A constructively valid counterpart to Bourbaki’s Fixpoint Lemma for chaincomplete partially ordered sets is presented to obtain a condition for one closure system in a complete lattice L to be stable under another closure operator of L. This is then used to deal with coproducts and other aspects of frames.

In this work a general closure for the conductive electron heat flux parallel to an inhomogeneous magnetic field is derived and examined. Free-streaming and collisional effects are present in the drift kinetic equation which is solved using an expansion of eigenfunctions of the bounce-averaged, pitch-angle scattering operator. For bounce times short compared to transit and collision times, the ...

In this article the notions of quasi mono (epi) as a generalization (epi), (quasi weakly hereditary) general closure operator $mathbf{C}$ on category $mathcal{X}$ with respect to class $mathcal{M}$ morphisms, and factorization structures in are introduced. It is shown that under certain conditions, if $(mathcal{E}, mathcal{M})$ structure $mathcal{X}$, then has right $mathcal{M}$-factorization l...

In an 〈E,M 〉-category X for sinks, we identify necessary conditions for Galois connections from the power collection of the class of (composable pairs) of morphisms in M to factor through the “lattice” of all closure operators on M , and to factor through certain sublattices. This leads to the notion of regular closure operator. As one byproduct of these results we not only arrive (in a novel w...

The es-splitting operation on binary matroids is a natural generalization of Slater's <em>n</em>-line splitting graphs. In this paper, we characterize the closure operator matroid M<sup>e</sup><sub>X</sub> in terms original M. We also describe ats and hyperplanes bi- nary hyperplanes, respectively

D We present a fixpoint semantics for disjunctive logic programs. We extend the concept of the Herbrand base of a logic program to consist of all positive clauses that may be formed using the atoms in the Herbrand base. A monotonic closure operator is defined, operating on the lattice formed by the power set of the extended Herbrand base. The closure operator is shown to achieve a least fixpoin...

Caminada and Amgoud have argued that logic-based argumentation systems should satisfy the intuitive and natural principles of logical closure and consistency. Prakken has developed this idea further for a richer logic. A question arises naturally whether a general structure guaranteeing the logical closure and consistency properties could be identified that is common for all underlying logics. ...