Congruence proofs for bisimulation on higher{order process calculi tend to be signiicantly more complex than their counterparts in rst{order process algebra frameworks. Moreover, a standard technique that allows us to cover strong forms of bisimulation on higher{order calculi seems to fail for the corresponding weak forms. Similar problems are posed by applicative simulation on {calculi and our...

We define and compare a selection of congruence properties of quasivarieties, including the relative congruence meet semi-distributivity, RSD(∧), and the weak extension property, WEP. We prove that if K ⊆ L ⊆ L′ are quasivarieties of finite signature, and L′ is finitely generated while K |= WEP, then K is finitely axiomatizable relative to L. We prove for any quasivariety K that K |= RSD(∧) iff...

The association between hyperstructures and binary relations had been intensively studied 5,6,10,11,2,4,20 . Chvalina 5,6 and Hort 2 use ordered structures for the construction of semigroups and hypergroups. Rosenberg 4 associated with any binary relation of full domain, a hypergroupoid and found conditions on , such that is a hypergroup. Corsini and Leoreanu 16 study hypergroups and binary rel...

In this project, we have extended previous work on the formalization of the process algebra CCS in HOL4. We have added full supports on weak bisimulation equivalence and observation congruence (rooted weak equivalence), with related definitions, theorems and algebraic laws. Some deep lemmas were also formally proved in this project, including Deng Lemma, Hennessy Lemma and several versions of t...

In [3] and [6] the concepts of smooth closure, smooth interior, smooth α-closure and smooth α-interior of a fuzzy set were introduced and some of their properties were obtained. In this paper, we introduce the concepts of several types of weak smooth compactness and weak smooth α-compactness in terms of these concepts introduced in [3] and [6] and investigate some of their properties.

Abstract This is the second of a series papers that investigate fragments quasi-Nelson logic (QNL) from an algebraic standpoint. QNL, recently introduced as common generalization intuitionistic and Nelson’s constructive with strong negation, axiomatic extension substructural $FL_{ew}$ (full Lambek calculus exchange weakening) by Nelson axiom. The counterpart QNL (quasi-Nelson algebras) class co...

Random intervals constitute one of the classes of random sets with a greater number of applications. In this paper, we regard them as the imprecise observation of a random variable, and study how to model the information about the probability distribution of this random variable. Two possible models are the probability distributions of the measurable selections and those bounded by the upper pr...

In this paper we propose a notion of weak bisimulation for a class of weighted automata with unobservable transitions where weights are taken from an idempotent semiring. In particular the (max/+), (min/+) or (max/min) dioid are considered. The proposed bisimulation is a natural extension of Milner’s well known weak bisimulation for untimed automata (i. e., weighted automata over the boolean se...

Imprecise choices can be described using either a probabilistic or a fuzzy formalism. No relation between them has been studied so far. In this contribution we present a connection between the two formalisms that strongly makes use of fuzzy implication operators and t-norms. In this framework, Luce’s Choice Axiom turns out to be a special case when the product t-norm is considered and other sim...

In the integers and in certain densely ordered rings that are not fields, projections of the solution set of finitely many homogeneous weak linear inequalities may be defined by finitely many congruence inequalities, where a congruence inequality combines a weak inequality with a system of congruences. These results extend well-known facts about systems of weak linear inequalities over ordered ...