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Syntax and Semantics Grammar, May 2014 Linguistics 220 PHRASE STRUCTURE RULES CP ! Comp S S ! NP VP (PPLOC) (PPTIME) VP ! (Qual) (Aux1) (Aux2) (Aux3) V (NP) (AP) (PP) (PP) (CP) NP ! (Det) (AP) N (PP) (PP) NP ! Name NP ! Pro AP ! (Deg) A (PP) PP ! (Deg) P (NP) (PP) Note: we do not assume an X’ template, or an Infl daughter of S, as stated in the textbook. Also, Adv(erbs) can appear in the same position of Qual, and some additional positions we have not clarified yet. TRANSFORMATIONS Yes/No Question transformation (optional, if no +Q Comp) Input condition: an S that contains a VP with one or more Aux’s. Output change: move the first Aux of the VP to the head position of the highest CP. WH-Movement (obligatory) Input Condition: CP must contain a ProWH Output Change: Move the ProWH to the Specifier position of CP SET THEORY Inclusion/subset relation: A is a subset of B if and only if all members of A are also members of B Proper Inclusion/proper subset relation: A is a proper subset of B if and only if A is a subset of B and there is some entity in B that is not a member of A Set intersection: the intersection of A and B is a set that contains all the entities that are members of both A and B SAMPLE LEXICON Format: spelling, pronunciation (symbols unimportant now), syntactic category, subcategorization, ‘meaning’ boy, [boj], Noun, ‘male human young’ Jake [dʒejk], Name, ‘picks out individual called the, [ð"], Det Jake’ fond, [fand], A [___ PPof] ‘likes’ he [hi], Pro faint, [fejnt], V [___] ‘to lose consciousness’ might [majt] Aux1 ‘it is possible’ nominate, [namɪnejt], V, [___ NP (PPfor)] will [wɪl] Aux1 FUTURE put [pʊt], V [___ NP PP] have1 [hæv] Aux2 ‘past, perfective’ at [æt], P have2 [hæv] V ‘to possess’ that [ðæt], Comp, [___ S] be1 [bi] Aux3 ‘action in progress’ said [sɛd], V, [___ NP or CP] be2 [bi] V ‘is a subset of (see below)’ FORMAL RELATIONS Daughter: Y is a daughter of X if and only if Y occurs on the righthand side of the PSR, and X occurs on the lefthand side of that PSR. Mother: X is a mother of Y if and only if Y is a daughter of X. Sister: Y is a sister of Z if and only if Y and Z are both daughters of some X. Descendent: X is a descendent of Y if and only if X is (a daughter of some constituent that is)* a daughter of Y. (* = Endlessly repeating.) Recursivity: A set of PSRs is recursive if and only if it can generate trees in which some instance of a category X is a descendent of another instance of X. FORM RULES Aux1 Input: Aux or V following Aux1 (=modals) Output: Aux or V is marked ‘bare’ Aux2 Input: Aux or V following Aux2 (=have1) Output: Aux or V is marked ‘-EN’ Aux3 Input: V following Aux3 (=be1) Output: V is marked ‘-ING’ Objective case Input: Pro daughter of NP that directly follows a V or P Output: make the Pro lexical category [+objective] Set union: the union of A and B is a set that contains all members of A and all members of B Complementation: the complement of A is all members in some domain, excluding all entities that are members of A TRANSLATION OF LINGUISTIC EXPRESSIONS INTO LOGICAL FORMULAS Basic expressions I: pronouns and names are translated as variables for entities Basic expressions II: adjectives, intransitive verbs, and common nouns are translated as descriptive sets Subject-predicate relation I: if the subject is pronoun or name, and the predicate VP is either a predicate adjective [is/are A], an intransitive verb, or a predicate nominal [is/are N] (but we ignore determiners), then translate as follows: x (= pronoun/name) is a member of the set corresponding to the predicate VP. Subject-predicate relation II: if the subject is a simple common noun, and the VP contains either a predicate adjective [is A], an intransitive verb, or predicate nominal [is/are N], then translate as follows: the set corresponding to the NP subject is a subset of the set corresponding the VP. Complex sets with modifiers and and: the meaning of an adjective modifier in [… A N] can combine with the meaning of the head noun, or the meanings of two Ns or As conjoined with and, using set intersection. LIMITATIONS At this time, we are unable to analyze the meaning of sentences that contain the following types of expressions: transitive verbs and all quantifiers (e.g., most, every, all, some, several, the).