adding similarity based reasoning capabilities to a horn fragment of possibilistic logic with fuzzy constants plfc is a first order possibilistic logic dealing with fuzzy constants and fuzzily restricted quantifiers the refutation proof method in plfc is mainly based on a generalized resolution rule which allows an implicit graded unification among fuzzy constants however unification for precise object constants is classical in order to use plfc for similarity based reasoning in this paper we extend a horn rule sublogic of plfc with similarity based unification of object constants the horn rule sublogic of plfc we consider deals only with disjunctive fuzzy constants and it is equipped with a simple and efficient version of plfc proof method at the semantic level it is extended by equipping each sort with a fuzzy similarity relation and at the syntactic level by fuzzily enlarging each non fuzzy object constant in the antecedent of a horn rule by means of a fuzzy similarity relation

on the approximation of longest common nonsupersequences and shortest common nonsubsequences the longest common nonsupersequence lcns problem is shown to be np complete over the binary alphabet and max snp hard in general although it is open whether this problem and the shortest common nonsubsequence problem are max snp hard over the binary alphabet we show that their generalizations the mixed supersequence and the mixed subsequence problems indeed remain max snp hard over the binary alphabet

duality preserving discretization of the large time increment methods abstract the large time increment method is a well established iterative computational method for time dependent non linear structural analyses which has the peculiarity to produce at each iteration an approximation of the complete structural response over the whole considered history of loading the method establishes a converging iterative sequence by exploiting the specific structure of the equations governing the continuum problem the relatively large body of literature on the subject has been mostly concerned with assessing conceptual and practical properties of the method by referring to the continuum problem so far computer implementations where based on heuristic considerations and standard finite element technology in the present paper a different approach is followed a space and time discretization which preserves the duality structure of the continuum problem is introduced first then the method is reformulated for the discrete problem it is shown how the so called generalized variable modelling preserves the fundamental duality structure of the continuum problem a proof of convergence of the iterative scheme to the solution of the discrete problem is also outlined

the shortest common supersequence problem over binary alphabet is np complete abstract we consider the complexity of the shortest common supersequence scs problem i e the problem of finding for finite strings s 1 s 2 s u a shortest string s such that every s i can be obtained by deleting zero or more elements from s the scs problem is shown to be np complete for strings over an alphabet of size 2

on residuation in multilattices filters congruences and homomorphisms continuing with our general study of algebraic hyperstructures we focus on the residuated operation in the framework of multilattices firstly we recall the existing relation between filters homomorphisms and congruences in the framework of multilattices then introduce the notion of residuated multilattice and further study the notion of filter which has to be suitably modified so that the results in the first section are conveniently preserved also in the residuated case

a comparison of fuzzy and annotated logic programming the aim of this paper is to contribute to the study of relationships between different formalism for handling uncertainty in logic programming knowledge based systems and deductive databases generalized annotated programs with restricted semantics rga programs are well suited to fit real world data we show that rga programs with constant annotations in body are equivalent to programs with left discontinuous annotation and with possibly non computable semantics our model of fuzzy logic programming flp can well handle recursive programs we show that flp has the same expressive power as rga programs without constant annotations in body of rules we introduce several syntactical transformations of programs and study their models and production operators we introduce a new efficient procedural semantics for rga programs and show connections between different sorts of computed answers

fuzzy prolog a new approach using soft constraints propagation we present a definition of a fuzzy prolog language that models b 0 1 valued fuzzy logic and subsumes former approaches because it uses a truth value representation based on a union of sub intervals on 0 1 and is defined using general operators that can model different logics this extension to prolog is implemented by interpreting fuzzy reasoning as a set of constraints that are propagated through the rules by means of aggregation operators declarative and procedural semantics for fuzzy logic programs are given and their equivalence is proven in addition we present the implementation of an interpreter for this conceived language using constraint logic programming over real numbers

fuzzy turing machines normal form and limitative theorems abstract a normal form for fuzzy turing machines is proposed and examined this normal form is arithmetical in nature since the truth values are substituted by n ples of natural numbers and the operation interpreting the conjunction becomes a sort of truncated sum also some of the results in the paper enable us to emphasize the inadequacy of the notion of fuzzy turing machine for fuzzy computability i e that this notion is not a good candidate for a church thesis in the fuzzy mathematics framework

on ordered categories as a framework for fuzzification of algebraic and topological structures using the framework of ordered categories the paper considers a generalization of the fuzzification machinery of algebraic structures introduced by rosenfeld as well as provides a new approach to fuzzification of topological structures which amounts to fuzzifying the underlying set of a structure in a suitably compatible way leaving the structure itself crisp the latter machinery allows the so called double fuzzification i e a fuzzification of something that is already fuzzified

finitary coalgebraic multisemilattices and multilattices in this paper we continue the coalgebraization of the structure of multilattice specifically we introduce a coalgebraic characterization of the notion of finitary multi semi lattice a generalization of that of semilattice which arises naturally in several areas of computer science and provides the possibility of handling non determinism

categorically algebraic topology versus universal topology this paper continues to develop the theory of categorically algebraic catalg topology introduced as a common framework for the majority of the existing many valued topological settings to provide convenient means of interaction between different approaches motivated by the results of universal topology of h herrlich we show that a concrete category is fibre small and topological if and only if it is concretely isomorphic to a subcategory of a category of catalg topological structures which is definable by topological co axioms

