on convergence classes inl fuzzy topological spaces abstract convergence theory is a primary topic in topology in fact topology and so called convergence class are characterized by each other in fuzzy topology l fuzzy topology more than 40 papers published in the last ten years were concerned with convergence theory among these papers the problem of convergence class was solved for the case of l 0 1 7 since the neighbor structure so called quasi coincident neighborhood system of an l fuzzy point in an l fuzzy topological space is in general not directed under the inclusion order the conditions of convergence class in 0 1 fuzzy topology will not be valid any longer in the case of lattice moreover quite different from the cases of 0 1 fuzzy topology i e ordinary topology and 0 1 fuzzy topology the so called bolzano weierstrass property does not hold i e a net with a cluster point in an l fuzzy topological space is not still necessary to have a subnet converging to the point in this paper a necessary and sufficient condition for the bolzano weierstrass property is produced the result is also used in a satisfactory theory of convergence classes in l fuzzy topological spaces and the associated characterization theorem between l fuzzy topologies and convergence classes is established

even continuity and equicontinuity in fuzzy topology we study the notion of even continuity in the category fcs of fuzzy convergence spaces and in fns the category of fuzzy neighborhood spaces we further compare this notion to equicontinuity in fus the category of fuzzy uniform spaces

lattice valued fuzzy interior operators a category of lattice valued fuzzy interior operator spaces is defined and studied axioms are given in order for this category to be isomorphic to the category whose objects consist of all the stratified lattice valued pretopological convergence spaces

categories isomorphic to fns the main result in this paper is that the category of fuzzy neighborhood spaces is isomorphic to that of fuzzifying topological spaces

the categorical topology approach to fuzzy topology and fuzzy convergence it is the purpose of this paper to have a look at fuzzy topology from the point of view of categorical topology we first look at interesting subcategories of fts and determine whether they are bireflective and or coreflective we also describe the set of all subcategories of fts which are at the same time bireflective and coreflective due to the fact that top is one of these subcategories of fts ffs itself can be neither cartesian closed nor extensional we therefore secondly construct a supercategory of bts which is a topological quasitopos the construction of this quasitopos is based on the theory of convergence in fts

fuzzy convergence open and proper maps the notions of open and proper maps are introduced in the category fcs of fuzzy convergence spaces and each is shown to be an extension of the same notion with respect to the embedding functor from the category pcs of probabilistic convergence spaces proper maps in fcs are shown to be productive and moreover preserve closures of fuzzy sets regularity and local precompactness all projection maps in fcs are open and open maps are finitely productive

local compactness in fuzzy convergence spaces abstract two notions of local precompactness in the realm of fuzzy convergence spaces are investigated it is shown that the property of local precompactness possesses a good extension moreover for each given fuzzy convergence space there exists a coarsest locally precompact space which is finer than the original space continuity between fuzzy spaces is preserved between the associated locally precompact spaces invariance of regularity with respect to taking locally precompact modifications is discussed

regularity in fuzzy convergence spaces the notions of regularity and weak regularity are introduced in the category of fuzzy convergence spaces and each is shown to be an extension of regularity with respect to the embedding functor from the category of convergence spaces moreover the category whose objects are weakly regular fuzzy spaces is topological and thus initial and final regular structures exist the relationship between regularity and a diagonal condition is given

stable subconstructs of fts iii exotic cases abstract in this paper we study stable subconstructs of fts which neither contain nor are contained in top hence in contrast to similar subconstructs studied previously they do not constitute a viable alternative theory of fuzzy topology for that reason we call them exotic

completeness of type assignment systems with intersection union and type quantifiers this paper develops type assignment systems with intersection and union types and type quantifiers we show that the known system for these types is not semantically complete however the following two hold for a certain class of typing statements called stable statements which include all statements without type quantifier 1 the validity of stable statements for kripke models is equivalent to that for standard models 2 if we add two axioms expressing the distributive laws of intersection over union and existential type quantifier then the resulting system is complete for kripke models as a consequence the known system with the axioms for distributive laws is complete for standard models if we restrict statements to stable ones all the results are obtained in a systematic way with sequent style formulations of type assignment and the cut elimination property for them

