Minimalist Machine Derivations

Minimalist Machine Derivations

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Examples:

Relative clause examples from Sag 1997 (Fong & Ginsburg, ms.) collapse

Example	Instruction stream (clickable)	Notes
(23a) the book which inspired them (Example (24a); Sag 1997: 448 (23b) *the book which that inspired them	[they,d,inspire,'v*',[book,which_rel],'Tpast',c_rel,the]	Subject relative. DP [book, which_rel] is attracted to the edge of C_rel by uRel on C_rel. By economy, which_rel values both uT and uRel on C_rel, and the T-to-C option is impossible, i.e. *which that in (23b). However, which_rel cannot value uD so book will raise further and uD is valued during the merge with the.
(24) the person whose mother died (Example (24b); Sag 1997: 448)	[mother, '\'s', [person, who_rel], die, 'v~unacc', 'Tpast', c_rel, the]	Assume whose here is who_rel + 's and die is unaccusative, i.e. [[who_rel person]['s mother]] is theta-merged at the internal argument position. Furthermore, permit uRel on C_rel to find iRel on who_rel at the edge of possessive 's. [[who_rel person]['s mother]] is attracted to the edge of C_rel. However, who_rel cannot value uD on person. Next, person raises and its uD is valued when merged with the.
(25) the person whose mother's dog died (Example (24d); Sag 1997: 448)	[dog, '\'s', [mother, '\'s', [person, who_rel]], die, 'v~unacc', 'Tpast', c_rel, the]	Analysis is the same as for (24) above, except we permit uRel on C_rel to recursively look for iRel at the edge of possessive 's. Internal argument is [[[who_rel person] 's mother]['s dog]].
(26a) the person whose mother's dog we were (all) fond of (Example (24d); Sag 1997: 448) (26b) the person whose mother's dog that we were (all) fond of (26c) the person of whose mother's dog we were (all) fond (26d) the person of whose mother's dog that we were (all) fond	[dog, '\'s', [mother, '\'s', [person, who_rel]],of,fond,[we,d],v_be,'Tpast',c_rel,the]	[[[who_rel person] 's mother]['s dog]] is attracted to the edge of C_rel by uRel on C_rel. We assume, following (25), that uRel on C_rel can find recursively iRel at the edge of possessive 's. who_rel cannot value uD on person. Next, person raises and its uD is valued when merged with the. (26b) is predicted as [[[who_rel person] 's mother]['s dog]] is not a nominative subject, so economy does not apply. The option of T-to-C generates the complementizer that. (26c-d) are blocked by a spellout rule *of who, designed to block *the girl of who friends bought the cake.
(27a) the person to whom they dedicated the building (Example (24e); Sag 1997: 448) (27b) the person whom they dedicated the building to	[person,who_rel,to,[building,the],dedicate,'v*',[they,d],'Tpast',c_rel,the]	We assume dyadic to, i.e. the VP is [dedicate [[the building] [to [who_Rel person]]]]. [who_Rel person] is attracted to the edge of C_rel by uRel on C_rel. who_rel cannot value uD on person. Next, person raises and its uD is valued when merged with the. Pied-piping is permitted as who_rel is overt. Note: after the two successful derivations, at step 41, the system tries unsuccessfully to employ monadic to with [dedicate [to [who_Rel person]]]. The problem is the merge of [the building]. At step 48, the attempted XP-YP pair merge of [the building] fails. At step 59, the corresponding XP-YP set merge fails. After that, there are a further two parallel attempts pushing [to [who_Rel person]] onto the stack.
(28) [Give me] the phone number of the person whose mother's friend's sister's dog's appearance had offended the audience (Example (31a); Sag 1997: 450)	[audience,the,offend,'v*',[appearance,'\'s',[dog,'\'s',[sister,'\'s',[friend,'\'s',[mother,'\'s',[person,who_rel]]]]]],perf,v,'Tpast',c_rel,the,of,number,phone,the]	The DP with the relative pronoun who_rel is deeply embedded recursively within the specifier of possessive 's for the head noun appearance. However, it must be visible to uRel probing. Therefore, [[[[[[who_rel person]['s mother]]['s friend]]['s sister]]['s dog]]['s appearance]] is attracted to the edge of C_rel by uRel on C_rel. who_rel cannot value uD, so person will raise further to form a new head. Determiner the merges with the NP headed by person, valuing uD on person.
(29a) [This is] the senator to whose mother's friend's sister's favorite charity the lobbyist had donated a small fortune (Example (31b); Sag 1997: 450) (29b) [This is] the senator to whose mother's friend's sister's favorite charity that the lobbyist had donated a small fortune (29c) [This is] the senator whose mother's friend's sister's favorite charity the lobbyist had donated a small fortune to (29d) [This is] the senator to whose mother's friend's sister's favorite charity that the lobbyist had donated a small fortune	[charity,favorite,'\'s',[sister,'\'s',[friend,'\'s',[mother,'\'s',[senator,who_rel]]]],to,[small,fortune,a],donate,'v*',[lobbyist,the],'Tpast',c_rel,the]	Similar derivation to example (28). We wh-relativize senator from the lobbyist donated a small fortune to the senator's mother's friend's sister's favorite charity. [[[[[who_rel senator]['s mother]]['s friend]]['s sister]]['s favorite charity]] is attracted to the edge of C_rel by uRel on C_rel. who_rel cannot value uD, so senator will raise further to form a new head. Determiner the merges with the NP headed by senator, valuing uD on senator. There are four parses as the options of inserting the complementizer that and the pied-piping of prepositional to are both freely available.
