When R is a local ring with a nilpotent maximal ideal, the Ore extension R[x;σ, δ] will or will not be 2-primal depending on the δ-stability of the maximal ideal of R. In the case where R[x;σ, δ] is 2-primal, it will satisfy an even stronger condition; in the case where R[x;σ, δ] is not 2-primal, it will fail to satisfy an even weaker condition. 1. Background and motivation In [13, Proposition ...

Many DPLL-based [1] SAT solvers use an implementation of the two-literal watching scheme (TLWS) first used in Chaff [6] for boolean constraint propagation (BCP). For the extreme case of binary clauses this otherwise efficient algorithm has a large overhead in memory usage. In this report a technique called implication table for augmenting TLWS will be described and mathematically analyzed, that...

Firstly, two kinds of natural distances between intuitionistic fuzzy sets are generated by the classical natural distance between fuzzy sets under a unified framework of residual intuitionistic implication operators. Secondly, the continuity and approximation property of a method for solving intuitionistic fuzzy reasoning are defined. It is proved that the triple implication method for intuitio...