local error estimates for discontinuous solutions of nonlinear hyperbolic equations let u x t be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smooth initial data suppose u varepsilon x t is the solution of an approximate viscosity regularization where varepsilon 0 is the small viscosity amplitude it is shown that by post processing the small viscosity approximation u varepsilon pointwise values of u and its derivatives with an error as close to e as desired can be recovered the analysis relies on the adjoint problem of the forward error equation which in this case amounts to a backward linear transport equation with discontinuous coefficients the novelty of our approach is to use a generalized e condition of the forward problem in order to deduce a w 1 infty energy estimate for the discontinuous backward transport equation this in turn leads to e uniform estimate on moments of the error u varepsilon u the approach presented does not follow the characteristics and therefore applies mutatis mutandis to o

the role of the diagonal operator in fuzzy topology abstract in this paper we reveal the exact role of the fuzzy versions of the diagonal condition of kowalsky 2 and of the weak diagonal condition of e lowen colebunders 3 in the setting of convergence in fuzzy topology

filter models for conjunctive disjunctive l calculi abstract the distinction between the conjunctive nature of non determinism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work calculus is extended with both a non deterministic choice and a parallel operator a notion of reduction is introduced extending reduction of the classical calculus we study type assignment systems for this calculus together with a denotational semantics which is initially defined constructing a set semimodel via simple types we enrich the type system with intersection and union types dually reflecting the disjunctive and conjunctive behaviour of the operators and we build a filter model the theory of this model is compared both with a morris style operational semantics and with a semantics based on a notion of capabilities

the sharp form of oleĭnik s entropy condition in several space variables we investigate the conditions under which the volpert kruzkov solution of a single conservation law in several space variables with flux f will satisfy the simplified entropy condition div f u s l t and when this condition guarantees uniqueness for given lx cauchy data we show that when f is c1 our condition guarantees uniqueness iff f is isotropic and that for such f the volpert kruzkov solution always satisfies our condition

relative compact fuzzy subsets in fuzzy convergence spaces abstract besides compactness the weaker notion of relative compactness plays an important role in topology this paper generalizes a definition of relative compactness given by chadwick 1 for fuzzy topological spaces to fuzzy convergence spaces as studied by the author 4 6 8 we prove that it is a good extension develop the necessary theory and finally give two applications to the theory of the fuzzy richardson compactification and to the theory of fuzzy function spaces

on level topologies and maximality of fuzzy topological spaces abstract wuyts 1984 discussed the problem of the reconstruction of a fuzzy topological space from a given family of level topologies and necessary and sufficient conditions were given for the existence of a solution the main purpose of this note is to give new formulations for these conditions and some related ones

nondeterministic extensions of untyped λ calculus the main concern of this paper is the interplay between functionality and nondeterminism we ask whether the analysis of parallelism in terms of sequentiality and nondeterminism which is usual in the algebraic treatment of concurrency remains correct in the presence of functional application and abstraction we argue in favour of a distinction between nondeterminism and parallelism due to the conjunctive nature of the former in contrast to the disjunctive character of the latter this is the basis of our analysis of the operational and denotational semantics of the nondeterministic calculus which is the classical calculus plus a choice operator and of our election of bounded indeterminacy as the semantic counterpart of conjunctive nondeterminism this leads to operational semantics based on the idea of must preorder coming from the classical theory of solvability and from the theory of process algebras to characterize this relation we build a model using the inverse limit construction over nondeterministic algebras and we prove it fully abstract using a generalization of bohm trees we further prove conservativity theorems for the equational theory of the model and for other theories related to nondeterministic calculus with respect to classical theories

what is a model of the lambda calculus an elementary purely algebraic definition of model for the untyped lambda calculus is given this definition is shown to be equivalent to the natural semantic definition based on environments these definitions of model are consistent with and yield a completeness theorem for the standard axioms for lambda convertibility a simple construction of models for lambda calculus is reviewed the algebraic formulation clarifies the relation between combinators and lambda terms

