speeding up inferences using relevance reasoning a formalism and algorithms abstract irrelevance reasoning refers to the process in which a system reasons about which parts of its knowledge are relevant or irrelevant to a specific query aside from its importance in speeding up inferences from large knowledge bases relevance reasoning is crucial in advanced applications such as modeling complex physical devices and information gathering in distributed heterogeneous systems this article presents a novel framework for studying the various kinds of irrelevance that arise in inference and efficient algorithms for relevance reasoning we present a proof theoretic framework for analyzing definitions of irrelevance the framework makes the necessary distinctions between different notions of irrelevance that are important when using them for speeding up inferences we describe the query tree algorithm which is a sound complete and efficient algorithm for automatically deriving certain kinds of irrelevance claims for horn rule knowledge bases and several extensions finally we describe experimental results that show that significant speedups often orders of magnitude are obtained by employing the query tree in inference

convergence of the new composite implicit iteration process with random errors abstract in this paper strong convergence theorems for approximation of common fixed points of a finite family of asymptotically demicontractive mappings are proved in banach spaces using the new composite implicit iteration scheme with errors our results of this paper improve and extend the corresponding results of chen song zhou r d chen y s song h y zhou convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings j math anal appl 314 2006 701 709 osilike m o osilike implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps j math anal appl 294 2004 73 81 gu f gu the new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings j math anal appl 329 2007 766 776 and yang and hu l p yang g hu convergence of implicit iteration process with random errors acta math sinica chin ser 51 1 2008 11 22

implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps convergence theorems for approximation of common fixed points of strictly pseudocontractive mappings of browder petryshyn type are proved in banach spaces using an implicit iteration scheme recently introduced by xu and ori numer funct anal optim 22 2001 767 773

composite implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps abstract let e be a real banach space and let k be a nonempty closed convex subset of e let t i i 1 n be n strictly pseudocontractive self maps of k such that f i 1 n f t i where f t i x k t i x x and let n n 1 n n 1 0 1 be two real sequence satisfying the conditions i n 1 1 n ii n 1 1 n 2 iii n 1 1 n iv 1 n 1 n l 2 1 n 1 where l 1 is common lipschitz constant of t i i 1 n for x 0 k let x n n 1 be new implicit process defined by x n n x n 1 1 n t n y n y n n x n 1 1 n t n x n where t n t n mod n then i lim n x n p exists for all p f ii lim inf n x n t n x n 0 the results of this paper generalize and improve the results of osilike in 2004 in this paper the proof methods of the main results are also different from that of osilike

horn silver distributions in d dimensional euclidean spaces a geometric interpretation is found for a class of finite discrete probability distributions that generalizes the distribution found by horn and silver to represent an unusual distribution of neutral versus charged pions in some hadronic production models connections to de finetti s representation theorem are discussed

characterizing diagnoses and systems abstract most approaches to model based diagnosis describe a diagnosis for a system as a set of failing components that explains the symptoms in order to characterize the typically very large number of diagnoses usually only the minimal such sets of failing components are represented this method of characterizing all diagnoses is inadequate in general in part because not every superset of the faulty components of a diagnosis necessarily provides a diagnosis in this paper we analyze the concept of diagnosis in depth exploiting the notions of implicate implicant and prime implicate implicant we use these notions to consider two alternative approaches for addressing the inadequacy of the concept of minimal diagnosis first we propose a new concept that of kernel diagnosis which is free of this problem with minimal diagnosis this concept is useful to both the consistency and abductive views of diagnosis second we consider restricting the axioms used to describe the system to ensure that the concept of minimal diagnosis is adequate

demiclosedness principle and convergence theorems for strictly pseudocontractive mappings of browder petryshyn type abstract let e be a real q uniformly smooth banach space which is also uniformly convex for example lp or lp spaces 1