(30a) the time when I got drunk (30b) *the time when that I got drunk	[drunk,get,v_unerg,[i,d],'Tpast',[time,when_rel],c_rel,the]	Assume the time expression [when_rel time] is merged at TP level for semantic reasons. Both pair merge and set merge options are tested. Because extraction must take place for relativization, only the set merge option can succeed. (Pair merged adjuncts are inaccessible to probing.) [when_rel time] is attracted to the edge of C_rel by uRel on C_rel. when_rel cannot value uD on time. Next, time raises and its uD is valued when merged with the. However, when_rel can value uT (as well as uRel) on C_rel. By economy, no T-to-C, that in (30b), is possible.
(31a) the town where I grew up (31b) *the town up where I grew	[up,grow,[town,where_rel],'v_unerg',[i,d],'Tpast',c_rel,the]	Assume the location adverbial [where_rel town] is merged at the VP level. Both pair merge and set merge options are tested. Because extraction must take place for relativization, only the set merge option can succeed. (Pair merged adjuncts are inaccessible to probing.) [where_rel town] is attracted to the edge of C_rel by uRel on C_rel. where_rel cannot value uD on town. Next, town raises and its uD is valued when merged with the. However, where_rel can value uT (as well as uRel) on C_rel. By economy, no T-to-C (that) is possible. Finally, up does not head a PP with complement [where_rel town] (merged at VP level instead). Therefore no pied-piping, as in (31b), is possible.
(33a) someone to rely on (33b) *someone on to rely	[someone, d_rel, on, rely, 'v*', ['PRO', d0], 'Tinf', c_rel, d]	[d_rel someone] is attracted to the edge of C_rel by uRel on C_rel. d_rel cannot value uD, so someone will raise further. T_inf checks uT on C_rel. (d_rel cannot value uT on C_rel, uT is valued by T_inf instead. Pied-piping is blocked by the empty determiner d_rel, cf. overt who_rel in (35a). (Note: this lexicon contains both simple prepositional on and dyadic on, e.g. put the book on the shelf. Step 17 onwards using dyadic on fails to derive.)
(34a) someone for you to rely on (34b) *someone on for you to rely	[someone, d_rel, on, rely, 'v*', [you, d], 'Tinf', for, c_rel, d]	Assume complementizer for generally licenses an overt subject, you, by assigning Case, cf. PRO in (33a). C_rel, containing uRel, piggy-backs onto for, attracting [d_rel someone] to its edge. Covert d_rel in [on [d_rel someone]] incompatible with pied-piping of on, so (34b) is blocked. As described in (33a), someone will raise further and merge with covert d.
(35a) the baker in whom to place your trust (Example (63a); Sag 1997:461) (35b) *the baker whom to place your trust in (Example (63d); Sag 1997:461)	[baker, who_rel, in, [ trust, '\'s', [you, d]], place, 'v*', ['PRO', d0], 'Tinf', c_rel, the]	Both (35a-b) are predicted to be grammatical here, i.e. pied-piping is permitted. (Judgements shown are from Sag.) Assume in is dyadic, i.e. VP structure is [place [your trust [in [who baker]]]]. (Note: the derivations with dyadic in begin at step 51 and end at step 103. Simple preposition in is tried first, but fails to converge at step 50.) Either [in [who_rel baker]] (for pied-piping) or [who_rel baker], the internal argument of in, may be attracted to edge of C_rel by uRel on C_rel. NB: who_rel is defective, i.e. it doesn't value the uD feature on baker. Therefore, baker raises from edge of C and its uD feature is checked by determiner the.
(36a) the baker to place your trust in (36b) *the baker in to place your trust	[baker, d_rel, in, [ trust, '\'s', [you, d]], place, 'v*', ['PRO', d0], 'Tinf', c_rel, the]	No overt who_rel here, cf. (35a-b). Covert d_rel is used instead, i.e. internal argument of in is [d_rel baker]. [d_rel baker] is attracted to the edge of C_rel by uRel on C_rel. Pied-piping is not an option since d_rel is an empty category, cf. (35b). d_rel cannot value uD so baker will raise further and its uD will be checked by the. Assume uT on C_rel is valued by T_inf. (Note: the derivation with dyadic in begins at step 28 and concludes at step 54. Simple preposition in is tried first, but fails to converge at steps 16 and 27 for pair and set merge, respectively.)
(37) the person for us to visit (Example (75b); Sag 1997: 464)	[person, d_rel, visit, 'v*', [we, d], 'Tinf', for, c_rel, the]	Similar to (34a), assume complementizer for generally licenses an overt subject, we, in a tenseless clause by assigning Case. C_rel, containing uRel, piggy-backs onto the complementizer for, attracting [d_rel person] to its edge. d_rel cannot value uD on person. The head person raises further and merges with the, which values person's uD feature.
(38) the person to visit (Example (75c); Sag 1997: 464)	[person, d_rel, visit, 'v*', ['PRO', d0], 'Tinf', c_rel, the]	Compared with (37), there is no for with an overt subject; instead, we assume the covert subject is PRO. [d_rel person] is attracted to the edge of C_rel by uRel on C_rel. d_rel cannot value uD on person. The head person raises further and merges with the, which values person's uD feature.

