Perhaps the best way to understand how to write a link grammar for English is to study an example. The following dictionary does not cover the complete grammar of the words it contains, but it does handle a number of phenomena: verb-noun agreement, adjectives, questions, infinitives, prepositional phrases, and relative clauses.
the: D+; a: Ds+; John Mary: J- or O- or (({C- or CL-} & S+) or SI-); dog cat park bone stick: {@A-} & Ds- & {@M+ or (C+ & Bs+)} & (J- or O- or ({C- or CL-} & Ss+) or SIs-); dogs cats parks bones sticks: {@A-} & {Dm-} & {@M+ or (C+ & Bp+)} & (J- or O- or ({C- or CL-} & Sp+) or SIp-); has: (SIs+ or Ss- or (Z- & B-)) & (((B- or O+) & {@EV+}) or T+); did: (SI+ & I+) or ((S- or (Z- & B-)) & (((B- or O+) & {@EV+}) or I+)); can may will must: (SI+ or S- or (Z- & B-)) & I+; is was: (Ss- or (Z- & Bs-) or SIs+) & (AI+ or O+ or B- or V+ or Mp+); touch chase meet: (Sp- or (Z- & Bp-) or I-) & (O+ or B-) & {@EV+}; touches chases meets: (Ss- or (Z- & Bs-)) & (O+ or B-) & {@EV+}; touched chased met: (V- or M- or ((S- or (Z- & B- ) or T-) & (O+ or B-))) & {@EV+}; touching chasing meeting: (GI- or M-) & (O+ or B-) & {@EV+}; die arrive: (Sp- or (Z- & Bp-) or I-) & {@EV+}; dies arrives: (Ss- or (Z- & Bs-)) & {@EV+}; died arrived: (S- or (Z- & B-) or T-) & {@EV+}; dying arriving: (GI- or M-) & {@EV+}; with in by: J+ & (Mp- or EV-); big black ugly: A+ or (AI- & {@EV+}); who: (C- & {Z+ or CL+}) or B+ or Ss+;