linear fuzzy neighborhood spaces some of the properties of linear fuzzy neighborhood spaces are studied a special class of these spaces is the family of all fuzzy linear spaces whose topology is given by probabilistic seminorms as in the classical case it is shown that a linear fuzzy neighborhood space is probabilistic normable iff it is hausdorff and it has an n bounded convex fuzzy neighborhood of zero

l fuzzifying topologies as l topologies it is proved in this paper that for every completely distributive lattice l with a locally multiplicative way below relation the category of l fuzzifying topological spaces can be embedded in the category of l topological spaces stratified chang goguen topological spaces as a simultaneously bireflective and bicoreflective full subcategory several equivalent descriptions of this subcategory are given

coppo dezani types do not correspond to propositional logic abstract this note gives a simple counterexample to back up pottinger s explanation of the difference between propositional logic and the type theories of pottinger 1980 and coppo dezani 1978 the example depends on a theorem of ben yelles 1979

a short note on fuzzy neighbourhood convergence spaces we show that every topological fuzzy neighborhood convergence space is a fuzzy neighborhood space consequently the meet of the categories fncs and fts is the category fns

fuzzy t locality spaces abstract a lowen fuzzy topological space is said to be localizable at points if it is completely determined in some prescribed manner by a system of fuzzy neighbourhoods called here fuzzy localities of its ordinary points we introduce for each lower semicontinuous triangular norm t a new type of those spaces which we call fuzzy t locality spaces the particularity of a fuzzy t locality space is that its fuzzy interior operator is obtained from its t locality system through a definition of fuzzy containment of fuzzy sets that employs the t residuated implication operator the origins of this new theory lie in the theory of probabilistic metric spaces indeed fuzzy t locality spaces provide a fuzzy topological framework for a naturally defined notion of metric t continuity of functions between probabilistic t metric spaces in a manner described in the last two sections of this article before that we establish characterizations and aspects of good behaviour for fuzzy t locality spaces including that every t locality system has an open basis we briefly study their level topologies and we show that all topologically generated spaces are fuzzy t locality spaces we prove that the category t fls of fuzzy t locality spaces and continuous functions between them is a topological category we show that it is closed in fts under the formation of optimal lifts of sources we provide a condition on t under which t fls becomes closed in fts also under the formation of co optimal lifts of sinks

a localic l fuzzy modification of topological spaces abstract an l fuzzy modification of the category of the topological spaces is obtained in this paper by establishing a theory of l fuzzy locales which is meant to bridge the study of l fuzzy topologies and that of locales

degrees of compactness in fuzzy convergence spaces we develop a theory of compactness in the category of fuzzy convergence spaces in the spirit of lowen i e we define for each fuzzy subset of a fuzzy convergence space a degree of being compact these degrees of compactness generalize at the same time the theory of compactness in the category of fuzzy convergence spaces and some known measures of compactness in fuzzy topological spaces together with degrees of closedness and of even continuity they prove useful in the development of a theory of compactness for fuzzy function spaces

discrimination by parallel observers the algorithm abstract the main result of the paper is a constructive proof of the following equivalence two pure terms are observationally equivalent in the lazy concurrent calculus iff they have the same levy longo trees an algorithm which allows to build a context discriminating any two pure terms with different levy longo trees is described it follows that contextual equivalence coincides with behavioural equivalence bisimulation as considered by sangiorgi another consequence is that the discriminating power of concurrent lambda contexts is the same as that of boudol laneve s contexts with multiplicities

net convergence in fuzzy neighborhood spaces our aim is to introduce a concept of net convergence in the well behaved subcategory of lowen fuzzy neighborhood spaces of the category of fuzzy topological spaces in doing so we notice that our present notion of net convergence in addition to katsaras and papageorgeou net convergence is generalized sequential convergence we also apply this notion of net convergence in fuzzy neighborhood groups and fuzzy neighborhood linear spaces

