conglomerability of probability measures on boolean algebras for the case where b is a boolean algebra of events and p is a probability finitely additive definetti 1972 considered the question of conglomerability of p and found that in many circumstances this natural notion was equivalent to countable additivity of p schervish seidenfeld and kadane 1984 pursued these investigations on the connection between countable additivity and conglomerability in greater detail for the case where b is a algebra hill and lane 1985 and zame 1988 give alternative proofs this article is an extension for the most part of schervish seidenfeld and kadane s work to the case where b is an arbitrary boolean algebra the more restrictive notion of positive conglomerability for a class of algebras including the countable algebras complete algebras and inifinite product algebras is treated completely this class is described by the requirement that a 0 1 valued measure be countably additive if every countable family of negligible sets is contained within a negligible set i e corresponds to a p point of of the stone space in general positive conglomerability fails to be equivalent to countable additivity though the degree of failure is minor building on techniques of hill lane and zame we obtain partial results on conglomerability for non complete algebras

on fujita s spectrum conjecture abstract we prove fujita s spectrum conjecture on the discreteness of pseudo effective thresholds for polarized varieties

on the birational automorphisms of varieties of general type we show that the number of birational automorphisms of a variety of general type x is bounded by c vol x kx where c is a constant that only depends on the dimension of x

two integrals and some modified versions critical remarks the aim of this paper is to discuss different constructions of integrals sections 3 and 4 based on decomposable measures section 1 according to the classification of the continuous t conorms in essentially two types namely v and archimedean t conorms there exist mainly two types of integrals namely the constructions of sugeno section 3 and of weber section 4 further constructions corresponding to the archimedean case result to be special cases or not well defined section 4 in all cases a crucial property is some restricted distribution law for the pair with an appropriate operation section 2 some applications shall illustrate the use of the two integrals section 5

de finetti s coherence and statistical inference on donne la definition d une inference coherente en conformite avec une theorie des probabilites conditionnelles derivee du principe de coherence de de finetti et on effectue une comparaison critique d une telle definition avec celle proposee par heath lane et sudderth

log canonical singularities are du bois a recurring difficulty in the minimal model program mmp is that while log terminal singularities are quite well behaved for instance they are rational log canonical singularities are much more complicated they need not even be cohenmacaulay the aim of this paper is to prove that as conjectured in kol92 1 13 log canonical singularities are du bois the concept of du bois singularities abbreviated as db was introduced by steenbrink in ste83 as a weakening of rationality it is not clear how to define du bois singularities in positive characteristic so we work over a field of characteristic 0 throughout the paper the precise definition is rather involved see 1 10 but our main applications rely only on the following consequence

on the proper moduli spaces of smoothable kahler einstein fano varieties in this paper we investigate the geometry of the orbit space of the closure of the subscheme parameterizing smooth kahler einstein fano manifolds inside an appropriate hilbert scheme in particular we prove that being k semistable is a zariski open condition and we establish the uniqueness of the gromov hausdorff limit for a punctured flat family of kahler einstein fano manifolds based on these we construct a proper scheme parameterizing the s equivalent classes of q gorenstein smoothable k semistable q fano varieties and we verify various necessary properties to guarantee that it is a good moduli space

t conditional possibilities coherence and inference in this paper we refer to an axiomatic definition of t conditional possibility where t is any t norm we characterize a full t conditional possibility in terms of a suitable set of unconditional possibilities starting from this characterization we are able to manage coherent conditional possibility assessments and their enlargements to compare t conditional possibility related to different t norm t we study binary relations locally representable by a t conditional possibility

possibility theory conditional independence the subtle notion of conditioning is controversial in several contexts for example in possibility theory where in fact different definitions have been introduced we refer to a general axiomatic definition of conditional possibility and then we deal with partial assessments on not necessarily structured domains containing only elements of interest we study a notion of coherence which assures the extendability of an assessment as a conditional possibility and we introduce a procedure for checking coherence moreover we propose a definition of independence for conditional possibility which avoids some counterintuitive situations and we study its main properties in order to compare it with other definitions introduced in literature then we check which properties among the graphoid ones are satisfied this allows to compare our definition with other independence notions given in the context of other uncertainty formalisms this analysis is relevant for graphical models in order to single out and visualize dependence relations among random variables

