We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gröbner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite fields. We analyze the theoretical complexity of the algorithm and show its application in the formal analysis of a biological controller model.

Using theorem prover Coq [4] for the verification of concurrent systems usually includes the formalization of the modal μ–calculus [8] in that logical framework [13] [11] [15]. These implementations build upon the following interpretation: given the state space S of a system, the meaning of a formula is the subset of states where it is satisfied. Then, a formula α(X) with a free variable X can ...

A type system for the lambda-calculus enriched with recursive and corecursive functions over equi-inductive and -coinductive types is presented in which all well-typed programs are strongly normalizing. The choice of equi-inductive types, instead of the more common isoinductive types, in uences both reduction rules and the strong normalization proof. By embedding isointo equi-types, the latter ...

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...

The foldness of PI( , , ⊆)BCK -ideals and PI(⊆, ⊆, ⊆)BCK -ideals is considered, and their properties are investigated. Hyper homomorphic inverse image of PI( , , ⊆)BCK -ideals, PI( , ⊆, ⊆)BCK -ideals, PI(⊆, ⊆, ⊆)BCK -ideals, and PI( , , )BCK -ideals are discussed.

Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

in this note we consider the notion of intuitionistic fuzzy (weak) dual hyper k-ideals and obtain related results. then we classify this notion according to level sets. after that we determine the relationships between intuitionistic fuzzy (weak) dual hyper k-ideals and intuitionistic fuzzy (weak) hyper k-ideals. finally, we define the notion of the product of two intuitionistic fuzzy (weak) du...

One basic activity in combinatorics is to establish combinatorial identities by so-called ‘bijective proofs,’ which consists in constructing explicit bijections between two types of the combinatorial objects under consideration. We show how such bijective proofs can be established in a systematic way from the ‘lattice properties’ of partition ideals, and how the desired bijections are computed ...

In this paper we introduce the definitions of generalized ideals and generalized filters in pseudo effect algebras. From the generalized ideals (filters), we obtain some equivalent characterization of ideals (filters). The relationships among generalized ideals, ideals and local ideals are studied in detail. We also establish an isomorphism between the set of supports and the set of generalized...