strictly minimal fuzzy neighborhood division rings abstract the aim of this article is on the one hand to determine suitable classes of fuzzy neighborhood division rings that can be used as scalar domains for linear fuzzy neighborhood spaces so as to accommodate 1 a a nonvanishing linear transformation t is continuous on the space if and only if the kernel of t is n hyperclosed 2 b a nonvanishing linear transformation t is continuous on the space if and only if it has n hyperclosed graph 3 c every finite dimensional linear space admits exactly one admissible fuzzy neighborhood system and on the other hand to examine several elegant features of those classes of fuzzy neighborhood division rings

stratified lmn convergence tower groups and their stratified lmn uniform convergence tower structures abstract if l and m are frames and n is a quantale then using stratification mappings between frames we introduce a category of stratified lmn convergence tower groups a topological category we then prove that every stratified lmn limit tower group induces a stratified lmn uniform convergence tower space also we introduce a category of stratified lmn cauchy tower groups and show that the category of strongly normal stratified lmn limit tower groups is isomorphic to the category of stratified lmn cauchy tower groups we provide various examples in support of our theories so far developed herein the text

generating fuzzy topologies with semi closure operators let x be an l fuzzy topological space for a e l 1 and a x x ec a a if and only if g fuzzy open and g x a imply there is a e a with g a 0 under certain restrictions on a which are always satisfied if l is linearly ordered c a is a semi closure operator this paper contains necessary and sufficient conditions under which a collection of semi closure operators generates a fuzzy topology in general such a collection does not generate a unique topology the class of topologies generated is shown to be closed under suprema and its largest member is characterized the topology for the fuzzy unit interval is characterized among those generated by its a closure operators

the vectorial λ calculus we describe a type system for the linear algebraic calculus the type system accounts for the linear algebraic aspects of this extension of calculus it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs this gives rise to an original type theory where types in the same way as terms can be superposed into linear combinations we prove that the resulting typed calculus is strongly normalising and features weak subject reduction finally we show how to naturally encode matrices and vectors in this typed calculus

some categorical aspects of fuzzy topology research in recent years has revealed that the construct of fuzzy topological spaces behaves quite differently from that of topological spaces with respect to certain categorical properties in this paper we discuss some of these aspects since the topological construct l fts contains nontrivial both initially and finally closed full subconstructs and each such construct gives rise to a natural autonomous theory of fuzzy topology it can be said to some extent that fuzzy topology should consist of a system of closely related topology theories including the classical topology theory as a special case with each applying to one such subconstruct therefore in the first part of this paper the theory of sobriety is established for each finally and initially closed full subconstruct of l fts to illustrate this idea the second topic of this paper is the relationship between the construct of stratified l fuzzy topological spaces and several other familiar constructs in fuzzy topology for example the constructs of sostak fuzzy topological spaces and l fuzzifying topological spaces

a binary modal logic for the intersection types of lambda calculus abstract intersection types discipline allows to define a wide variety of models for the type free lambda calculus but the curry howard isomorphism breaks down for this kind of type systems in this paper we show that the correspondence between types and suitable logical formulas can still be recovered appealing to the fact that there is a strict connection between the semantics for lambda calculus induced by the intersection types and a kripke style semantics for modal and relevant logics indeed we present a modal logic hinted by the analysis of the sub typing relation for intersection types and we show that the deduction relation for such a modal system is a conservative extension of the relation of sub typing then we define a kripke style semantics for the formulas of such a system present suitable sequential calculi prove a completeness theorem and give a syntactical proof of the cut elimination property finally we define a decision procedure for theorem hood and we show that it yields the finite model property and cut redundancy

on fuzzy neighborhood modules and algebra abstract the notion of fuzzy neighborhood module over a ring and fuzzy neighborhood algebra over a field is introduced some characterization theorems with fundamental results are deduced

