We study the properties of input-consuming derivations of moded logic programs. Inputconsuming derivations can be used to model the behavior of logic programs using dynamic scheduling and employing constructs such as delay declarations. We consider the class of nicely-moded programs and queries. We show that for these programs a weak version of the well-known switching lemma holds also for inpu...

In a system of sequents for intuitionistic predicate logic a theorem, which corresponds to Prawitz’s Normal Form Theorem for natural deduction, are proved. In sequent derivations a special kind of cuts, maximum cuts, are defined. Maximum cuts from sequent derivations are connected with maximum segments from natural deduction derivations, i.e., sequent derivations without maximum cuts correspond...

Structured derivations were introduced by Back and von Wright as an extension of the calculational proof style originally proposed by E.W. Dijkstra and his colleagues. Structured derivations added nested subderivations and inherited assumptions to the original calculational style. This paper introduces a further extension of the structured derivation format, and gives a precise syntax and seman...

1. Derivations in general 1 1.1. Definitions and conventions . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. Basic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3. The module of derivations . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4. The k-algebra RA (M) . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5. Compositions and tensor products . ....

We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of (α, β)-derivation to (α, β)higher derivation and demonstrate that a filter of a hereditary torsion theory that is invariant for α and β is (α, β)-higher derivation invariant. As a consequence, any higher derivation can be extended from a module to its module of quotients. Then...

In the theory of rings, the properties of derivations are important. In [15], Jun and Xin applied the notion of derivations in ring and near-ring theory to BCI-algebras, and they also introduced a new concept called a regular derivation in BCI-algebras. They investigated some properties of its .In this manuscript, the concept of fuzzy left (right) derivations BCCideals in BCC-algebras is introd...

Although derivations from Banach algebras to particular coefficient modules have been much studied, interest has usually focused on the existence or otherwise of non-trivial bounded derivations, rather than their characterisation. Even in the special case of derivations from a commutative Banach algebra to its dual (as in [2] or [5] for example), there are comparatively few examples where the s...