Dis-unification

Dis-unification, in computer science and logic, is an algorithmic process of solving inequations between symbolic expressions.

• Alain Colmerauer (1984). "Equations and Inequations on Finite and Infinite Trees". In ICOT (ed.). Proc. Int. Conf. on Fifth Generation Computer Systems. pp.85–99.
• Hubert Comon (1986). "Sufficient Completeness, Term Rewriting Systems and 'Anti-Unification'". Proc. 8th International Conference on Automated Deduction. LNCS. Vol.230. Springer. pp.128–140.
  "Anti-Unification" here refers to inequation-solving, a naming which nowadays has become quite unusual, cf. Anti-unification (computer science).
• Claude Kirchner; Pierre Lescanne (1987). "Solving Disequations". Proc. LICS . pp.347–352.
• Claude Kirchner and Pierre Lescanne (1987). Solving disequations (Research Report). INRIA.
• Hubert Comon (1988). Unification et disunification: Théorie et applications (PDF) (Ph.D.). I.N.P. de Grenoble.
• Hubert Comon; Pierre Lescanne (Mar–Apr 1989). "Equational Problems and Disunification". J. Symb. Comput. 7 (3–4): 371–425. CiteSeerX 10.1.1.139.4769 . doi:10.1016/S0747-7171(89)80017-3 .
• Comon, Hubert (1990). "Equational Formulas in Order-Sorted Algebras". Proc. ICALP.
  Comon shows that the first-order logic theory of equality and sort membership is decidable, that is, each first-order logic formula built from arbitrary function symbols, "=" and "∈", but no other predicates, can effectively be proven or disproven. Using the logical negation (¬), non-equality (≠) can be expressed in formulas, but order relations (<) cannot. As an application, he proves sufficient completeness of term rewriting systems.
• Hubert Comon (1991). "Disunification: A Survey". In Jean-Louis Lassez; Gordon Plotkin (eds.). Computational Logic — Essays in Honor of Alan Robinson . MIT Press. pp.322–359.
• Hubert Comon (1993). "Complete Axiomatizations of some Quotient Term Algebras" (PDF). Proc. 18th Int. Coll. on Automata, Languages, and Programming. LNCS. Vol.510. Springer. pp.148–164. Retrieved 29 June 2013.

• Unification (computer science): solving equations between symbolic expressions
• Constraint logic programming: incorporating solving algorithms for particular classes of inequalities (and other relations) into Prolog
• Constraint programming: solving algorithms for particular classes of inequalities
• Simplex algorithm: solving algorithm for linear inequations
• Inequation: kinds of inequations in mathematics in general, including a brief section on solving
• Equation solving: how to solve equations in mathematics