on many valued stratified l fuzzy convergence spaces based on complete residuated lattices the relations between stratified l fuzzy convergence spaces and enriched l fuzzy topological spaces are studied it is shown that as a reflective subcategory the category of enriched l fuzzy topological spaces can embedded in the category of stratified l fuzzy convergence spaces also the specialization l preorder of stratified l fuzzy convergence spaces is investigated

characterization theorems for a filter lambda model the filter model is a model of the calculus based on a system of type assignment which extends the basic functionality theory of curry invented in order to give a completeness proof for scott s semantics of curry s type assignment in this paper the local structure of this model i e the syntactical characterization of the equality and inclusion relation is given

relationships between l ordered convergence structures and strong l topologies by making use of the intrinsic fuzzy inclusion orders on the fuzzy power set the relationships between l ordered convergence spaces and strong l topological spaces are researched where l is a commutative unital quantale it is shown that the category of strong l topological spaces can be embedded in the category of l ordered convergence spaces as a reflective subcategory as a result we observe that there is a galois correspondence between the category of l ordered convergence spaces and the category of strong l topological spaces further it is proved that the class of all strong l topological l ordered convergence spaces precisely is the class of all strong l topological spaces and the class of spaces with non idempotent l ordered interior operators is characterized as a subclass of the class of l ordered convergence spaces

principal type schemes for an extended type theory we consider the extension of curry s basic functionality theory presented by barendregt et al to appear and we define for any term x a principal type scheme p t s we prove that all and the only type schemes deducible for x can be obtained from the p t s of x by suitable operations

the hyperspace of fuzzy sets a natural nontopological fuzzy topological space let x be a uniform topological space then on the family ix resp d x of all nonzero functions resp nonzero uppersemicontinuous functions from x to the unit interval i a fuzzy uniform topology is constructed such that 2x resp 61 x the family of all nonvoid resp nonvoid closed subsets of x equipped with the hausdorff bourbaki structure is isomorphically injected in ix resp i x the main result of this paper is a complete description of convergence in ix by means of a notion of degree of incidence of members of ix immediate consequences are that first it can be shown that this notion of convergence refines some particular useful notions of convergence of fuzzy sets used in applications and that second it follows from its construction and properties that for each ordinary uniform topological space x there exists a natural nontopological fuzzy uniform topology on ix

fuzzy preorder and fuzzy topology this paper presents by means of alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces a systematic investigation of the interrelationship between fuzzy preordered sets topological spaces and fuzzy topological spaces

stratified l ordered convergence structures in this paper a new kind of lattice valued convergence structures on a universal set called stratified l ordered convergence structures are presented by modifying the axiom for stratified l generalized convergence structures in the fuzzy setting so as to make use of the intrinsic fuzzy inclusion order on the fuzzy power set the category of stratified l ordered convergence spaces described here is shown to be a reflective full subcategory in the category of stratified l generalized convergence spaces and hence it is topological and cartesian closed as preparation a further investigation of stratified l filters is presented from the viewpoint that latticed valued filters should be compatible with the intrinsic fuzzy inclusion order on the fuzzy power set

completeness of intersection and union type assignment systems for call by value λ models we study a version of intersection and union type assignment system union elimination rule of which is allowed only when subject of its major premise is a value of call by value e calculus the system is shown to be sound and complete under some abstract notion of membership relation defined over simple semantics for call by value models and to be invariant under call by value conversion of subjects we prove it by constructing a filter call by value lgr model copyright 2002 elsevier science b v

compactness in fuzzy convergence spaces abstract lowen and lowen applications of category theory to fuzzy subsets kluwer 1992 p 153 and lowen et al fuzzy sets and systems 40 1991 347 recently introduced the category fcs of fuzzy convergence spaces a topological quasitopos which is a supercategory of fts the category of fuzzy topological spaces in this paper compactness in fcs is examined doing so we found that to define compactness as an absolute property we had to generalize the definition of fuzzy convergence space to fuzzy subsets all basic theorems are proved including the tychonoff product theorem based on the theory developed here in a following publication a richardson compactification for fuzzy convergence spaces will be given

