Parsing with category cooccurance restrictions

(1) Any LT wi th S as i t s roo t m u s t have A as a daughte r . (2) No LT wi th C as a d a u g h t e r a l so has D as a daughter . S t a t e m e n t s such as (1) and (2) are CCRs. CCRs are exp re s s ions of f i r s t o rde r predica te logic us ing t wo pr imi t ive pred ica tes , R(a, t) 'el is the roo t o f LT t' and D(eL, t) 'el is a d a u g h t e r in LT t'. [1] CCRs have one of the th ree forms V t: Ix D ~ V t: to Vt: o ::) ix where li is a d i s junc t ion of posi t ive l i t e ra l s R(c~, t) and to is a schema, whereby the no t ion of a poss ib le schema is def ined as fo l lows : (a) D(a, t) is o f fo rm ~ ; (b) if ~b is o f fo rm to, then (~~) is of form 6~; (c) if ~ and :~ are bo th of fo rm t~, t hen (~bx)~) is o f fo rm to, where × E {V, A, D, =}; (d) t he se are a l l exp re s s ions of form to. Fur thermore , a l l p red ica tes wi th in a CCR have the var iable t as s econd a rgument ; a l l f i r s t a r g u m e n t s are c o n s t a n t s de s i gna t i ng ca tegor ies . Pa ren theses may be o m i t t e d fo l l owing the usua l convent ions in predica te logic. CCRs will be no rma l ly be w r i t t e n in the th ree forms g ' I [ to ' ] l I[to'] l I[to'] l ix' where each occurrence of D(~, t) in to is rep laced s imply by c~ in to', and each occurrence of R(a , t) in p by a in ix'. Using th is no ta t ion , (1) and (2) may be r e s t a t e d as (3) and (4.), respec t ive ly :