Categorical universal algebra can be developed either using Lawvere theories (single-sorted finite product theories) or using monads, and the category of Lawvere theories is equivalent to the category of finitary monads on Set. We show how this equivalence, and the basic results of universal algebra, can be generalized in three ways: replacing Set by another category, working in an enriched set...

We deene and discuss various conceivable notions of induc-tive validity for rst-order equational clauses. This is done within the framework of constructor-based positive/negative conditional equational speciications which permits to treat negation and incomplete function deenitions in an adequate and natural fashion. Moreover, we show that under some reasonable assumptions all these notions are...

The key-generation algorithm for the RSA cryptosystem is specified in several standards, such as PKCS#1, IEEE 1363-2000, FIPS 186-3, ANSI X9.44, or ISO/IEC 18033-2. All of them substantially differ in their requirements. This indicates that for computing a “secure” RSA modulus it does not matter how exactly one generates RSA integers. In this work we show that this is indeed the case to a large...

We consider several ordinal formulations of submodularity, defined for arbitrary binary relations on lattices. Two of these formulations are essentially due to David Kreps (A Representation Theorem for “Preference for Flexibility”, Econometrica, 1979) and one is a weakening of a notion due to Paul Milgrom and Chris Shannon (Monotone Comparative Statics, Econometrica, 1994). We show that any ref...

Five algebraic notions of termination are formalised, analysed and compared: well-foundedness or Noetherity, Löb’s formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings, which are additively idempotent semirings with forward and backward modal operators. To reason about infinite behaviour, semirings are extended to divergence semi...

The notion of a completely saturated packing [1] is a sharper version of maximum density, and the analogous notion of a completely reduced covering is a sharper version of minimum density. We define two related notions: uniformly recurrent dense packings and diffusively dominant packings. Every compact domain in Euclidean space has a uniformly recurrent dense packing. If the domain self-nests, ...

We state precise definitions of the basic notions of Sowa’s framework [Sowa 84] and provide related results. These results mainly concern the structure of the specialization relation, correspondence between graph operations and logical operations, and algorithmic complexity of the model handling. RESUME. Nous définissons précisément les notions de base du modèle des graphes conceptuels de Sowa ...

We argue that diagnosis should not be seen as solving a problem with a unique definition, but rather that there exists a whole space of reasonable notions of diagnosis. These notions can be seen as mutual approximations. We present a number of reasons for choosing among different notions of diagnosis. We also present an exhaustive categorisation of techniques that can be employed to obtain appr...

The review presents modern data on the genetics and etiopathogenetic features of Clostridium perfringens toxins, including role enterotoxin, in development food poisoning a number intestinal diseases humans, animals birds.

In this paper rst we dene the notions of positive implicativehyper MV -ideals of types 1,2,3 and 4 in hyper MV -algebras and we investigatethe relationship between of them . Then by some examples we show that thesenotions are not equivalent. Finally we give some relations between these notionsand the notions of (weak) hyper MV -ideals and (weak) hyper MV -deductivesystems of hyper MV -algebras.