lambda calculi for strict parallel functions we introduce two calculi and show that they are expressive for two canonical domains of parallel functions the first calculus is an enrichment of the lazy call by name calculus with call by value abstractions and parallel composition while in the second the usual call by name abstractions are disallowed the corresponding domains are respectively abramsky s domain d d d a lifted function space and d d d a lifted domain of strict functions these domains are lattices and we show that the parallelism is adequately represented by the join operator while call by value abstractions correspond to strict functions the proofs of the results rely on a completeness theorem for the logical presentation of the semantics

the long time asymptotics of solutions to the generalized burgers equation the long time i e range following a wavefront behaviour of finite amplitude sound waves in ducts horns of variable cross section is considered the wave evolution being governed by a generalized form of burgers equation the type of initial data far behind and far ahead of the wavefront is restricted to a transition from one constant state to another it is proved that the form of the wave for large range is dependent on the limiting value of a certain function of the duct parameters we have termed the various cases that arise supercylindrical cylindrical and subcylindrical for reasons that should be clear from the details to follow the analytic form of the limiting profile is determined in all but one case in particular it is shown that the similarity solution for cylindrical waves possesses very strong global stability properties

lowen lm fuzzy topological spaces the aim of this paper is to define and study lowen lm fuzzy topological spaces we discuss the basic properties of lowen lm fuzzy topological spaces and introduce the notions of interior lowen topology and exterior lowen topology of an lm fuzzy topology and prove that llm ftop the category of lowen lm fuzzy topological spaces is isomorphism closed and simultaneously bireflective and bicoreflective in slm ftop the category of stratified lm fuzzy topological spaces moreover we also prove that an lm fuzzy topological space is an induced lm fuzzy topological space iff it is a lowen lm fuzzy topological space and an ic lm fuzzy topological space

l fuzzy version of stone s representation theorem for distributive lattices abstract in this paper the category of l fuzzy locales is introduced which is proved to play the same role with respect to stratified l fuzzy topological spaces as the locales play for topological spaces secondly stone s representation theorem for distributive lattices is generalized to the l fuzzy case and the notion of l fuzzy spectrum of distributive lattices is introduced and its properties are systematically studied moreover the harmony between the localic version of stone s representation theorem and spectral spaces of distributive lattices is also valid in the l fuzzy case

a comparison of various uniformities in fuzzy topology it is known that the construct fts of stratified fuzzy topological spaces contains non trivial concretely both reflective and coreflective full subconstructs since each of these subconstructs is both initially and finally closed in fts it gives rise to a perfectly viable and autonomous theory of fuzzy topology in this paper this idea is applied to analyze the interrelations between the various notions of uniformity in fuzzy set theory the results show that these notions can be put into a coherent and clear picture if we interpret them as notions of uniformity for certain subconstructs of fts that are concretely both reflective and coreflective or some superconstructs of fuzzy topological spaces

on stratified l convergence spaces pretopological axioms and diagonal axioms this paper focuses on pretopological and diagonal axioms for stratified l convergence spaces recently defined by the authors in 2011 this notion is slightly stronger than jager s stratified l generalized convergence spaces in particular one pretopological axiom is stated without resorting to the notion of neighborhood l filters some generalizations of kowalsky s and fischer s diagonal conditions are presented the relationship between these axioms are investigated

the epireflective hull of the sierpinski object in fts abstract in the category top of topological spaces the epireflective hull of the standard two point sierpinski space is known to coincide with the subcategory of t0 topological spaces in this note we determine the epireflective hulls of the recently found sierpinski objects in the categories fts fns and top of respectively fuzzy topological spaces fuzzy neighborhood spaces and topologically generated fuzzy topological spaces we thereby identify the corresponding t0 objects in these categories and note that the categories fts fns and top are universal

weak topological categories in order to provide a categorical framework for fuzzy topology this paper proposes the concept of weak topological category a weaker form of topological category properties of weak topological categories are investigated and some examples of such category are provided moreover the relationship between a useful weak topological category ltop the category of l fuzzy topological spaces and continuous l valued zadeh functions and some of its subcategories is studied