quick simultaneous confidence intervals for multinomial proportions abstract opinion polls often give an indication of sampling error based on the standard conservative confidence intervals for a single binomial proportion we give a lower bound for the simultaneous coverage probability when such intervals are applied to all of the proportions in a poll this bound is equal to 1 2 for small values of the same result is shown to apply to the standard confidence intervals for changes in proportions between surveys

relationship of algebraic theories to powersets over objects in set and set c this paper deals with a particular question when do powersets in lattice valued mathematics form algebraic theories or monads in clone form our approach in this and related papers is to consider powersets over objects in the ground categories set and setxc from the standpoint of algebraic theories in clone form c is a particular subcategory of the dual of the category of semi quantales for both fixed basis powersets over objects of set and variable basis powersets over objects of setxc necessary and sufficient conditions are found under which the family of all such powersets over a ground object forms an algebraic theory in clone form of standard construction in such results a distinguished role emerges for unital quantales

on the definition of suitable orderings to generate adjunctions over an unstructured codomain given a mappingf a b from a pre ordered set a into an unstructured set b we study the problem of defining a suitable pre ordering relation on b such that there exists a mapping g b a such that the pair of mappings f g forms an adjunction between pre ordered sets the necessary and sufficient conditions obtained are then expressed in terms of closure operators and closure systems

a survey of fuzzy set and topos theory abstract this paper is a comparison and contrast of approaches to many valued mathematics offered by fuzzy set theory and topos theory it gives a survey of the categorical foundations of fuzzy set theory and related topoi topoi are not a basis for fuzzy set theory butthey do suggest appropriate directions to go and questions to ask for a synthesis which does provide a foundation one possible structure which has a lopos like internal logic and the rich variety of loggical connectives used in fuzzy sets is included

on the concept of possibility probability consistency both probability and possibility may be seen as information about an experiment it is conceivable to have at some time these two forms of information about a same experiment and then the question of the relation between them arises at once in this paper some aspects of the concept of possibility probability consistency are studied the consistency is considered as a fuzzy property relative to the coherence between possibilistic and probabilistic information we analyse several measures of the degree of consistency and introduce an axiomatic to characterize them

dealing with uncertainties in engineering problems using only available data abstract this paper is the second in the series of three addressing the problem of how to deal with uncertainties in the modelings of engineering problems using only available data the problem of the heat exchanger was selected as the example because it is sufficiently complex but still simple so that the difficulties and ideas will be apparent there are various theories on how to treat the uncertainties in the first paper in the series we use only the fuzzy set respectively the possibility theory in this paper we use the fuzzy approach for some model parameters and the probability approach for the others the third paper will use the bayesian theory

on reductants in the framework of multi adjoint logic programming reductants are a special kind of fuzzy rules which constitute an essential theoretical tool for proving correctness properties as it has been reported when interpreted on a partially ordered structure a multi adjoint logic program has to include all its reductants in order to preserve the approximate completeness property after a short survey of the different notions of reductant that have been developed for multi adjoint logic programs we introduce a new and more adequate notion of reductant in the multi adjoint framework we study some of its properties and its relationships with other notions of reductants and provide an algorithm for computing all the reductants associated with a multi adjoint logic program

maximal common subsequences and minimal common supersequences the problems of finding a longest common subsequence and a shortest common supersequence of a set of strings are well known they can be solved in polynomial time for two strings in fact the problems are dual in this case or for any fixed number of strings by dynamic programming but both problems are np hard in general for an arbitrary numberkof strings here we study the related problems of finding a shortest maximal common subsequence and a longest minimal common supersequence we describe dynamic programming algorithms for the case of two strings for which case the problems are no longer dual which can be extended to any fixed number of strings we also show that both problems are np hard in general forkstrings although the latter problem unlike shortest common supersequence is solvable in polynomial time for strings of length 2 finally we prove a strong negative approximability result for the shortest maximal common subsequence problem

on a generalization of goguen s category set l the paper considers a category which generalizes goguen s category set l of l fuzzy sets with a fixed basis l we show the necessary and sufficient conditions for the generalized category to be a quasitopos and consider additional inner structure supplied by the latter property

on the dedekindmacneille completion and formal concept analysis based on multilattices the dedekindmacneille completion of a poset p can be seen as the least complete lattice containing p in this work we analyze some results concerning the use of this completion within the framework of formal concept analysis in terms of the poset of concepts associated with a galois connection between posets specifically we show an interesting property of the dedekindmacneille completion in that the completion of the concept poset of a galois connection between posets coincides with the concept lattice of the galois connection extended to the corresponding completions moreover we study the specific case when p has multilattice structure and state and prove the corresponding representation theorem

an index theory for quantum dynamical semigroups w arveson showed a way of associating continuous tensor product systems of hilbert spaces with endomorphism semigroups of type i factors we do the same for general quantum dynamical semigroups through a dilation procedure the product system so obtained is the index and its dimension is a numerical invariant for the original semigroup

multiary α resolution principle for a lattice valued logic this paper focuses on resolution based automated reasoning theory in a lattice valued logic system with truth values that are defined in a lattice valued logical algebraic structure lattice implication algebras lias which essentially aims to extend the classical logic to handle automated deduction under an uncertain environment concretely we investigate a generalization of the known conjunctive normal form cnf in the classical logic representation that we call the generalized conjunctive normal form gcnf which aims to characterize the constants and implication connectives that are essentially different from the ones in classical logic we then extend the established resolution principle at a certain truth value level called resolution in this lattice valued logic to a more general form i e from binary resolution to multiary resolution the extension to multiary resolution starts from lattice valued propositional logic lp x while its theorems of both soundness and completeness are proved multiary resolution principle is then further established in the corresponding lattice valued first order logic lf x along with its soundness theorem lifting lemma and completeness theorem meanwhile an important result that multiary resolution principle in lf x can be equivalently transformed into that in lp x to some extent is obtained all these works will theoretically support the establishment of an automated reasoning algorithm and its implementation with further applications into automated deduction and decision making problems under uncertainty