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

some consequences of exchangeability in random matrix theory properties of infinite sequences of exchangeable random variables result directly in explicit expressions for calculating asymptotic densities of eigenvalues of any ensemble of random matrices h whose distribution depends only on tr h h where h is the hermitian conjugate of h for real symmetric matrices and for hermitian matrices the densities are constructed by summing up wigner semicircles with varying radii and weights as confirmed by monte carlo simulations extensions to more general matrix ensembles are also considered

conditional independence in propositional logic independence the study of what is relevant to a given problem of reasoning is an important ai topic in this paper we investigate several notions of conditional independence in propositional logic darwiche and pearl s conditional independence and some more restricted forms of it many characterizations and properties of these independence relations are provided we show them related to many other notions of independence pointed out so far in the literature mainly formula variable independence irrelevance and novelty under various forms separability interactivity we identify the computational complexity of conditional independence and of all these related independence relations

axiomatisation of functional dependencies in incomplete relations abstract incomplete relations are relations which contain null values whose meaning is value is at present unknown such relations give rise to two types of functional dependency fd the first type called the strong fd sfd is satisfied in an incomplete relation if for all possible worlds of this relation the fd is satisfied in the standard way the second type called the weak fd wfd is satisfied in an incomplete relation if there exists a possible world of this relation in which the fd is satisfied in the standard way we exhibit a sound and complete axiom system for both strong and weak fds which takes into account the interaction between sfds and wfds an interesting feature of the combined axiom system is that it is not k ary for any natural number k 0 we show that the combined implication problem for sfds and wfds can be solved in time polynomial in the size of the input set of fds finally we show that armstrong relations exist for sfds and wfds

tractable reasoning via approximation abstract problems in logic are well known to be hard to solve in the worst case two different strategies for dealing with this aspect are known from the literature language restriction and theory approximation in this paper we are concerned with the second strategy our main goal is to define a semantically well founded logic for approximate reasoning which is justifiable from the intuitive point of view and to provide fast algorithms for dealing with it even when using expressive languages we also want our logic to be useful to perform approximate reasoning in different contexts we define a method for the approximation of decision reasoning problems based on multivalued logics our work expands and generalizes in several directions ideas presented by other researchers the major features of our technique are 1 approximate answers give semantically clear information about the problem at hand 2 approximate answers are easier to compute than answers to the original problem 3 approximate answers can be improved and eventually they converge to the right answer 4 both sound approximations and complete ones are described the method we propose is flexible enough to be applied to a wide range of reasoning problems in our research we considered approximation of several decidable problems with different worstcase complexity involving both propositional and first order languages in particular we defined approximation techniques for propositional logic fragments of first order logic concept description languages and modal logic in our research we also addressed the issue of representing the knowledge of a reasoner with limited resources and how to use such a knowledge for approximate reasoning purposes

an assumption based tms abstract this paper presents a new view of problem solving motivated by a new kind of truth maintenance system unlike previous truth maintenance systems which were based on manipulating justifications this truth maintenance system is in addition based on manipulating assumption sets as a consequence it is possible to work effectively and efficiently with inconsistent information context switching is free and most backtracking and all retraction is avoided these capabilities motivate a different kind of problem solving architecture in which multiple potential solutions are explored simultaneously this architecture is particularly well suited for tasks where a reasonable fraction of the potential solutions must be explored

a logical notion of conditional independence properties and applications abstract we propose a notion of conditional independence with respect to prepositional logic and study some of its key properties we present several equivalent formulations of the proposed notion each oriented towards a specific application of logical reasoning such as abduction and diagnosis we suggest a framework for utilizing logical independence computationally by structuring a propositional logic database around a directed acyclic graph this structuring explicates many of the independences satisfied by the underlying database based on these structural independences we develop an algorithm for a class of structured databases that is not necessarily horn the algorithm is linear in the size of a database structure and can be used for deciding entailment computing abductions and diagnoses the presented results are motivated by similar results in the literature on probabilistic and constraint based reasoning

the new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings abstract convergence theorems for approximation of common fixed points of strictly pseudocontractive mappings of browder petryshyn type are proved in banach spaces using a new composite implicit iteration scheme with errors the results presented in this paper generalize and improve the corresponding results of m o osilike m o osilike implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps j math anal appl 294 2004 73 81

reasoning about functional and full hierarchical dependencies over partial relations we study the implication problem for the combined class of functional and full hierarchical dependencies in the presence of sql s not null constraints two different notions of implication are addressed one where a dependency is implied by the given set of dependencies plus the underlying schema and one where a dependency is implied by the given set of dependencies alone we establish axiomatizations for both notions of implication and reveal deep relationships between them

some convergence theorems of non implicit iteration process with errors for a finite families of i asymptotically nonexpansive mappings the purpose of this paper is to study the weak and strong convergence of non implicit iteration process with errors to a common fixed point for a finite family of i asymptotically quasi nonexpansive mappings in banach spaces the results presented in this paper extend and improve the corresponding results of several authors 1 2 7 14 17 19 22 29

