Dis-unification
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Dis-unification, in computer science and logic, is an algorithmic process of solving inequations between symbolic expressions.
Publications on dis-unification
[edit]- 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.
See also
[edit]- 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