on expansions of wnm t norm based logics with truth constants this paper focuses on completeness results about generic expansions of propositional weak nilpotent minimum wnm logics with truth constants indeed we consider algebraic semantics for expansions of these logics with a set of truth constants r r c for a suitable countable c 0 1 and provide a full description of completeness results when i the t norm is a weak nilpotent minimum satisfying the finite partition property and ii the set of truth constants covers all the unit interval in the sense that each interval of the partition contains values of c in its interior

on the approximation of shortest common supersequencesand longest common subsequences the problems of finding shortest common supersequences scs and longest common subsequences lcs are two well known bf np hard problems that have applications in many areas including computational molecular biology data compression robot motion planning and scheduling text editing etc a lot of fruitless effort has been spent in searching for good approximation algorithms for these problems in this paper we show that these problems are inherently hard to approximate in the worst case in particular we prove that i scs does not have a polynomial time linear approximation algorithm unless bf p bf np ii there exists a constant delta 0 such that if scs has a polynomial time approximation algorithm with ratio log delta n where n is the number of input sequences then bf np is contained in bf dtime 2 polylog n iii there exists a constant delta 0 such that if lcs has a polynomial time approximation algorithm with performance ratio n delta then bf p bf np the proofs utilize the recent results of arora et al proc 23rd ieee symposium on foundations of computer science 1992 pp 14 23 on the complexity of approximation problems in the second part of the paper we introduce a new method for analyzing the average case performance of algorithms for sequences based on kolmogorov complexity despite the above nonapproximability results we show that near optimal solutions for both scs and lcs can be found on the average more precisely consider a fixed alphabet sigma and suppose that the input sequences are generated randomly according to the uniform probability distribution and are of the same length n moreover assume that the number of input sequences is polynomial in n then there are simple greedy algorithms which approximate scs and lcs with expected additive errors o n 0 707 and o n frac 1 2 epsilon for any epsilon 0 respectively incidentally our analyses also provide tight upper and lower bounds on the expected lcs and scs lengths for a set of random sequences solving a generalization of another well known open question on the expected lcs length for two random sequences k alexander the rate of convergence of the mean length of the longest common subsequence 1992 manuscript v chvatal and d sankoff j appl probab 12 1975 pp 306 315 d sankoff and j kruskall eds time warps string edits and macromolecules the theory and practice of sequence comparison addison wesley reading ma 1983

a fuzzy datalog deductive database system this paper describes a proposal for a deductive database system with fuzzy small mathsf datalog as its query language concepts supporting the fuzzy logic programming system small mathsf bousi sim small mathsf prolog are tailored to the needs of the deductive database system small mathsf des we develop a version of fuzzy small mathsf datalog where programs and queries are compiled to the small mathsf des core small mathsf datalog language weak unification and weak sld resolution are adapted for this setting and extended to allow rules with truth degree annotations we provide a public implementation in small mathsf prolog which is open source multiplatform portable and in memory featuring a graphical user interface a distinctive feature of this system is that unlike others we have formally demonstrated that our implementation techniques fit the proposed operational semantics we also study the efficiency of these implementation techniques through a series of detailed experiments moreover a database example for a recommender system is used to illustrate some of the features of the system and its usefulness

formal theories and linguistic descriptions abstract in this contribution we discuss properties which a formal logical theory we call it the theory of evaluating expressions should have to serve us as a tool for modeling of the meaning of a certain class of natural language expressions called evaluating linguistic expressions we further construct a formal theory for modeling of the meaning of sets of fuzzy if then rules called linguistic descriptions and finally present a basic schema of fuzzy logic deduction the basis for our study is first order fuzzy logic with evaluated syntax

simultaneous confidence intervals and sample size determination for multinomial proportions abstract simultaneous confidence interval procedures for multinomial proportions are used in many areas of science in this article two new simultaneous confidence interval procedures are introduced numerical results are presented to evaluate these procedures and compare their performance with established methods that have been used in statistical literature from the results presented in this article it is evident that the new procedures are more accurate than the established ones where the accuracy of the procedure is measured by the volume of the confidence region corresponding to the nominal coverage probability and the probability of coverage it achieves in the sample size determination problem the new procedures provide a sizable amount of savings as compared to the procedures that have been used in many applications because both procedures performed equally well the procedure that requires the least amount of computing time is recommended

linear approximation of shortest superstrings we consider the following problem given a collection of strings s 1 s m find the shortest string s such that each s i appears as a substring a consecutive block of s although this problem is known to be np hard a simple greedy procedure appears to do quite well and is routinely used in dna sequencing and data compression practice namely repeatedly merge the pair of distinct strings with maximum overlap until only one string remains let n denote the length of the optimal superstring a common conjecture states that the above greedy procedure produces a superstring of length o n in fact 2 n yet the only previous nontrivial bound known for any polynomial time algorithm is a recent o n log n result we show that the greedy algorithm does in fact achieve a constant factor approximation proving an upper bound of 4 n furthermore we present a simple modified version of the greedy algorithm that we show produces a superstring of length at most 3 n we also show the superstring problem to be maxsnp hard which implies that a polynomial time approximation scheme for this problem is unlikely