existence and uniqueness of solutions for a non uniformly parabolic equation abstract in this paper we study a generalized burgers equation ut u2 x tuxx which is a non uniformly parabolic equation for t 0 we show the existence and uniqueness of classical solutions to the initial value problem of the generalized burgers equation with rough initial data belonging to l r

semantic subtyping dealing set theoretically with function union intersection and negation types subtyping relations are usually defined either syntactically by a formal system or semantically by an interpretation of types into an untyped denotational model this work shows how to define a subtyping relation semantically in the presence of boolean connectives functional types and dynamic dispatch on types without the complexity of denotational models and how to derive a complete subtyping algorithm

the urysohn lemma for fuzzy neighbourhood spaces abstract the framework fns of lowen s fuzzy neighbourhood spaces is a special environment for the study of fuzzy topology it encompasses its own metrics uniformities and proximities among other interesting constructions this is a fresh and fast growing field of research it promises to develop quickly to a calculus which combines depth with applicability within this framework we establish the urysohn lemma for the mashhour morsi axiom of n normality the formulation employs the mashhour morsi n euclidean space as the suitable fuzzy analogue of the real line the proof makes use of the artico moresco fuzzy proximities the lowen fuzzy uniformities and the mashhour morsi axiom of n complete regularity

intersection and union types type assignment systems with intersection and union types are introduced although the subject reduction property with respect to s reduction does not hold for a natural deduction like system we manage to overcome this problem in two different ways the first is to adopt a notion of parallel reduction which is a refinement of gross knuth reduction the second is to introduce type theories to refine the system among which is the theory called that induces an assignment system preserving s reduction this type assignment system further clarifies the relation with the intersection discipline through the decomposition first of a disjunctive type into a set of conjunctive types and second of a derivation in the new type assignment system into a set of derivations in the intersection type assignment system for this system we propose three semantics and prove soundness and completeness theorems

automatic synthesis of typed λ programs on term algebras abstract the notion of iteratively defined functions from and to heterogeneous term algebras is introduced as the solution of a finite set of equations of a special shape such a notion has remarkable consequences 1 choosing the second order typed lamdda calculus for short as a programming language enables one to represent algebra elements and iterative functions by automatic uniform synthesis paradigms using neither conditional nor recursive constructs 2 a completeness theorem for terms with type of degree at most two and a companion corollary for programs have been proved 3 a new congruence relation for the last mentioned terms which is stronger than convertibility is introduced and proved to have the meaning of a program equivalence moreover an extension of the paradigms to the synthesis of functions of higher complexity is considered and exemplified all the concepts are explained and motivated by examples over integers list and tree structures

fuzzy neighborhood spaces abstract in this paper we introduce a subcategory of the category of fuzzy topological spaces and we prove basic properties of this subcategory the main idea behind these spaces is the notion of fuzzy neighborhoods which enables us to introduce a local theory of fuzzy topologies

characterizing strong normalization in the curien herbelin symmetric lambda calculus extending the coppo dezani heritage we develop an intersection type system for the email protected email protected email protected calculus of curien and herbelin this calculus provides a symmetric computational interpretation of classical sequent style logic and gives a simple account of call by name and call by value the present system improves upon earlier type disciplines for email protected email protected email protected in addition to characterizing the email protected email protected email protected expressions that are strongly normalizing under free unrestricted reduction the system enjoys the subject reduction and the subject expansion properties

existence and decay rates of solutions to the generalized burgers equation in this paper we study the generalized burgers equation ut u 2 2 x f t uxx w here f t 0 for t 0 we show the existence and uniqueness of classical solutions to the initial value problem of the generalized burgers equation with rough initial data belonging to l r as well it is obtained the decay rates of u in l p norm are algebra order for p 1

concerning the constants in fuzzy topology on etudie les cas mathematiquement importants qui justifient l etude des topologies quasi floues