Machine Parameters: expand

Animation:
(37) the person for us to visit (Example (75b); Sag 1997: 464)

Derivation:
(37) the person for us to visit (Example (75b); Sag 1997: 464)

Stream:	[[person!D],[d_rel!case!N],[visit],[v*!phi],[[we!D],[d!case!N]],[Tinf!phi],[for!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):
SO:	[]

Step 1.

Head of stream [person!D] is the initial SO

Stream:	[[d_rel!case!N],[visit],[v*!phi],[[we!D],[d!case!N]],[Tinf!phi],[for!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):
SO:	[person!D]

Step 2.

Merge [d_rel!case!N] and [person!D]

Label from [d_rel!case!N] (syntactic head with an unvalued uF)

Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [person!D]

[person!D] values N on [d_rel!case!N]

Push [person!D] (unvalued uF) onto stack

Stream:	[[visit],[v*!phi],[[we!D],[d!case!N]],[Tinf!phi],[for!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[person!D]
SO:	[d_rel!case[d_rel][person!D]]

Step 3.

Merge [visit] and [d_rel!case[d_rel][person!D]]

Label from [visit] (syntactic head merging with a non-head)

Theta-mark [d_rel!case[d_rel][person!D]]

Push [d_rel!case[d_rel][person!D]] (unvalued uF) onto stack

Stream:	[[v*!phi],[[we!D],[d!case!N]],[Tinf!phi],[for!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d_rel!case[d_rel][person!D]] [person!D]
SO:	[visit[visit][d_rel!case[d_rel][person!D]]]

Step 4.

Merge [v*!phi] and [visit[visit][d_rel!case[d_rel..][person..]]]