proximity based unification theory similarity based logic programming has been proposed to enhance the logic programming paradigm with similarity relations in order to represent and manage vague or imprecise information a similarity relation is a reflexive symmetric transitive fuzzy binary relation extending the standard notion of equivalence relation with the purpose of weakening the concept of equality as is reported similarity relations have significant limitations due to the transitivity restriction that can lead to representing fuzzy information incorrectly in some situations recently we have proposed the use of proximity relations i e reflexive symmetric fuzzy binary relations in the context of a logic programming system called bousi prolog as a way of solving this problem and generalizing later approaches exclusively based on similarity relations however a naive combination of proximity relations and the existing unification algorithms may cause incompleteness problems hence in this paper we introduce an accurate definition of proximity between expressions terms or atomic formulas and a new unification algorithm able to manage proximity relations properly the so called weak unification algorithm is an extension of martelli and montanari s unification algorithm supported by the new notion of proximity as major relevant properties we prove that the weak unification algorithm terminates and it is sound i e it produces a weak unifier of two expressions if they are unifiable and complete i e it is able to compute a weak most general unifier for two unifiable expressions

fuzzy logic programming reduced to reasoning with attribute implications abstract we present a link between two types of logic systems for reasoning with graded if then rules the system of fuzzy logic programming flp in sense of vojtas and the system of fuzzy attribute logic fal in sense of belohlavek and vychodil we show that each finite theory consisting of formulas of fal can be represented by a definite program so that the semantic entailment in fal can be characterized by correct answers for the program conversely we show that for each definite program there is a collection of formulas of fal so that the correct answers can be represented by the entailment in fal using the link we can transport results from fal to flp and vice versa which gives us e g a syntactic characterization of correct answers based on pavelka style armstrong like axiomatization of fal we further show that entailment in flp is reducible to reasoning with boolean attribute implications and elaborate on related issues including properties of least models

a relationship between probability interval and random sets and its application to linear optimization with uncertainties abstract random sets and probability intervals could be represented as uncertain parameters in a linear program however they are not the same this paper presents a method by which an intersection of random sets provides an approximation of a given probability interval two specific random sets generating this approximation are used to construct probability density mass functions that provide the smallest and the largest expected values with respect to the probability interval uncertainty we show that our construction is computationally more efficient than computing directly from probability intervals these results are applied to linear programs with random set and probability interval uncertainties to obtain optimal solutions with respect to pessimistic optimistic and minimax regret approaches

fuzzy logic programming in this paper we consider the theory of fuzzy logic programming without negation our results cover logical systems with a wide variety of connectives ranging from t norm and conorms through conjunctors and disjunctors and their residuals to aggregation operators rules of our programs are many valued implications we emphasize that in contrast to other approaches our logic is truth functional i e according to p hajek we work in fuzzy logic in narrow sense we prove the soundness and the completeness of our formal model we deal with applications to threshold computation abduction fuzzy unification based on similarity we show that fuzzy unification based on similarities has applications to fuzzy databases and flexible querying

generating linear extensions fast one of the most important sets associated with a poset cal p is its set of linear extensions e cal p this paper presents an algorithm to generate all of the linear extensions of a poset in constant amortized time that is in time o e cp where e cp e cp the fastest previously known algorithm for generating the linear extensions of a poset runs in time o n cdot e cp where n is the number of elements of the poset the algorithm presented here is the first constant amortized time algorithm for generating a naturally defined class of combinatorial objects for which the corresponding counting problem is p complete furthermore it is shown that linear extensions can be generated in constant amortized time where each extension differs from its predecessor by one or two adjacent transpositions the algorithm is practical and can be modified to count linear extensions efficiently and to compute p x y for all pairs x y in time o n 2 e cal p

proof systems for moss coalgebraic logic we study gentzen style proof theory of the finitary version of the coalgebraic logic introduced by l moss the logic captures the behaviour of coalgebras for a large class of set functors the syntax of the logic defined uniformly with respect to a finitary coalgebraic type functor t uses a single modal operator t t of arity given by the functor t itself and its semantics is defined in terms of a relation lifting functor view the mathml sourcet an axiomatization of the logic consisting of modal distributive laws has been given together with an algebraic completeness proof in work of c kupke a kurz and y venema in this paper following our previous work on structural proof theory of the logic in the special case of the finitary powerset functor we present cut free one and two sided sequent calculi for the finitary version of moss coalgebraic logic for a general finitary functor t in a uniform way for the two sided calculi to be cut free we use a language extended with the boolean dual of the nabla modality

extending fuzzy logics with many hedges abstract fuzzy logic aims at modeling logical reasoning with vague or imprecise statements which may contain linguistic hedges in fact many hedges e g very highly rather and slightly can be used simultaneously to express different levels of emphasis moreover each hedge might have a dual one e g slightly can be seen as a dual hedge of very thus it is necessary to extend systems of fuzzy logic with multiple hedges this work proposes two axiomatizations for multiple hedges as an expansion of a core fuzzy logic in one axiomatization hedges do not have any dual one while in the other each hedge can have its own dual one it is shown that the proposed logics not only cover a large class of hedge functions but also have all completeness properties as the underlying logic w r t the class of their chains as well as distinguished subclasses of their chains including standard completeness the axiomatizations are also extended to the first order level furthermore we present a method to build linguistic fuzzy logics based on the axiomatizations and a hedge algebra whose corresponding algebras use a linguistic truth domain taken from the hedge algebra for representing and reasoning with linguistically expressed human knowledge where truth values of vague sentences are given in linguistic terms

