An introduction to the formal study of meaning in natural language, with a focus on how sentence meanings are systematically composed. We begin by developing a truth-conditional notion of literal meaning, then introduce tools from logic to model how the meanings of complex expressions are derived from the meanings of their parts and how they are combined. Throughout, the course emphasizes a linguist’s perspective on the interface between form and meaning.
Additional Requirements for Graduate Students: Undergraduate evaluation will be based on regular take-home assignments and a comprehensive final take-home test. Graduate students, in addition to these assignments and final test, will be required to write a 5-6 page literature review of 5-7 peer-reviewed journal articles on a topic in semantics.
Athena Title
Compositional Semantics
Undergraduate Prerequisite
[(LING 3150 or LING 3150W) and (PHIL 2500 or PHIL 2500H or PHIL 2500E)] or permission of department
Graduate Prerequisite
LING 8150 and permission of department
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Student Learning Outcomes
Students will be able to explain core concepts in formal semantics like truth-conditional meaning and compositionality.
Students will be able to apply diagnostic tests to distinguish between different implication relations such as entailment and presupposition.
Students will compare and evaluate competing semantic and pragmatic accounts of natural language phenomena.
Students will analyze linguistic data applying methods and formal tools from math and logic and support analyses based on empirical evidence.
Students will be able to explain how the meanings of words and phrases combine to yield sentence meanings.
Students will Investigate and analyze ambiguity and other natural language phenomena in a systematic way.
Students will develop problem-solving skills in semantics by working through data-driven exercises to test hypotheses about meaning.
Students will evaluate if specific analyses and theoretical frameworks for natural language phenomena may be applicable crosslinguistically.
Students will be able to represent formally natural language expressions of differing complexity using tools from propositional and predicate logic, lambda calculus, and model-theoretic semantics.
Students will learn to balance and adapt between two distinct registers of communication: (i) formal symbolic notation, which represents meaning in a precise way, and (ii) natural-language prose explanations, which describe and justify semantic analyses in a clear and accessible language to broader audiences.
Students will communicate reasoning about meaning by engaging critically with arguments in scholarly literature.
Topical Outline
Compositional semantics: implication relations; entailment, implicature, presupposition; semantics and pragmatics; Square of opposition; direct and indirect semantic interpretation
Set theory: what are sets; relations among sets; operations on sets; a theory of quantification in English; subset vs. element; relations and functions; ordered pairs
Propositional logic: formulas and propositional letters; Boolean connectives; conditionals and biconditionals; equivalence, contradiction and tautology; syntax and semantics of propositional logic
Predicate logic: constants and variables; predicates; identity; syntax of quantifiers; semantics of non-logical constants, predication, identity statements, connectives; variables and assignment functions; semantics of quantifiers; syntax and semantics of predicate logic
Typed lambda calculus: types, lambda abstraction; functional application; beta reduction; syntax and semantics of typed lambda calculus
Function application: negation and quantifiers; generalized quantifiers
Adjectives, relative clauses, pronouns, and quantifiers in object position: Type-Shifting rules, Predicate Modification rule; Pronouns and Traces rule, Predicate Abstraction rule; Quantifier Raising rule, Type-Shifting approach; indexicality
Presupposition: the definite determiner; definedness conditions; designing a three-valued logic; a partialized lambda calculus; presupposition accommodation; the projection problem
Coordination and plurals: coordination, collective predication and mereology; plural definite descriptions; cumulative readings
Event semantics: events as verbal arguments; Aktionsart; composition in Neo-Davidsonian event semantics; quantification, conjunction, and negation in event semantics
Tense and aspect: a formal theory of tense; a partial, context-sensitive logic with times; English tense and aspect
Intensional semantics: modality; necessity and possibility; modal logic; possible worlds semantics; modal flavors and attitudes; de dicto vs. de re readings; compositionality with Ty2