Label from [v*!phi] (syntactic head merging with a non-head)

[d_rel!case[d_rel][person!D]] values uPhi on [v*!phi]

[v*] values acc case on [d_rel!case[d_rel][person!D]]

Stream:	[[[we!D],[d!case!N]],[Tinf!phi],[for!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d_rel[d_rel][person!D]] [person!D]
SO:	[v[v][visit[visit][d_rel[d_rel][person!D]]]]

Step 5.

Begin substream

Stream:	[[we!D],[d!case!N]]
Stack (⥥):
SO:	[]

Step 6.

Head of stream [we!D] is the initial SO

Stream:	[[d!case!N]]
Stack (⥥):
SO:	[we!D]

Step 7.

Merge [d!case!N] and [we!D]

Label from [d!case!N] (syntactic head with an unvalued uF)

Inherit interpretable feature(s) [f(phi,[3,pl,mf])] from [we!D]

[d!case!N] values D on [we!D]

[we] values N on [d!case!N]

Stream:	[]
Stack (⥥):
SO:	[d!case[d][we]]

End substream, SO [d!case[d][we]] re-inserted into main stream

Step 8.

Stream:	[[d!case[d][we]],[Tinf!phi],[for!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d_rel[d_rel][person!D]] [person!D]
SO:	[v[v][visit[visit][d_rel[d_rel][person!D]]]]

Step 9.

Merge [v*[v*][visit[visit..][d_rel..]]] and [d!case[d][we]]

Label from [v*[v*][visit[visit..][d_rel..]]] (edge feature)

Theta-mark [d!case[d][we]]

Push [d!case[d][we]] (unvalued uF) onto stack

Stream:	[[Tinf!phi],[for!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d!case[d][we]] [d_rel[d_rel][person!D]] [person!D]
SO:	[v[d!case[d][we]][v[v*][visit[visit][d_rel[d_rel][person!D]]]]]

Step 10.

Merge [Tinf!phi] and [v*[d!case[d..][we..]][v*[v*..][visit..]]]

Label from [Tinf!phi] (syntactic head merging with a non-head)

[d!case[d][we]] values uPhi on [Tinf!phi]

Stream:	[[for!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d!case[d][we]] [d_rel[d_rel][person!D]] [person!D]
SO:	[Tinf[Tinf][v[d!case[d][we]][v[v*][visit[visit][d_rel[d_rel][person!D]]]]]]

Step 11.

Internal merge selected

Merge [Tinf[Tinf][v*[d..][v*..]]] and [d!case[d][we]]

Label from [Tinf[Tinf][v*[d..][v*..]]] (edge feature)

Stream:	[[for!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d!case[d][we]] [d_rel[d_rel][person!D]] [person!D]
SO:	[Tinf[d!case[d][we]][Tinf[Tinf][v[d[d][we]][v[v*][visit[visit][d_rel[d_rel][person!D]]]]]]]

Step 12.

Merge [for!phi] and [Tinf[d!case[d..][we..]][Tinf[Tinf..][v*..]]]

Label from [for!phi] (syntactic head merging with a non-head)

[d!case[d][we]] values uPhi on [for!phi]

[for] values obq case on [d!case[d][we]]

Stream:	[[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d[d][we]] [d_rel[d_rel][person!D]] [person!D]
SO:	[for[for][Tinf[d[d][we]][Tinf[Tinf][v[d[d][we]][v[v*][visit[visit][d_rel[d_rel][person!D]]]]]]]]

Step 13.

Local Extent boundary at [for[for][Tinf[d..][Tinf..]]]

Stack element [d_rel[d_rel][person!D]] with unvalued uF found

Stack element [person!D] with unvalued uF found

New boundary (b) marker stacked

Restack [person!D] onto stack

Restack [d_rel[d_rel][person!D]] onto stack

Stream:	[[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d_rel[d_rel][person!D]] [person!D] b [d[d][we]]
SO:	[for[for][Tinf[d[d][we]][Tinf[Tinf][v[d[d][we]][v[v*][visit[visit][d_rel[d_rel][person!D]]]]]]]]

Step 14.

Merge [c_rel!rel!T!phi] and [for[for][Tinf[d..][Tinf..]]]