stone coalgebras we argue that the category of stone spaces forms an interesting base category for coalgebras in particular if one considers the vietoris functor as an analogue to the power set functor on the category of sets we prove that the so called descriptive general frames which play a fundamental role in the semantics of modal logics can be seen as stone coalgebras in a natural way this yields a duality between modal algebras and coalgebras for the vietoris functor building on this idea we introduce the notion of a vietoris polynomial functor over the category of stone spaces for each such functor t we provide an adjunction between t sorted boolean algebras with operators and the stone coalgebras for t we also identify the subcategory of algebras on which the adjunction restricts to an equivalence and show that the final t coalgebra is the dual of the initial t bao

fuzzy logic programming via multilattices we investigate the use of multilattices as the set of truth values underlying a general fuzzy logic programming framework on the one hand some theoretical results about ideals of a multilattice are presented in order to provide an ideal based semantics on the other hand a restricted semantics in which interpretations assign elements of a multilattice to each propositional symbol is presented and analysed

a comparative study of adjoint triples adjoint triples are helpful as basic operators used in several domains for example adjoint triples play an important role in two important frameworks multi adjoint logic programming and multi adjoint concept lattices this paper shows that adjoint triples are an interesting generalization of t norms and their residuated implications since they preserve their main properties as well as they help to increase the flexibility of the operators used for computation in the considered framework furthermore these operators will be related to other important general triples specifically implication triples and the definition of these latter operators will be improved

on fixed points of multivalued functions on complete lattices and their application to generalized logic programs unlike monotone single valued functions multivalued mappings may have zero one or possibly infinitely many minimal fixed points the contribution of this work is twofold first we overview and investigate the existence and computation of minimal fixed points of multivalued mappings whose domain is a complete lattice and whose range is its power set second we show how these results are applied to a general form of logic programs where the truth space is a complete lattice we show that a multivalued operator can be defined whose fixed points are in one to one correspondence with the models of the logic program

on finding minimal maximal and consistent sequences over a binary alphabet abstract in this paper we investigate the complexity of finding various kinds of common super and subsequences with respect to one or two given sets of strings we show that longest minimal common supersequence shortest maximal common subsequence and shortest maximal common non supersequence are max snp hard over a binary alphabet moreover we show that shortest common supersequence longest common subsequence longest common non supersequence shortest common non subsequence and longest minimal common non supersequence are max snp hard over a binary alphabet if the number of zeros is fixed by the instance we show how these problems can be related to finding sequences consistent with respect to two given sets of strings this leads to a unified approach for characterizing the complexity of such problems

universal coalgebra a theory of systems in the semantics of programming finite data types such as finite lists have traditionally been modelled by initial algebras later final coalgebras were used in order to deal with infinite data types coalgebras which are the dual of algebras turned out to be suited moreover as models for certain types of automata and more generally for transition and dynamical systems an important property of initial algebras is that they satisfy the familiar principle of induction such a principle was missing for coalgebras until the work of aczel 1988 on a theory of non wellfounded sets in which he introduced a proof principle nowadays called coinduction it was formulated in terms of bisimulation a notion originally stemming from the world of concurrent programming languages milner 1980 park 1981 using the notion of coalgebra homomorphism the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras aczel and mendler 1989 thus the three basic notions of universal algebra algebra homomorphism of algebras and congruence turn out to correspond to coalgebra homomorphism of coalgebras and bisimulation respectively in this paper the latter are taken as the basic ingredients of a theory called universal coalgebra some standard results from universal algebra are reformulated using the afore mentioned correspondence and proved for a large class of coalgebras leading to a series of results on e g the lattices of subcoalgebras and bisimulations simple coalgebras and coinduction and a covariety theorem for coalgebras similar to birkhoff s variety theorem

pavelka style fuzzy logic in retrospect and prospect we trace the origin and development of pavelka style fuzzy logic discuss its significance and clarify some related misconceptions

on type ii0 e0 semigroups induced by boundary weight doubles powers has shown that each spatial e0 semigroup can be obtained from the boundary weight map of a cp flow acting on b k l2 0 for some separable hilbert space k in this paper we define boundary weight maps through boundary weight doubles where mn c mn c is a q positive map and is a boundary weight over l2 0 these doubles induce cp flows over k for 1 1 n n

the shortest common nonsubsequence problem is np complete abstract the shortest common nonsubsequence scns problem is given a finite set l of strings over an alphabet and an integer k n is there a string of length k over that is not a subsequence of any string in l the scns problem is shown to be np complete for strings over an alphabet of size 2

categories of lattice valued sets as categories of arrows in this paper we introduce a category x a which is a generalization of the category of lattice valued subsets of sets set jcpos introduced by us earlier we show the necessary and sufficient conditions for x a to be topological over xxa

constructing membership functions using statistical data abstract determination of the membership functions is vital in practical applications of the fuzzy set theory this paper presents a guideline to construct the membership functions for fuzzy sets whose elements have a defining feature with a known probability density function pdf in the universe of discourse the method finds the smallest fuzzy set which assigns high average membership values to those objects with the defining features distributed according to the given pdf it is show that for any pdf the method is capable of generating membership functions in accordance with the possibility probability consistency principle membership functions derived from some of the well known pdfs and an application in solving noise contaminated linear system of equations are presented

