Islands coordination and parasitic gaps

We present type logical grammar of left extraction with attention to islands coordination and parasitic gaps We consider implementation in proof nets The account suggests a measure of the semigrammaticality of island violations Data Coordination might be thought a test for constituency but it is possible to coordinate elements which are non constituents on most any theory Consider for example Right Node Raising Postal Bresnan and Left Node Raising Schachter and Mordechay a John liked and Mary disliked London b Bill met John on Monday and Sue on Tuesday The Right Node Raising in a suggests that a subject can form a constituent with a transitive verb A certain prosodic markedness accompanies the construction Generally it might be assumed that the conjunts are sentences with gaps in object position and that this situation is signalled prosodically However the Left Node Raising b suggests even more radically that an object can form a constituent with an adverbial and this time there is no prosodic markedness Coordination might also be thought a test for category identity but coordination of apparently unlike categories is possible Sag et al is Bond and teetotal In the conjunts are respectively a proper name and an adjective In these respects coordination con icts with common basic assumptions and motivates type logical grammar Morrill Moortgat Carpenter which characterizes all of the above as indeed coordination of like constituents Our concern in this paper is with left extraction including relations to coordination and including parasitic gaps E mail morrill lsi upc es http www lsi upc es morrill To appear in Abrusci V M and C Casadio eds New Perspectives in Logic and Formal Linguistics Proceedings Vth Roma Worshop Bulzoni Editore Roma Work partially supported by CICYT project PB C Although left extraction such as interrogativization topicalization and relativization is unbounded in distance it is not unconstrained Coordinate structures are islands to extraction Coordinate Structure Constraint Ross man thati Suzy met Bill and Mary married ei Extraction becomes grammatical if it is Across the Board ATB man thati Suzy met ei and Mary married ei However not even ATB extraction is possible of entire conjunts man thati Suzy met the friend of ei and ei Adverbials and nominal subjects are weak islands Adverbial Island Constraint Sub ject Condition Chomsky a man thati the friends of ei smiled b paper thati John slept without reading ei Extraction from weak islands becomes ne if accompanied by a cobound non island ex traction a man thati the friends of ei admire ei b paper thati John led ei without reading ei This is referred to as parasitic extraction Ross Taraldsen Engdahl Sag The idea is to say that parasitic gaps in islands are dependent on or licensed by non island host gaps Note that in judging we even experience pressure to force a transitive reading on the intransitive verbs We assume here that as the term suggests a parasitic gap must fall within an island slave thati John sold ei to ei Thus we must consider the co bound extraction in cf Postal a where neither gap falls within an island some other kind of symbiotic extraction man whoi Mary convinced ei that John wanted to visit ei A host gap can licence more than one parasitic gap but only in di erent islands a paper thati the editor of ei led ei without reading ei b slave whoi the fact that John sold ei to ei surprised ei A host gap cannot directly licence a parasitic gap in an island within an island Postal s Island Condition However it seems that one parasitic gap can in turn be host to another a man whoi the fact that the friends of ei admire ei surprises ei b paper thati John published ei without the editor of ei rereading ei c man whoi the fact that the friends of ei admire ei without praising ei surprises ei Sentential subjects are strong islands and do not seem to allow parasitic gaps a man whoi that Mary likes ei surprises John b man whoi that Mary likes ei surprises ei Fixed Subject Constraint Bresnan Chomsky and Lasnik violations are out man whoi John said that ei left The subjects of uncomplementized embedded sentences however can be extracted and can licence parasitic gaps a man thati John thinks ei left b man thati the friends of ei think ei left Main subject relativization seems not to license parasitic gaps man thati left without John meeting ei As well as involving the puzzling distribution of parasitic gaps these data are challeng ing because some judgements are not categorical a full story will need to say something about degrees of acceptability despite ungrammaticality or degrees of unacceptability despite grammaticality or both Our labels leave open the question as to whether the ambivalence arises from the former or the latter In our account it will sometimes be due to the one sometimes to the other potentially sometimes to both Section presents the basic framework Section considers islands section coordi nation section left extraction and section parasitic gaps In section we consider proof nets for the account developed and in section we consider semigrammaticality and acceptability Type Logical Grammar A j j sorted algebra hfD g f o go i comprises a indexed family fD g of domains a set of operators and an indexed set f o go i of operations where o n is an n place operation mapping fromD D n intoD An algebra hD f oigoi i N i is a sorted algebra where oi is an i place operation on the domain D we call a list of the arities of the operations the arity of the algebra Given sets X and Y the functional exponentiation X is the set of all functions from Y to X the Cartesian product X Y is the set of all ordered pairs of elements from X rst and Y second the disjoint sum X Y is f g X f g Y A frame is a family of domains which is closed under disjoint sum Cartesian product and functional exponentiation i e an algebra hfDg i Given some set d of atomic semantic type indices e g fe og for entities and propositions we de ne semantic type indices T by T d j T T j T !T j T T A semantic algebra is a sorted algebra hfD g T f g T i where D D D D D D D D D That is fD g T is a T indexed frame and m h mi and m h mi rst and second injection m m hm m i ordered pairing and m m m m functional application A semigroup is an algebra hL i of arity the operation of which is associative s s s s s s I cannot resist observing the cardinal homomorphism from the algebra of frames to the algebra of arithmetic jX Y j jXj jY j jX Y j jXj jY j jX j jX jjY j Because is associative we can omit its parentheses We call a semigroup hL i the underlying prosodic algebra of the prosodic algebra hP L n i where A B fs s j s A and s Bg AnB fsj for all s A s s Bg B A fsj for all s A s s Bg A B fsj s A and s Bg A B fsj s A or s Bg We call the powerset residuated lattice algebra of the underlying prosodic algebra Suppose partial knowledge of a prosodic algebra for example dreaming NnS John N knows NnS S letter CN likes NnS N man CN Mary N reading NnS N ran NnS slept NnS that CNnCN S N the N"CN without NnS n NnS " NnS S Then further facts regarding the prosodic algebra are entailed for example a John knows Mary knows John ran S b man that John knows Mary likes CN c John slept without dreaming S A residuated semigroup is a structure hD i of arity such that B A C i A B C i A C B equivalently A A B B A A B and B A A B B A A and is a partial order we say that is a residuated triple with respect to We see that hP L n i is a residuated semigroup and that n is a residuated triple We ignore here features see e g Morrill ch There is the following natural deduction calculus for the prosodic algebra