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Abstract: We show that T (F )= =E can be completely axiomatized when =E is a quasi-free theory. Quasi-free theories are a wider class of theories than permutative theories of [Mal71] for which Mal'cev gave decision results. As an example of application, we show that the first order theory of T (F )= =E is decidable when E is a set of ground equations. Besides, we prove that the \Sigma 1 -fragment of the theory of T (F )= =E is decidable when E is a compact set of axioms. In particular, the existential... (Update)
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...each restriction is needed to decide unifiability. In future, it would be nice to use TTSGs to deal with equational disunification [25, 26], i.e. finding substitutions that are not the solution of a given equation. This may be achieved if it is possible to compute the set...
.... er pre x is of the form 9 8 9 ) On the decidability side, it is known that the 1 part (existential formulas) is decidable [C93]. Also several papers (including [LM93] and [F93] were written about the decidability of some special cases of so called AC complement...
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BibTeX entry: (Update)
H. Comon. Complete axiomatizations of some quotient term algebras. Theoretical Computer Science, 118(2), 1993. http://citeseer.ist.psu.edu/comon93complete.html More
@article{ comon93complete,
author = "Hubert Comon",
title = "Complete axiomatizations of some quotient term algebras",
journal = "Theoretical Computer Science",
volume = "118",
number = "2",
pages = "167--191",
year = "1993",
url = "citeseer.ist.psu.edu/comon93complete.html" }
Citations (may not include all citations):788 Rewrite systems - Dershowitz, Jouannaud - 1990 ACM DBLP
181 Mathematical Logic (context) - Shoenfield - 1967
151 Proving termination with multiset orderings (context) - Dershowitz, Manna - 1979 ACM DBLP
118 Complete axiomatizations of the algebras of finite (context) - Maher - 1988
111 Fast decision procedures based on congruence closure (context) - Nelson, Oppen - 1980 ACM DBLP
70 Equational problems and disunification (context) - Comon, Lescanne - 1989 ACM DBLP
48 Disunification: a survey - Comon - 1991 DBLP
42 The theory of ground rewrite systems is decidable (context) - Dauchet, Tison - 1990 DBLP
31 Decidability of the purely existential fragment of the theor.. (context) - Venkataraman - 1987 ACM DBLP
30 A new method for undecidability proofs of first order theori.. - Treinen - 1990 ACM DBLP
27 Solving equations in abstract algebras: A rule-based survey .. (context) - Jouannaud, Kirchner - 1991 DBLP
20 Syntactic theories and unification (context) - Kirchner, Klay - 1990 DBLP
20 Solving inequations in term algebras (context) - Comon - 1990
20 Equational formulas in order-sorted algebras (context) - Comon - 1990 ACM DBLP
17 Complete axiomatizations of some quotient term algebras - Comon - 1991 ACM DBLP
15 M'ethodes et outils de conception syst'ematique d'algorithme.. (context) - Kirchner - 1985
13 Higher-order unification (context) - Nipkow - 1990
6 Solving disequations in equational theories (context) - Burckert - 1988
6 Decidability of the existential theory of infinite terms wit.. (context) - Tulipani - 1991 ACM DBLP
3 Syntactic theories (context) - Jouannaud - 1990 ACM DBLP
2 Unification revisited (context) - Lassez, Maher et al. - 1986 ACM DBLP
The graph only includes citing articles where the year of publication is known.
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A Methodological View of Constraint Solving - Comon, al. (1997) (Correct)
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