The Collaborative International Dictionary of English v.0.48:

Dialectics \Di`a*lec"tics\, n. [L. dialectica (sc. ars), Gr. ?
   (sc. ?): cf. F. dialectique.]
   That branch of logic which teaches the rules and modes of
   reasoning; the application of logical principles to
   discursive reasoning; the science or art of discriminating
   truth from error; logical discussion.
   [1913 Webster]

   Note: Dialectics was defined by Aristotle to be the method of
         arguing with probability on any given problem, and of
         defending a tenet without inconsistency. By Plato, it
         was used in the following senses:

   1. Discussion by dialogue as a method of scientific
      investigation.

   2. The method of investigating the truth by analysis.

   3. The science of ideas or of the nature and laws of being --
      higher metaphysics. By Kant, it was employed to signify
      the logic of appearances or illusions, whether these arise
      from accident or error, or from those necessary
      limitations which, according to this philosopher,
      originate in the constitution of the human intellect.
      [1913 Webster]

WordNet (r) 3.0 (2006):

dialectics
    n 1: a rationale for dialectical materialism based on change
         through the conflict of opposing forces

Moby Thesaurus II by Grady Ward, 1.0:

20 Moby Thesaurus words for "dialectics":
   Aristotelian logic, Boolean algebra, Ramistic logic,
   algebra of classes, algebra of relations, dialectic,
   doctrine of inference, doctrine of terms, epistemological logic,
   experimental logic, formal logic, logic, logics, logistic,
   material logic, mathematical logic, propositional calculus,
   psychological logic, psychologism, set theory