**Time:** 2020 April 10-12

**Venue:** Tsinghua University

Monotonicity, in various forms, is a pervasive phenomenon in logic, linguistics, and related areas. In theoretical linguistics, monotonicity properties (and lattice-theoretic notions such as additivity), as semantic properties of intra-sentential environments, determine the syntactic distribution of a class of terms robustly attested across languages called Negative Polarity Items (NPIs, Ladusaw 1979), such as English *any *in (1), and is relevant to a large array of semantic phenomena such as the interpretation of donkey pronouns (Kanzanawa 1994, (2)), plural definites (Krifka 1996, (3)), plural morphemes and so on, and to the presence of pragmatic inferences such as scalar implicatures (Grice 1989), as illustrated by the interpretative difference of disjunction in (4) (Chierchia 2004) .

(1) a. *Somebody bought **any **cookies.

b. Nobody bought **any **cookies.

(2) a. Every farmer who owns a donkey beats **it**. (Universal interpretation of *it*)

b. No farmer who owns a donkey beats **it**. (Existential interpretation of *it*)

(3) a. Mary has read **the files **on her desk. (Universal interpretation of *the files*)

b. Mary has not read **the files **on her desk. (Existential interpretation of *the files*)

(4) a. If everything will go well, we’ll hire either Mary **or **Sue. (Exclusive interpretation of *or*)

b. If we hire either Mary **or **Sue, everything will go well. (Inclusive interpretation of *or*)

In logic and mathematics, a function f between pre-ordered sets is monotone or increasing (antitone or decreasing) if x ≤ y implies f(x) ≤ f(y) (f(y) ≤ f(x)). Monotonicity guarantees the existence of fixed points (points x such that f(x)=x) and the well-formedness of inductive definitions, and logical languages with expressive means for talking about fixed points, such as first-order fixed point logic or the modal µ-calculus, is a growing area of study in logic and computer science. Also, monotonicity is closely tied to reasoning, in formal as well as natural languages. Corresponding to the semantic properties of monotonicity and antitonicity there is the syntactic property of (positive or negative) polarity. Monotonicity Reasoning, which involves replacement of predicates in syntactic contexts of given polarity, is a simple yet surprisingly powerful mode of inference. Starting with work of van Benthem and Sánchez-Valencia in the 1980s, the idea of Natural Logic, comprising algorithms for polarity marking and formal calculi for monotonicity reasoning, is an active research project (Icard and Moss 2014). Likewise, much of the current study of syllogistic reasoning (Moss 2015) formally exploits patterns of monotonicity.

Recent logical and linguistic work on monotonicity has also found its way into computation systems for natural language processing (e.g. systems for Recognizing Textual Entailment, MacCartney and Manning 2009), and cognitive models of human reasoning (Geurts 2003).

The goal of our workshop is to bring together researchers working on monotonicity or related properties, from different fields and perspectives. Topics of the workshop may include (but are not limited to) the following:

- linguistic phenomena sensitive to monotonicity and their analyses
- different types of monotonicity (logical monotonicity, Strawson monotonicity and perceived monotonicity; Chemla, Homer and Rothschild 2012)
- monotonicity beyond quantificational determiners and negation (monotonicity of embedding verbs and modals, monotonicity in questions)
- cognitive and computational aspects of monotonicity
- representation of monotonicity in formal and natural languages
- logics based on fixed points
- formal calculi of monotonicity and related properties
- Natural Logic: theory and applications
- logics for syllogistic fragments

**Invited Speakers:**

Gennaro Chierchia (Harvard University)

Jo-wang Lin (Institute of Linguistics at Academia Sinica, Taiwan)

Floris Roelofsen (University of Amsterdam)

Jakub Szymanik (University of Amsterdam)

The workshop is in collaboration with another event that will take place in Zhejiang University, right before the TLLM 2020: the Zhejiang Logic for AI Summit, 6-9 April 2020!