algorithms for possibility assessments coherence and extension in this paper we study the computational aspects of coherence and extension of partial possibility assessments both in an unconditional and a conditional setting providing complexity results and algorithms for each problem in particular we propose an algorithm to check the coherence of a partial unconditional assessment which is based on propositional satisfiability for the conditional case we firstly prove a new characterization of coherent conditional assessments that allows us to define an algorithm again based on propositional satisfiability the extension problem in both settings is solved by means of a search algorithm which relies on the corresponding coherence procedure

finitely maxitive conditional possibilities bayesian like inference disintegrability and conglomerability the aim of the paper is to study bayesian like inference processes involving coherent finitely maxitive t conditional possibilities assessed on infinite sets of conditional events coherence of an assessment consisting of an arbitrary possibilistic prior and an arbitrary possibilistic likelihood function is proved thus a closed form expression for the envelopes of the relevant joint and posterior possibilities is given when t is the minimum or a strict t norm the notions of disintegrability and conglomerability are also studied and their relevance in the infinite version of the possibilistic bayes formula is highlighted

generalized possibility measures we define a generalized possibility measure gpm on a set x to be a function from the power set of x to the unit interval i 0 1 whereby the measure of a finite union of subsets of x equals the maximum of their measures we characterize gpms as the infima of downward directed families of possibility measures this helps to confer an intuitive meaning on gpms we discuss all directed families of possibility measures or equivalently of possibility distributions which generate a given gpm and we identify the largest such family we introduce extensions of gpms to real functions on ix obtained through a continuous triangular norm we provide characterizations and alternative descriptions for those extensions

subadjunction of log canonical divisors ii we extend a subadjunction formula of log canonical divisors as in kawamata contemp math 207 1997 79 88 to the case when the codimension of the minimal center is arbitrary by using the positivity of the hodge bundles

the extent of non conglomerability of finitely additive probabilities an arbitrary finitely additive probability can be decomposed uniquely into a convex combination of a countably additive probability and a purely finitely additive pfa one the coefficient of the pfa probability is an upper bound on the extent to which conglomerability may fail in a finitely additive probability with that decomposition if the probability is defined on a field the bound is sharp hence non conglomerability or equivalently non disintegrability characterizes finitely as opposed to countably additive probability nonetheless there exists a pfa probability which is simultaneously conglomerable over an arbitrary finite set of partitions neither conglomerability nor non conglomerability in a given partition is closed under convex combinations but the convex combination of pfa ultrafilter probabilities each of which cannot be made conglomerable in a common margin is singular with respect to any finitely additive probability that is conglomerable in that margin

shokurov s acc conjecture for log canonical thresholds on smooth varieties shokurov conjectured that the set of all log canonical thresholds on varieties of bounded dimension satisfies the ascending chain condition in this paper we prove that the conjecture holds for log canonical thresholds on smooth varieties and more generally on locally complete intersection varieties and on varieties with quotient singularities

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

possibility and necessity integrals abstract in this paper we introduce seminormed and semiconormed fuzzy integrals associated with confidence measures these confidence measures have a field of sets as their domain and a complete lattice as their codomain in introducing these integrals the analogy with the classical introduction of lebesgue integrals is explored and exploited it is amongst other things shown that our integrals are the most general integrals that satisfy a number of natural basic properties in this way our dual classes of fuzzy integrals constitute a significant generalization of sugeno s fuzzy integrals a large number of important general properties of these integrals is studied furthermore and most importantly the combination of seminormed fuzzy integrals and possibility measures on the one hand and semiconormed fuzzy integrals and necessity measures on the other hand is extensively studied it is shown that these combinations are very natural and have properties which are analogous to the combination of lebesgue integrals and classical measures using these results the very basis is laid for a unifying measure and integral theoretic account of possibility and necessity theory in very much the same way as the theory of lebesgue integration provides a proper framework for a unifying and formal account of probability theory

qualitative conditioning in an interval based possibilistic setting abstract possibility theory and possibilistic logic are well known uncertainty frameworks particularly suited for representing and reasoning with uncertain partial and qualitative information belief update plays a crucial role when updating beliefs and uncertain pieces of information in the light of new evidence this paper deals with conditioning uncertain information in a qualitative interval valued possibilistic setting the first important contribution concerns a set of three natural postulates for conditioning interval based possibility distributions we show that any interval based conditioning satisfying these three postulates is necessarily based on the set of compatible standard possibility distributions the second contribution consists in a proposal of efficient procedures to compute the lower and upper endpoints of the conditional interval based possibility distribution while the third important contribution provides a syntactic counterpart of conditioning interval based possibility distributions in case where these latter are compactly encoded in the form of possibilistic knowledge bases