unknown quantum states the quantum de finetti representation we present an elementary proof of the quantum de finetti representation theorem a quantum analog of de finetti s classical theorem on exchangeable probability assignments this contrasts with the original proof of hudson and moody z wahrschein verw geb 33 343 1976 which relies on advanced mathematics and does not share the same potential for generalization the classical de finetti theorem provides an operational definition of the concept of an unknown probability in bayesian probability theory where probabilities are taken to be degrees of belief instead of objective states of nature the quantum de finetti theorem in a closely analogous fashion deals with exchangeable density operator assignments and provides an operational definition of the concept of an unknown quantum state in quantum state tomography this result is especially important for information based interpretations of quantum mechanics where quantum states like probabilities are taken to be states of knowledge rather than

on strongest neccessary and weakest sufficient conditions abstract given a propositional theory t and a proposition q a sufficient condition of q is one that will make q true under t and a necessary condition of q is one that has to be true for q to be true under t in this paper we propose a notion of strongest necessary and weakest sufficient conditions intuitively the strongest necessary condition of a proposition is the most general consequence that we can deduce from the proposition under the given theory and the weakest sufficient condition is the most general abduction that we can make from the proposition under the given theory we show that these two conditions are dual ones and can be naturally extended to arbitrary formulas we investigate some computational properties of these two conditions and discuss some of their potential applications

circumspheres of sets of n 1 random points in the d dimensional euclidean unit ball 1 n d in the d dimensional euclidean space any set of n 1 independent random points uniformly distributed in the interior of a unit ball of center o determines almost surely a circumsphere of center c and radius 1 n d and an n flat 1 n d 1 the orthogonal projection of o onto this flat is called o while designates the distance o c the classical problem of the distance between two random points in a unit ball corresponds to n 1 the focus is set on the family of circumspheres which are contained in this unit ball for any d 2 and 1 n d 1 the joint probability density function of the distance o c and circumradius has a simple closed form expression the marginal probability density functions of and are both products of powers and a gauss hypergeometric function stochastic representations of the latter random variables are described in terms of geometric means of two independent beta random variables for n d 1 and have a joint dirichlet distribution with parameters d d2

frontiers for propositional reasoning about fragments of probabilistic conditional independence and hierarchical database decompositions abstract conditional independence provides an essential framework to deal with knowledge and uncertainty in artificial intelligence and is fundamental in probability and multivariate statistics its associated implication problem is paramount for building bayesian networks unfortunately the problem does not enjoy an axiomatization by a finite set of horn rules and is already conp complete to decide for some fragments of conditional independencies saturated conditional independencies form an important fragment whose implication problem is decidable in almost linear time we establish an axiomatization by a finite set of horn rules for the fragment of generalized saturated conditional independencies these state the conditional independence between finitely many sets of random variables the special case of two sets captures geiger and pearl s finite axiomatization for saturated conditional independencies even for this special case our completeness proof is new the proof argument utilizes special probability models where two events have probability one half special probability models allow us to establish an equivalence between the implication of generalized saturated conditional independencies and that of formulae in a boolean propositional fragment this duality is then extended to a trinity including the implication problem of delobel s full first order hierarchical database decompositions already for the independence between two sets of random variables the dualities cannot be extended to cover conditional independencies in general or first order hierarchical decompositions

relevance from an epistemic perspective abstract in this paper we study relevance relations in the context of prepositional logical theories and subject matters or topics of interest which we take to be sets of atomic propositions in particular we are interested in answering questions like the following when is a sentence or theory relevant to a subject matter or when is a topic relevant to another topic or sentence given some background theory relevance is studied from a subjective or epistemic point of view that is we try to capture relevance relations from an agent s point of view relative to his or her deductive capabilities for this purpose we start out with the definition of regular belief which covers a wide range of belief models from the very weak to those closed under classical logical implication in the paper we consider one example from each of the extremes which are called explicit and implicit belief respectively we define a notion of prime implicates which applies to all models of regular belief and which has its usual meaning under implicit belief prime implicates turn out to be the right primitive from which all definitions of relevance are derived among the main technical contributions is a detailed comparison between relevance under implicit belief and three other approaches in the literature this investigation reveals that all four share a lot of common ground even though some have very different starting points we also study the complexity of determining relevance relations for implicit as well as explicit belief while intractability obtains often but not always for implicit belief the analogous problems for explicit belief are almost always tractable