a short note on fuzzy neighbourhood spaces abstract lowen introduced the concept of fuzzy neighbourhood spaces fns s and proved that the family of level topologies of a fns is an antichain wuyts characterized fns s as being those fully stratified fuzzy topological spaces fts s whose level topologies form antichains and whose fuzzy topologies are the finest possible for thier level topologies mashhour et al introduced the axiom of structure a on fts s and derived for it several characterizations and fuzzy topological consequences we use those characterizations of structure a and wuyts characterization of fns s to prove that a fts is a fns iff it is of structure a and fully stratified

the completeness theorem for typing λ terms abstract rules for assigning type schemes to untyped terms are given three different semantics are described and the rules are proved complete with respect to two of these semantics the type schemes are built up from type variables not constants by the semantics are defined in arbitrary models of the untyped calculus such models do not come with a type structures as part of their definition the fact that two distinct semantics are completely captured by one set of rules says that the usual type language with as its only connective is not expressive enough to describe the differences between them i conjecture that the rules are also complete with respect to the third semantics

type inference abstract interpretation and strictness analysis abstract filter domains coppo et al 1984 can be seen as abstract domains for the interpretation of functional type free programming languages what is remarkable is the fact that in filter domains the interpretation of a term is given by the set of its types in the intersection type discipline with inclusion thus reducing the computation of an abstract interpretation to typechecking as a main example an abstract filter domain for strictness analysis of type free functional languages is presented the inclusion relation between types representing strictness properties has a complete recursive axiomatization type inference rules cannot be complete strictness being a 0 1 property but a complete extension of the type inference system is presented

l fuzzy q convergence structures abstract in this paper we construct a topological category of pretopological l fuzzy q convergence spaces which contains the category of topological l fuzzy q convergence spaces as a bireflective full subcategory considering the connections with l fuzzy topology it is proved that the category of topological l fuzzy q convergence spaces is isomorphic to the category of topological l fuzzy quasi coincident neighborhood spaces and the latter is isomorphic to the category of l fuzzy topological spaces moreover we find that our pretopological l fuzzy q convergence spaces can be characterized as a kind of l fuzzy quasi coincident neighborhood spaces which is called strong l fuzzy quasi coincident neighborhood space

the richardson compactification for fuzzy convergence spaces abstract in 4 we generalized the notion of fuzzy convergence space as defined by lowen et al 8 to fuzzy subsets in order to obtain an absolute definition of compactness for fuzzy convergence spaces here as an application a richardson compactification is constructed which generalizes in a natural sense the classical richardson compactification for limit spaces

reflectors and coreflectors in the category of fuzzy topological spaces abstract using a certain number of very elementary functors explicit formulas are given for the bireflection or and bicoreflection of top topological spaces fns fuzzy neighborhood spaces and max maximal with respect to the level topologies fuzzy topological spaces in the category fts of fuzzy topological spaces a subcategory of fts minimal with respect to certain associated topologies and dual in a certain sense to max arises in a natural way and is proved to be nothing else than fns

enriched lattice valued convergence groups considering a category sl gconv of stratified enriched cl premonoid valued generalized convergence spaces we present the category sl gconvgrp of stratified l generalized convergence groups and some of its subcategories we present two natural examples on stratified enriched cl premonoid valued convergence groups among other results we show that every stratified strong l limit group is sl ucs uniformizable

limit structures over completely distributive lattices the notion of a limit molecular lattice a completely distributive lattice with some kinds of convergence of ideals on it is introduced it is proved that the category of limit molecular lattices is a cartesian closed category containing the category of topological molecular lattices as a bireflective full subcategory and the category of limit spaces as a reflective and coreflective subcategory respectively noteworthy is the distinctive order property of the convergence of ideals on the limit molecular lattice compared to that of limit spaces the l fuzzy version of fuzzy limit space is introduced and it is proved that the category of l fuzzy limit spaces is a nonfull coreflective subcategory of the category of limit molecular lattices