a scalable multiscale latin method adapted to nonsmooth discrete media the simulation of discrete systems often leads to large scale problems for instance if they result of a discretization technique or a modeling at a small scale a multiscale analysis may involve an homogenized macroscopic problem as well as a coarse space mechanism to accelerate convergence of the numerical scheme a multilevel domain decomposition technique is used herein as both a numerical strategy to simulate the behaviour of a non smooth discrete media and to provide a macroscopic numerical behaviour of the same system several generic formulations for such systems are discussed in this article a multilevel domain decomposition is tested and several choices of the embedded coarse space are discussed in particular with respect of the emergence of weak interfaces characteristics of the discrete media substructuration the application problem is the quasi static simulation of a large scale tensegrity grid

a top k query answering procedure for fuzzy logic programming we present a top k query answering procedure for fuzzy logic programming in which arbitrary computable functions may appear in the rule bodies to manipulate truth values the top k ranking problem i e determining the top k answers to a query becomes important as soon as the set of facts becomes quite large

the asymptotic lift of a completely positive map starting with a unit preserving normal completely positive map l m m acting on a von neumann algebra or more generally a dual operator system we show that there is a unique reversible system n n i e a complete order automorphism of a dual operator system n that captures all of the asymptotic behavior of l called the asymptotic lift of l this provides a noncommutative generalization of the frobenius theorems that describe the asymptotic behavior of the sequence of powers of a stochastic n n matrix in cases where m is a von neumann algebra the asymptotic lift is shown to be a w dynamical system n z and we identify n z as the tail flow of the minimal dilation of l we are also able to identify the poisson boundary of l as the fixed algebra n in general we show the action of the asymptotic lift is trivial iff l is slowly oscillating in the sense that limn ln 1 ln 0 m hence is often a nontrivial automorphism of n the asymptotic lift of a variety of examples is calculated

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

a coalgebraic approach to non determinism applications to multilattices multilattices are a suitable generalization of lattices which enables to accommodate the formalization of non deterministic computation specifically the algebraic characterization for multilattices provides a formal framework to develop tools in several fields of computer science on the other hand the usefulness of coalgebra theory has been increasing in the recent years and its importance is undeniable in this paper somehow mimicking the use of universal algebra we define a new kind of coalgebras the nd coalgebras that allows to formalize non determinism and show that several concepts widely used in computer science are indeed nd coalgebras within this formal context we study a minimal set of properties which provides a coalgebraic definition of multilattices

fuzzy sets and statistical data abstract specific features of probability and possibility theories are discussed with emphasis on semantical aspects instead of putting forward the acknowledged usefulness of possibility theory for the non statistical modelling of subjective categories we try to figure out how statistical data and possibility theory could be matched as a result procedures for constructing weak possibilistic substitutes of probability measures and for processing imprecise statistical data are outlined they provide new insights on relationship between fuzzy sets and probability theories

fuzzy numbers from raw discrete data using linear regression this paper focuses on modelling fuzzy numbers with meaningful membership functions more precisely it proposes a method to construct trapezoidal fuzzy number approximations from raw discrete data in many applications input information is numerical and therefore particular fuzzy sets such as fuzzy numbers hold great interest and relevance in managing data imprecision and vagueness the proposed technique provides an efficient way to obtain trapezoidal numbers using linear regression the technique is simple fast and effective preliminary tests are performed using different types of input data a gaussian function a sigmoidal function three datasets of synthetic discrete data and an histogram obtained from a colour satellite image

syntax and semantics of multi adjoint normal logic programming abstract multi adjoint logic programming is a general framework with interesting features which involves other positive logic programming frameworks such as monotonic and residuated logic programming generalized annotated logic programs fuzzy logic programming and possibilistic logic programming one of the most interesting extensions of this framework is the possibility of considering a negation operator in the logic programs which will improve its flexibility and the range of real applications this paper introduces multi adjoint normal logic programming which is an extension of multi adjoint logic programming including a negation operator in the underlying lattice beside the introduction of the syntax and semantics of this paradigm we will provide sufficient conditions for the existence of stable models defined on a convex compact set of an euclidean space finally we will consider a particular algebraic structure in which sufficient conditions can be given in order to ensure the unicity of stable models of multi adjoint normal logic programs

classification of q pure q weight maps over finite dimensional hilbert spaces abstract an e 0 semigroup of b h is a one parameter strongly continuous semigroup of endomorphisms of b h that preserve the identity every e 0 semigroup that possesses a strongly continuous intertwining semigroup of isometries is cocycle conjugate to an e 0 semigroup induced by the bhat induction of a cp flow over a separable hilbert space k we say an e 0 semigroup is q pure if the cp subordinates of norm one i e t i 1 and t t is completely positive for all t 0 are totally ordered in the sense that if and are two cp subordinates of of norm one then or this paper shows how to construct and classify all q pure e 0 semigroups induced by cp flows over a finite dimensional hilbert space k up to cocycle conjugacy

fuzzy linear least squares for the identification of possibilistic regression models abstract the stochastic approach to regression e g the least squares method is a commonly used technique in a wide range of disciplines as it offers an intuitive and well founded solution to the problem of fitting a set of parameters to existing data specifically in the case where the parameters of meta models are identified the linear least squares formulation receives wide appreciation among engineers due to its simple yet powerful formulation and solution usually this approach provides a reasonable fit depending largely on the quality of the model that is employed however it has two main drawbacks from a statistical point of view the premises justifying its use cannot always be assumed in good faith and most importantly the resulting model will almost certainly fail at correctly predicting the output without falling victim to the effect of over fitting the presented fuzzy regression algorithm originates from a set of different axioms for the solution of the linear least squares problem it is able to provide the worst case optimal parameter variation necessary to cover all of the crisp data points while encoding meaningful information in the membership function this is accomplished by means of a sensible fuzzification procedure of the crisp data points and the application of an exact inverse fuzzy arithmetic for estimating the fuzzy valued parameters of the model in question