existence of log canonical closures let f x u be a projective morphism of normal varieties and x a dlt pair we prove that if there is an open set u 0 u such that x u u 0 has a good minimal model over u 0 and the images of all the non klt centers intersect u 0 then x has a good minimal model over u as consequences we show the existence of log canonical compactifications for open log canonical pairs and the fact that the moduli functor of stable schemes satisfies the valuative criterion for properness

effectiveness of demailly s strong openness conjecture and related problems in this article stimulated by the effectiveness in berndtsson s solution of the openness conjecture and continuing our solution of demailly s strong openness conjecture we discuss conditions to guarantee the effectiveness of the conjecture and establish such an effectiveness result we explicitly point out a lower semicontinuity property of plurisubharmonic functions with a multiplier which is implicitly contained in guan and zhou 2014 arxiv 1401 7158 we also obtain optimal effectiveness of the conjectures of demailly kollar and jonsson mustat respectively

lagrange wavelets for signal processing this paper deals with the design of interpolating wavelets based on a variety of lagrange functions combined with novel signal processing techniques for digital imaging halfband lagrange wavelets b spline lagrange wavelets and gaussian lagrange lagrange distributed approximating functional daf wavelets are presented as specific examples of the generalized lagrange wavelets our approach combines the perceptually dependent visual group normalization vgn technique and a softer logic masking slm method these are utilized to rescale the wavelet coefficients remove perceptual redundancy and obtain good visual performance for digital image processing

ascending chain condition for log canonical thresholds and termination of log flips we prove that the ascending chain condition acc for log canonical lc thresholds in dimension d existence of log flips in dimension d and the log minimal model program lmmp in dimension d 1 imply termination of any sequence of log flips starting with a d dimensional effective lc pair and also imply termination of flops in dimension d in particular the latter terminations in dimension 4 follow from the alexeev borisov conjecture in dimension 3

possibilistic and probabilistic likelihood functions and their extensions common features and specific characteristics we deal with conditional probability in the sense of de finetti and with t conditional possibility with t a triangular norm we prove that dubois and prade conditional possibility is a particular min conditional possibility and then we compare the two notions of conditioning by an inferential point of view moreover we study t conditional possibilities as functions of the conditioning event putting in evidence analogies and differences with conditional probabilities this allows to characterize likelihood functions and their aggregations consistent either with a t conditional possibility or a conditional probability this analysis highlights many syntactical coincidences nevertheless the main difference is a weak form of monotonicity which arises only in the possibilistic case

boundedness of pluricanonical maps of varieties of general type using the techniques of 20 and 10 we prove that certain log forms may be lifted from a divisor to the ambient variety as a consequence of this result following 22 we show that for any positive integer n there exists an integer rn such that if x is a smooth projective variety of general type and dimension n then phi rk x colon x dasharrow mathbb p h 0 mathcal o x rk x is birational for all r rn

on the adjunction formula for 3 folds in characteristic p 5 in this article we prove a relative kawamata viehweg vanishing type theorem for plt 3 folds in characteristic p 5 we use this to prove the normality of minimal log canonical centers and the adjunction formula for codimension two subvarieties on mathbb q factorial 3 folds in characteristic p 5

conditioning in possibility theory with strict order norms the general order norm based approach of defining the conditional possibility a b as the greatest solution of the equation t x b a b with t a t norm and of defining the conditional necessity n a b as the smallest solution of the equation l x n cob n a cob with l a t conorm is carefully studied in particular it is investigated under which conditions the conditional possibilities resp necessities again establish a possibility resp necessity measure due to the new characterization of strict t norms resp t conorms presented in this paper it is shown that in general only a strict t norm resp t conorm can be used or in other words a transformation of the algebraic product resp probabilistic sum by means of an order preserving permutation of the unit interval this indicates that the algebraic product not only has a probabilistic but also a surprising possibilistic nature

non rational centers of log canonical singularities abstract we show that if x b is a log canonical pair with dim x d 2 whose non klt centers have dimension d then x has depth d 2 at every closed point