an equivalence between relational database dependencies and a fragment of propositional logic it is known that there is an eqmvalence between functional dependencies m a relatmonal database and a certain fragment of proposmonal logic thins eqmvalence is extended to include both functional and multivalued dependencmes thus for each dependency there is a corresponding statement m proposmonal logic it ms then shown that a dependency funcuonal or multivalued is a consequence of a set of dependencies ff and only ff the corresponding proposiuonal statement s a consequence of the corresponding set of proposmonal statements examples are given to show that these techniques are valuable mn provmdmg much shorter proofs of theorems about dependencies than have been obtained by more tradmonal means it is shown that this eqmvalence cannot be extended to include either join dependencies or embedded multmvalued dependencies

null inclusion dependencies in relational databases abstract functional dependencies fds and inclusion dependencies inds are the most fundamental integrity constraints that arise in practice in relational databases we introduce null inclusion dependencies ninds to cater for the situation when a database is incomplete and contains null values we show that the implication problem for ninds is the same as that for inds we then present a sound and complete axiom system for null functional dependencies nfds and ninds and prove that the implication problem for nfds and ninds is decidable and exptime complete by contrast when no nulls are allowed this implication problem is undecidable this undecidability result has motivated several researchers to restrict their attention to fds and noncircular inds in which case the implication problem was shown to be exptime complete our results imply that when considering nulls in relational database design we need not assume that ninds are noncircular

a satisfiability tester for non clausal propositional calculus an algorithm for satisfiability testing in the propositional calculus with a worst case running time that grows at a rate less than 2 25 e l is described where l can be either the length of the input expression or the number of occurrences of literals i e leaves in it this represents a new upper bound on the complexity of non clausal satisfiability testing the performance is achieved by using lemmas concerning assignments and pruning that preserve satisfiability together with choosing a good variable upon which to recur for expressions in clause form it is shown that the davis putnam procedure satisfies the same upper bound

the equivalence of the convergence of four kinds of iterations for a finite family of uniformly asymptotically o pseudocontractive mappings in this paper we prove the equivalences of the strong convergence each other the modified mann iterative process with errors the modified ishikawa iterative process with errors the implicit iterative process with errors and the composite implicit iterative process with errors for a finite family of uniformly asymptotically o pseudocontractive mappings in arbitrary real banach space the results presented in this paper generalize and improve the corresponding results of roades soltuz and huang

weak and strong convergence of the ishikawa iterative process for a finite family of asymptotically nonexpansive mappings abstract in this paper we introduce an ishikawa implicit iterative process with errors for a finite family of n asymptotically nonexpansive mappings as follows x n 1 n n x n 1 n t i n k n y n n u n y n 1 n n x n n t i n k n x n n v n n 1 where for any n n fixed k n 1 denotes the quotient of the division of n by n and i n the rest i e n k n 1 n i n i n 1 n the sequences n n n n are four real sequences in 0 1 satisfying n n 1 and n n 1 for all n 1 un vn are two bounded sequences and x0 is a given point in the setting of uniformly convex banach spaces we give some results of weak and strong convergence of the above iterative process the results presented here are situated on the line of research of the corresponding results of sun j math anal appl 286 1 2003 351 358 osilike j math anal appl 294 1 2004 73 81 chang et al j math anal appl 313 1 2006 273 283 gu j math anal appl 329 2 2007 766 776 huang and noor appl math comput 190 1 2007 356 361 su and qin appl math comput 186 1 2007 271 278 zhou et al appl math comput 173 1 2006 196 212 and some others

an extension of classical functional dependency dynamic fuzzy functional dependency abstract relational data model has constituted an incontestable success in database history in this context a lot of attention has been paid to functional dependencies due to their paramount importance in the design of relational database for about fifteen years several attempts to formalize soft real world constraints imposed on the data has been made leading to the emergence of the concept of fuzzy functional dependency in this paper an overview of the different proposals of the fuzzy functional dependency is presented a new extension of classical functional dependency based on the lukasiewicz implication is presented and called dynamic fuzzy functional dependency the associated axiomatic system is introduced and proved to be sound

on the implicit iterative process for strictly pseudo contractive mappings in banach spaces in this paper we consider a composite implicit iterative process for an infinite family of strictly pseudo contractive mappings strong convergence theorems are established in an arbitrary real banach space the results presented in this paper improve and extend the recent ones announced by many others