foundations of fuzzy sets abstract this paper gives an overview of the origins of fuzzy set theory and the problems for the foundations of fuzzy sets arising from those origins and current practice it then gives detailed accounts of categorical approaches using a closed structure to capture the fuzzy and connective within these categories weak forms of subobject representations provide an internal second order logic an approach to fuzzy real numbers and fuzzy topology is included to illustrate the use of this internal second order theory

a new approach in non linear mechanics the large time increment method a new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non linearities and is tested on some examples in elastoplasticity the method considerably reduces the number of transfers between local and global levels hence the numerical cost of calculation is also diminished

inferring a possibility distribution from empirical data several transformations from probabilities to possibilities have been proposed in particular dubois and prade s procedure produces the most specific possibility distribution among the ones dominating a given probability distribution in this paper this method is generalized to the case where the probabilities are unknown the only information being a data sample represented by a histogram it is proposed to characterize the probabilities of the different classes by simultaneous confidence intervals with a given confidence level email protected from this imprecise specification a procedure for constructing a possibility distribution is described insuring that the resulting possibility distribution will dominate the true probability distribution in at least 100 email protected of the cases finally a simple efficient algorithm is given which makes the computations tractable even if the number of classes is high

a categorical semantics for fuzzy predicate logic the object of this study is to look at categorical approaches to many valued logic both propositional and predicate to see how different logical properties result from different parts of the situation in particular the relationship between the categorical fabric i introduced at linz in 2004 and the fuzzy logics studied by hajek 2003 5 esteva et al 2003 1 and hajek 1998 4 comes from restricting the kind of structures used for truth values we see how the structure of the various kinds of algebras shows up in the categorical logic giving a variant on natural deduction for these logics quantification typically needs more completeness than is present in the algebras used in hajek 1998 4 hence the need for safe interpretations the categorical setting gives a predicate logic without variables the language in the more traditional sense comes from a structure built on a particular freely generated cartesian category formulas have a clear meaning in that more restricted context interpretation of the language in other categorical fabrics is given by application of a product preserving functor traditional completeness results relate to this kind of interpretation completeness can also be understood as showing that the derivable truths in the general fabric are the necessary truths those which are true in all of the possible worlds

combined super substring and super subsequence problems super substring problems and super subsequence problems are well known problems in stringology that have applications in a variety of areas such as manufacturing systems design and molecular biology here we investigate the complexity of a new type of such problem that forms a combination of a super substring and a super subsequence problem moreover we introduce different types of minimal superstring and maximal substring problems in particular we consider the following problems given a set l of strings and a string s i find a minimal superstring or maximal substring of l that is also a supersequence or a subsequence of s ii find a minimal supersequence or maximal subsequence of l that is also a superstring or a substring of s in addition some non super non substring and non super nonsubsequence variants are studied we obtain several np hardness or even max snp hardness results and also identify types of weak minimal superstrings and weak maximal substrings for which i is polynomial time solvable

specifying coalgebras with modal logic abstract we propose to use modal logic as a logic for coalgebras and discuss it in view of the work done on coalgebras as a semantics of object oriented programming two approaches are taken first standard concepts of modal logic are applied to coalgebras for a certain kind of functor it is shown that the logic exactly captures the notion of bisimulation and a complete calculus is given examples of verifications of object properties are given second we discuss the relationship of this approach with the coalgebraic logic of moss coalgebraic logic ann pure appl logic 96 1999 277 317

the latin multiscale computational method and the proper generalized decomposition this paper deals with the synergy between the latin multiscale method and what is called the proper generalized decomposition pgd which is the key of its performances

e0 semigroups of type ii0 and q purity boundary weight maps of range rank one and two abstract a cp flow over a separable hilbert space k is a continuous one parameter semigroup of completely positive maps on b k l 2 0 which is intertwined by the right shift semigroup and cp flows are obtained from boundary weight maps in this paper we generalize concepts of q purity considered previously by defining an e0 semigroup to be q pure if it is a cp flow and its set of cp flow subordinates is totally ordered by subordination we provide a complete description of all q pure e0 semigroups of type ii0 arising from boundary weight maps with range rank one and we provide a criterion to determine if two such boundary weight maps give rise to cocycle conjugate q pure e0 semigroups when dim k we also show that boundary weight maps of range rank two do not give rise to q pure e0 semigroups of type ii0

interpreted systems and kripke models for multiagent systems from a categorical perspective both kripke models and interpreted systems have been put forward as basic models of multi agent systems and for reasoning about knowledge in such systems this paper enriches previous comparisons of these two forms of semantics by considering categories of models in both cases and then shows that constructions given by lomuscio and ryan extend to give an adjoint equivalence between the two settings this equivalence is exploited in a discussion of colimits of interpreted systems

adding truth constants to logics of continuous t norms axiomatization and completeness results in this paper we study generic expansions of logics of continuous t norms with truth constants taking advantage of previous results for lukasiewicz logic and more recent results for godel and product logics indeed we consider algebraic semantics for expansions of logics of continuous t norms with a set of truth constants r r c for a suitable countable c 0 1 and provide a full description of completeness results when i the t norm is a finite ordinal sum of lukasiewicz godel and product components ii the set of truth constants covers all the unit interval in the sense that each component of the t norm contains at least one value of c different from the bounds of the component and iii the truth constants in lukasiewicz components behave as rational numbers

