The Collaborative International Dictionary of English v.0.48:

Ratiocinate \Ra`ti*oc"i*nate\ (r[a^]sh`[i^]*[o^]s"[i^]*n[=a]t),
   v. i. [L. ratiocinatus, p. p. of ratiocinari, fr. ratio
   reason. See Ratio.]
   To reason, esp. deductively; to offer reason or argument.
   [1913 Webster]

WordNet (r) 3.0 (2006):

ratiocinate
    v 1: reason methodologically and logically