referred to as Dual prohibition.'

(1) Angie can take Spanish or Calculus.

~> Angie can choose between the two

(2) Angie cannot take Spanish or Calculus.

~> Angie can take neither of the two

The Free choice-Dual prohibition pattern has sparked an industry of theories in philosophy of language and formal semantics/pragmatics since the seventies. A theory of this pattern not only has to derive free choice in positive contexts and dual prohibition in negative ones; it should also answer questions about these readings such as: are they part of the semantics of sentences like the above or do they arise as extra inferences? And what is the status of these readings? Are they at-issue or not at issue meanings? How do they interact with other aspects of meaning?

There are two main approaches in the literature, differing in particular as to whether they derive free choice as an implicature or not. We will outline the two approaches and their divergent predictions and explore how they fare against a range of experimental evidence in the literature from both adults and children. In addition, we will discuss the interaction between free choice and quantifiers, plurality, generics, and presuppositions. The goal of the course is to enable students to conduct their own experimental or theoretical research on this complex topic in semantics/pragmatics.

Jeremy Goodman and Cian Dorr. Theory-building in higher-order languages

This course will introduce higher-order logic as a language in which to rigorously theorize about modality, propositional attitudes, and the semantics of natural language. Unlike more familiar applications of higher-order languages in the foundations of mathematics, the aforementioned applications called for a non-extensional interpretation of higher-order quantification. This in turn raises hard questions about the granularity'' of higher-order reality, which have been the subject of a burgeoning literature in contemporary metaphysics and philosophical logic. The course will disseminate some of this recent work in a way that highlights issues that will be of interest to the ESSLLI audience. These include new technical results (both model constructions and inconsistency results) for `fine-grained'' theories, as well as applications to natural language semantics and to the semantic paradoxes. The course will stress the importance of combining fine-grained theories of sentence-meanings with corresponding accounts of sub-sentential-expression meanings, and of respecting limitative results like the Russell-Myhill paradox, Russell's paradox, and Tarski's theorem (relations between which will also be explored).