A. Reduction-closed barbed congruence (Section II) Definition 28 (Reduction-closed barbed congruence). Let L be a process calculus, in which a reduction relation −→L and barb predicates ↓a , for each a in a given set of names, have been defined. A relationR on the processes of L is context-closed if PRQ implies C[P ]RC[Q], for each context C of L; the relation is barb-preserving if for any name...

We propose a term rewriting approach to verify observational congruence between guarded recursive (finite-state) CCS expressions. Starting from the complete axiomatization of observational congruence for this subset of CCS, a non-terminating rewriting relation has been defined. This rewriting relation is co-canonical over a subclass of infinite derivations, structured fair derivations, which co...

In this paper we study relations which are congruences with respect to ∧ and ⊔p, where ⊔pis the p-cut of the L-fuzzy hyperoperation ⊔. The main idea is to start from an equivalence relation R1 which is a congruence with respect to ∧ and ⊔1and, for each p ∈ X , construct an equivalence relation Rp which is a congruence with respect to ∧ and ⊔p. Furthermore, for each x ∈ Rp we construct a quotien...

In this paper, we defined the congruence relation and proved its fundamental properties on the base of some useful theorems. Then we proved the existence of solution and the number of incongruent solution to a linear congruence and the linear congruent equation class, in particular, we proved the Chinese Remainder Theorem. Finally, we defined the complete residue system and proved its fundament...

We present a congruence relation on sequent-style classical proofs which identifies proofs up to trivial rule permutation. The study is performed in the framework of ∗X calculus which provides a CurryHoward correspondence for classical logic (with explicit structural rules) ensuring that proofs can be seen as terms and proof transformation as computation. Congruence equations provide an explici...

For an anti-congruence q we say that it is regular anti-congruence on semigroup (S,=, =, ·, α) ordered under anti-order α if there exists an antiorder θ on S/q such that the natural epimorphism is a reverse isotone homomorphism of semigroups. Anti-congruence q is regular if there exists a quasi-antiorder σ on S under α such that q = σ ∪ σ−1. Besides, for regular anti-congruence q on S, a constr...