fuzzy functional dependencies and independencies in extended fuzzy relational database models abstract in this paper we have considered data dependencies more specifically restricted fuzzy functional dependencies in the framework of extended fuzzy relational database model a formal system is presented for the derivation of fuzzy functional dependencies which is both sound and complete the problem of lossless join decomposition is discussed in the framework of extended fuzzy relational model then we introduce a formal statement of fuzzy functional independency which expresses the fact that the corresponding restricted fuzzy functional dependency is not a legitimate constraint of the real world a formal system is presented for the derivation of restricted fuzzy functional dependencies and independencies the various problems such as the membership problem the contradiction problem and the problem of canonical represents are discussed a cover called minimal cover of restricted fuzzy functional independencies is shown to be unique

generalized binomial distributions the definition properties and calculational advantages of the binomial transform representation of a class of finitely enumerated discrete probability distributions that generalize the standard binomial distribution are investigated discrete distributions of this type appear in various models of hadron multiparticle production among other physical applications the compact representations of the generating functions for factorial moments of these discrete distributions obtained using the binomial transform are used to relate the behavior of the complex zeros of the generating functions to different models for the distribution of charged and neutral particles in multihadron production

functional dependencies and constraints on null values in database relations database relations with incomplete information are considered the no information interpretation of null values is adopted due to its characteristics of generality and naturalness coherently with the framework and its motivation two meaningful classes of integrity constraints are studied a functional dependencies which have been widely investigated in the classical relational theory and b constraints on null values which control the presence of nulls in the relations specifically three types of constraints on null values are taken into account nullfree subschemes existence constraints disjunctive existence constraints and the interaction of each of them with functional dependencies is studied in each of the three cases the inference problem is solved the complexity of the algorithms for its solution analyzed and the existence of a complete axiomatization discussed

on the undecidability of implications between embedded multivalued database dependencies the implication and finite implication problems for embedded multivalued database dependencies are both shown to be algorithmically undecidable the proof is by an interpretation of semigroup word problems via systems of permuting equivalence relations into database dependencies in contrast it is shown that for each fixed premise h one has a decision procedure for implications h f

on the conditional independence implication problem a lattice theoretic approach abstract conditional independence is a crucial notion in the development of probabilistic systems which are successfully employed in areas such as computer vision computational biology and natural language processing we introduce a lattice theoretic framework that permits the study of the conditional independence ci implication problem relative to the class of discrete probability measures semi lattices are associated with ci statements and a finite sound and complete inference system relative to semi lattice inclusions is presented this system is shown to be 1 sound and complete for inferring general from saturated ci statements and 2 complete for inferring general from general ci statements we also show that the general probabilistic ci implication problem can be reduced to that for elementary ci statements the completeness of the inference system together with its lattice theoretic characterization yields a criterion we can use to falsify instances of the probabilistic ci implication problem as well as several heuristics that approximate this falsification criterion in polynomial time we also propose a validation criterion based on representing constraints and sets of constraints as sparse 0 1 vectors which encode their semi lattices the validation algorithm works by finding solutions to a linear programming problem involving these vectors and matrices we provide experimental results for this algorithm and show that it is more efficient than related approaches

axioms and algorithms for inferences involving probabilistic independence abstract this paper offers an axiomatic characterization of the probabilistic relation x is independent of y written x y where x and y are two disjoint sets of variables four axioms for x y are presented and shown to be complete based on these axioms a polynomial membership algorithm is developed to decide whether any given independence statement x y logically follows from a set of such statements i e whether x y holds in every probability distribution that satisfies the complexity of the algorithm is o k2 n where is the number of given statements n is the number of variables in x y and k is the number of variables in x y

fusion and propagation with multiple observations in belief networks abstract the polytree algorithm of kim and pearl 16 19 is a fundamental method for evidential reasoning in belief networks not only does it provide exact solutions to singly connected networks using efficient local computations but variations of it can be applied to more general networks as well when a belief network is singly connected the polytree algorithm can compute a posterior marginal distribution for each variable by visiting each node at most once for each piece of evidence by contrast the related algorithms based on undirected graphs 1 14 16 28 only need to visit each node at most twice no matter how much evidence is observed in this paper a revised polytree algorithm is developed with the same complexity as the undirected methods but within the directed framework of the polytree algorithm when this new algorithm is applied via cutset conditioning to general networks it obtains not just the corresponding significant improvement in speed but also a much simpler form for combination furthermore the revised algorithm requires only minor modifications to existing implementations of the polytree algorithm