Lecture 3 Ling 442

exercises 1.What is the difference between implicature and entailment? 2.What is the difference between presuppositions and entailments? 3.Provide examples of context-dependent (or indexical) expressions 4.Give examples of “one-place predicates” in English

Exercises (part 2) 5. Give examples of “two-place predicates” in English 6. How about “three-place predicates”? [caveat] categorematic vs. syncategorematic expressions (Basic idea: a categorematic expression has its own meaning, and a syntactegorematic expression does not. But ignore this because the point being made is very controversial.)

Predicate Logic It is an artificial language designed to talk about semantics. It is designed to talk about the semantic roles played by sentential connectives (including negation), different types of predicates, and quantifiers.

connectives binary: and, or, if … then, iff (if and only if) unary: it is not the case that … , , ,   Syntax: S  S Conn S, S   S Semantics: E.g. S1  S2 = true iff S1 = true and S2 = true Similarly for other connectives.

Possible issues  What if both sentences are true?  How do we use “if, … then” in colloquial English? Does the meaning of  match up with your intuitions about “if, then”?

Predicates One-place predicates Intransitive verbs, adjectives, common nouns, etc. Two-place predicates Transitive verbs, prepositions, some adjectives (like fond), some nouns (like father), etc. Three-place predicates Ditransitive verbs (e.g. give)

Terms (“arguments”) You should think of the terms that occupy argument positions of predicates as names in Predicate Logic. Mary likes John  Likes (j, m) You can use pronouns instead of names in these “argument positions”. She likes him  Likes (x, y)

Quantifiers The term “quantifier” is misleading because a quantifier does not necessarily deal with “quantities” of any sort (at least not straightforwardly). A quantifier could be defined as an expression that allows us to talk about “multiple cases”: e.g. every, some, no, most, three, etc. Think about quantifiers in languages other than English.