on data based estimation of possibility distributions abstract in this paper we show how a possibilistic description of uncertainty arises very naturally in statistical data analysis in combination with recent results in inverse uncertainty propagation and the consistent aggregation of marginal possibility distributions this estimation procedure enables a very general approach to possibilistic identification problems in the framework of imprecise probabilities i e the non parametric estimation of possibility distributions of uncertain variables from data with a clear interpretation

a multiscale large time increment fas algorithm with time space model reduction for frictional contact problems a multiscale strategy using model reduction for frictional contact computation is presented this new approach aims to improve computation time of finite element simulations involving frictional contact between linear and elastic bodies this strategy is based on a combination between the latin large time increment method and the fas multigrid solver the latin method is an iterative solver operating on the whole time space domain applying an a posteriori analysis on solutions of different frictional contact problems shows a great potential as far as reducibility for frictional contact problems is concerned time space vectors forming the so called reduced basis depict particular scales of the problem it becomes easy to make analogies with multigrid method to take full advantage of multiscale information

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

on fuzzification of topological categories this paper shows that l m fuzzy topology of u hohle t kubiak and a sostak is an instance of a general fuzzification procedure for topological categories which amounts to the construction of a new topological category from a given one this fuzzification procedure motivates a partial dualization of the machinery of tower extension of topological constructs of d zhang thereby providing the procedure of tower extension of topological categories with the help of this dualization we arrive at the meta mathematical result that the concept of l m fuzzy topology and the notion of approach space of r lowen are dual to each other

latin a new view and an extension to wave propagation in nonlinear media summary the latin acronym of large time increment method was originally devised as a non incremental procedure for the solution of quasi static problems in continuum mechanics with material nonlinearity in contrast to standard incremental methods like newton and modified newton latin is an iterative procedure applied to the entire loading path in each latin iteration two problems are solved a local problem which is nonlinear but algebraic and miniature and a global problem which involves the entire loading process but is linear the convergence of these iterations which has been shown to occur for a large class of nonlinear problems provides an approximate solution to the original problem in this paper the latin method is presented from a different viewpoint taking advantage of the causality principle in this new view latin is an incremental method and the latin iterations are performed within each load step similarly to the way that newton iterations are performed the advantages of the new approach are discussed in addition latin is extended for the solution of time dependent wave problems as a relatively simple model for illustrating the new formulation lateral wave propagation in a flat membrane made of a nonlinear material is considered numerical examples demonstrate the performance of the scheme in conjunction with finite element discretization in space and the newmark trapezoidal algorithm in time copyright 2017 john wiley sons ltd

extended multi adjoint logic programming abstract extended multi adjoint logic programming arises as an extension of multi adjoint normal logic programming where constraints and a special type of aggregator operator have been included the use of this general aggregator operator permits to consider for example different negation operators in the body of the rules of a logic program we have introduced the syntax and the semantics of this new paradigm as well as an interesting mechanism for obtaining a multi adjoint normal logic program from an extended multi adjoint logic program this mechanism will allow us to establish technical properties relating the different stable models of both logic programming frameworks moreover it makes possible that the already developed and future theory associated with stable models of multi adjoint normal logic programs can be applied to extended multi adjoint logic programs

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

on the category set jcpos category set jcpos of lattice valued subsets of sets is introduced and studied we prove that it is topological over setxjcpos and show its natural coalgebraic subcategory

a coalgebraic view on positive modal logic positive modal logic is the restriction of the modal local consequence relation defined by the class of all kripke models to the propositional negation free modal language the class of positive modal algebras is the one canonically associated with pml according to the theory of the algebrization of logics lecture notes in logic springer berlin 1996 a priestley style duality is established between the category of positive modal algebras and the category of k spaces in j igpl 7 6 1999 683 in this paper we establish a categorical equivalence between the category k of k spaces and the category coalg v of coalgebras of a suitable endofunctor v on the category of priestley spaces

toward an optimal a priori reduced basis strategy for frictional contact problems with latin solver abstract in this paper an efficient a priori model reduction strategy for frictional contact problems is presented we propose to solve this problem by using the finite element method and the non linear latin solver basically this non linear solver assumes a space time separated representation presaging nowadays pgd strategies we extend this family of solvers to frictional engineering applications with reduced subspaces and no prior knowledge about the solution contrary to a posteriori model reduction techniques hereinafter a hybrid a priori a posteriori latin pgd formulation for frictional contact problems is proposed indeed the suggested algorithm may or may not start with an initial guess of the reduced basis and is able to enrich the basis in order to reach a given level of accuracy moreover it provides progressively the solution of the considered problem into a quasi optimal space time separated form compared to the singular value decomposition svd some examples are provided in order to illustrate the efficiency and quasi optimality of the proposed a priori reduced basis latin solver

necessity of non stratified and anti stratified spaces in lattice valued topology this paper surveys the necessity of non stratified spaces from these viewpoints the characteristic functor the l spectrum and l soberification functors the upper free functor associated with l valued frames and two functorial embeddings associated with topological systems from semantic domains interestingly additional arguments also emerge en route for stratified spaces so that this paper ultimately argues for the necessity of both stratified and non stratified spaces in fixed basis topology the schemum of l top s and variable basis topology e g loc top