Label from [c_rel!rel!T!phi] (syntactic head merging with a non-head)

[d_rel[d_rel][person!D]] values rel on [c_rel!rel!T!phi]

Relativized TOS search for iF(T) skipping [d_rel[d_rel][person!D]]

Relativized TOS search for iF(T) skipping [person!D]

[c_rel!T!phi] attracts [for[for][Tinf[d..][Tinf..]]]

[d_rel[d_rel][person!D]] values phi on [c_rel!phi] (economy)

[c_rel] values obq case on [d_rel[d_rel][person!D]]

Internal merge selected

Merge [c_rel[c_rel][for[for..][Tinf..]]] and [for]

Label from [c_rel[c_rel][for[for..][Tinf..]]] (edge feature)

Merge [c_rel[for][c_rel[c_rel..][for..]]] and [d_rel[d_rel][person!D]]

Label from [c_rel[for][c_rel[c_rel..][for..]]] (edge feature)

Stream:	[[the!case!N]]
Stack (⥥):	[d_rel[d_rel][person!D]] [person!D] b [d[d][we]]
SO:	[c_rel[d_rel[d_rel][person!D]][c_rel[for][c_rel[c_rel][for[for][Tinf[d[d][we]][Tinf[Tinf][v[d[d][we]][v[v*][visit[visit][d_rel[d_rel][person!D]]]]]]]]]]]

Step 15.

Local Extent boundary at [c_rel[d_rel[d_rel..][person..]][c_rel[for..][c_rel..]]]

Stack element [d_rel[d_rel][person!D]] with unvalued uF found

Stack element [person!D] with unvalued uF found

New boundary (b) marker stacked

Restack [person!D] onto stack

Restack [d_rel[d_rel][person!D]] onto stack

Stream:	[[the!case!N]]
Stack (⥥):	[d_rel[d_rel][person!D]] [person!D] b b [d[d][we]]
SO:	[c_rel[d_rel[d_rel][person!D]][c_rel[for][c_rel[c_rel][for[for][Tinf[d[d][we]][Tinf[Tinf][v[d[d][we]][v[v*][visit[visit][d_rel[d_rel][person!D]]]]]]]]]]]

Step 16.

Merge [person!D] and [c_rel[d_rel[d_rel..][person..]][c_rel[for..][c_rel..]]]

Label from [person!D] (syntactic head merging with a non-head)

Stream:	[[the!case!N]]
Stack (⥥):	b b [d[d][we]]
SO:	[person!D[person!D][c_rel[d_rel[d_rel][person!D]][c_rel[for][c_rel[c_rel][for[for][Tinf[d[d][we]][Tinf[Tinf][v[d[d][we]][v[v*][visit[visit][d_rel[d_rel][person!D]]]]]]]]]]]]

Step 17.

Merge [the!case!N] and [person!D[person!D][c_rel[d_rel..][c_rel..]]]

Label from [the!case!N] (syntactic head merging with a non-head)

Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [person!D[person!D][c_rel[d_rel..][c_rel..]]]

[the!case!N] values D on [person!D[person!D][c_rel[d_rel..][c_rel..]]]

[person[person][c_rel[d_rel..][c_rel..]]] values N on [the!case!N]

Stream:	[]
Stack (⥥):	b b [d[d][we]]
SO:	[the!case[the][person[person][c_rel[d_rel[d_rel][person]][c_rel[for][c_rel[c_rel][for[for][Tinf[d[d][we]][Tinf[Tinf][v[d[d][we]][v[v*][visit[visit][d_rel[d_rel][person]]]]]]]]]]]]]

Parse:

Spell-out:

the person for -obq we to visit (after morpheme realization)

the person for we -obq to visit (after affix-hop)

the person for we -obq to visit (after morpheme realization, stage 2)

the person for us to visit

One derivation found.

Computational Cost:

Merge: 13, Agree: 14, Unify: 0, Push: 3, Boundaries: 2, Inject: 4

Non-TOS access: 2, Pop: 0, Depth cost: 25

Step:	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17
Stack depth:	0	0	1	2	2	0	0	0	2	3	3	3	3	4	4	5	3	3