The paper presents algebraic and logical developments. From the algebraic viewpoint, we introduce Monadic Equational Systems as an abstract enriched notion of equational presentation. From the logical viewpoint, we provide Equational Metalogic as a general formal deductive system for the derivability of equational consequences. Relating the two, a canonical model theory for Monadic Equational S...

Our goal in this note is to show that cohomology classes with coefficients in finite flat group schemes can be killed by finite covers of the base scheme, and similarly for abelian schemes with “finite covers” replaced by “proper covers.” We apply this result to commutative algebra by giving a new and more conceptual proof of Hochster-Huneke’s theorem on the existence of big Cohen-Macaulay alge...

We describe a learning inference control heuristic for an equational theorem prover. The heuristic selects a number of problems similar to a new problem from a knowledge base and compiles information about good search decisions for these selected problems into a term space map, which is used to evaluate the search alternatives at an important choice point in the theorem prover. Experiments on t...

We show that uniication in certain extensions of shallow equational theories is decidable. Our extensions generalize the known classes of shallow or standard equational theories. In order to prove de-cidability of uniication in the extensions, a class of Horn clause sets called sorted shallow equational theories is introduced. This class is a natural extension of tree automata with equality con...

For nite convergent term-rewriting systems it is shown that the equational unii-cation problem is recursively independent of the equational matching problem, the word matching problem, and the 2 nd-order equational matching problem. Apart from the latter these results are derived by considering term-rewriting systems on signatures that contain unary function symbols only (that is, string-rewrit...

The concept of iteration theory of Bloom and Ésik summarizes all equational properties that iteration has in usual applications, e.g., in Domain Theory where to every system of recursive equations the least solution is assigned. However, this assignment in Domain Theory is also functorial. Yet, functoriality is not included in the definition of iteration theory. Pitty: functorial iteration theo...