The standard notions of tautology and subsumption can be naturally generalized, (so that refutation completeness is preserved with respect to the associated deletion), within the context of (a speciied set of) modiied deduction rules for binary clausal resolution-refutation which build-in the reeexiv-ity, symmetry, transitivity and predicate substitutivity axioms for equality. The generalized n...

One of key issues for α-n(t) ary resolution automated reasoning based on lattice-valued logic with truthvalue in a lattice implication algebra is to investigate the α-n(t) ary resolution of some generalized literals. In this article, the determination of α-resolution of any 3-ary generalized literals which include the implication operators not more than 2 in LP(X). It not only lay the foundatio...

given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

for an $n$-gon with vertices at points $1,2,cdots,n$, the betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. in this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and betti numbers of the $s$-module $s/i$ where  $s=k[x_{1},cdots, x_{n}]$ and $i$ is the associated ideal to ...

A resolution of the intersection of a finite number of subgroups of an abelian group by means of their sums is constructed, provided the lattice generated by these subgroups is distributive. This is used for detecting singularities of modules over Dedekind rings. A generalized Chinese remainder theorem is derived as a consequence of the above resolution. The GelfandNaimark duality between finit...