On decidability of equational theories

On Equational Theories, Unification and Decidability

The following classes of equational theories, which are important in unification theory, are presented: permutative, finite, Noetherian, simple, almost collapse free, collapse free, regular, and ~-free theories. The relationships between the particular theories are shown and the connection between these classes and the unification hierarchy is pointed out. We give an equational theory that alwa...

On Equational Theories, Unification, and (Un)Decidability

We investigate the following classes of equational theories which are important in unification theory: permutative, finite, Noetherian, simple, almost collapse free, collapse free, regular, and O-free theories. We show some relationships between the particular classes and their connections to the unification hierarchy. Especially, we study conditions, under which minimal and complete sets of un...

On Decidability of T-norm-Based Equational Theories

The aim of this work is to show that the universal theory R of real closed fields [1] is interpretable in the equational theory of LPi1/2-algebras [2,3,6,7,8], and viceversa. Since R enjoys quantifier elimination, we will obtain that the full theory of R is interpretable in LPi1/2. This will also yield that any function definable in R is definable in LPi1/2. As a consequence of this constructio...

Decidability and Complexity of Finitely Closable Linear Equational Theories

We deene a subclass of the class of linear equational theories, called nitely closable linear theories. We consider uniication problems with no repeated variables. We show the decidability of this subclass, and give an algorithm in PSPACE. If all function symbols are monadic, then the running time is in NP, and quadratic for unitary monadic nitely closable linear theories.

A Note On Equational Theories