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...

We present an axiomatization of Conway theories which yields, as a corollary, a very concise axiomatization of iteration theories satisfying the functorial implication for base morphisms. It has been shown that most fixed point operations in computer science share the same equational properties. These equational properties are captured by the notion of iteration theories [1, 3]. Several axiomat...

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...

The paper discusses a language operation that we call context restriction. This operation is closely associated with context restriction rules (Koskenniemi, 1983; Kiraz, 2000), right-arrow rules or implication rules (Koskenniemi et al., 1992; Voutilainen, 1997) and the restriction operator (Beesley and Karttunen, 2003). The operation has been used in finite-state phonology and morphology in cer...

We prove that, on a set of size n, the number of clones that contain a group operation and all constant functions is finite if n is squarefree. This confirms a conjecture by Pawe l Idziak from [5] where the converse implication was shown. Our result follows from the observation that the polynomial clone of an expansion of a squarefree group is uniquely determined by its binary functions. We als...

The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of algebraic logic to the study of persistence based on a new operation on the ordered structure of the input diagram of vector spaces and linear maps given by a filtra...

After dropping the implication-like operation and reversing the order, an MTL-algebra becomes a partially ordered structure (L;≤,⊕, 0, 1) based on the single addition-like operation ⊕. Furthermore, ⊕ may be restricted to a partial, but cancellative addition + without loss of information. We deal in this paper with the case that the resulting partial algebra (L;≤,+, 0, 1) is embeddable into the ...

Three-way fuzzy inference is the theoretical basis of three-way control. The proposed TCRI method based on a Mamdani implication operator and uses one simple composition operation. In order to effectively improve method, this paper proposes full triple I algorithm for gives solution TFMP problem. emphasis our research R0 Go¨del solution, which related residual implication, as well Zadeh’s Mamda...