In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The approximation extends the signature and preserves unsatisfiability: if the simplified clause set is satisfiable in some model, so is the original clause set in the s...

We consider the problem of generalising boolean formulas in conjunctive normal form by allowing non-boolean variables, where our goal is to maintain combinatorial properties. Requiring that a literal involves only a single variable, the most general form of literals is given by the well-known “signed literals”, however we will argue that only the most restricted form of generalised clause-sets,...

We study the problem of (eeciently) deleting such clauses from conjunctive normal forms (clause-sets) which can not contribute to any proof of unsatissability. For that purpose we introduce the notion of an autarky system, associated with a canonical normal form for every clause-set by deleting superruous clauses. Clause-sets where no clauses can be deleted are called lean, a natural generaliza...

WOL is a Horn-clause language for specifying transformations involving complex types and recursive data-structures. Its declarative syntax makes programs easy to modify in response to schema evolution; the ability to specify partial clauses facilitates transformations when schemas are very large and data is drawn from multiple sources; and the inclusion of constraints enables a number of optimi...

The Agreement between the United States of America, Mexican States, and Canada (USMCA) includes a sunset clause that states agreement shall terminate 16 years after date its entry into force, unless each Party expresses will to continue for another years. We apply John H. Jackson’s theory on power oriented rule diplomacy analyze clause. argue offer strong incentives diplomacy, this likely affec...

There are at least four senses in which one can talk about clause or sentence types in a language. One way is in terms of the distinction between declarative, interrogative, and imperative sentences. This distinction, really one of sentence type, is discussed elsewhere in this anthology, in Chapter I.5 on Speech Act Distinctions in Syntax. A second sense of clause type is represented by the dis...

A formal basis for extending SQL in a natural way to complex ob ject databases is laid NSQL a language equivalent to the standard algebra for nested relational databases is obtained It is also shown that when allowing subqueries in the from clause the facility of sub queries in where clauses becomes redundant with regard to expressive power