An often mentioned obstacle for the use of Dempster-Shafer theory for the handling of uncertainty in expert systems is the computational complexity of the theory. One cause of this complexity is the fact that in Dempster-Shafer theory the evidence is represented by a belief function which is induced by a basic probability assignment, i.e. a probability measure on the powerset of possible answers to a question, and not by a probability measure on the set of possible answers to a question, like in a Bayesian approach. In this paper, we define a Bayesian approximation of a belief function and show that combining the Bayesian approximations of belief functions is computationally less involving than combining the belief functions themselves, while in many practical applications replacing the belief functions by their Bayesian approximations will not essentially affect the result.

Interpretations are much used in metamathematics. The first application that comes to mind is their use in reductive Hilbert-style programs. Think of the kind of program proposed by Simpson, Feferman or Nelson (see Simpson[1988], Feferman[1988], Nelson[1986]). Here they serve to compare the strength of theories, or better to prove

We answer a question of Lambek and Scott (see [LS] p.99) by proving the following: Theorem. Let 9vt be a C-monoid, with C-structure (7t, 7t', £, (_)*, <_,_>). Then there exists a cartesian closed category A with exactly two objects U and T, such that End(U) =!M The construction of. is entirely by hand. The intuitive idea is as follows.!may be viewed as a collection of endomorphisms of a set U. Let T _ { *I be a one-point set; then u- X*.u is a one-to-one correspondence between U and the set of all functions from T to U. Now if. is a cartesian closed category with just U and T for its objects, where T is terminal, then in A we must have Hom(U,U) = Hom(TxU,U) = Hom(T,UU) = _ Hom(T,U); so if we put Hom(U,U) = iM, and like to think of Hom(T,U) as HomSets({*},U), we must have M _ U, as sets. Since it does not matter much what the elements of U are, we take M=U. Then we have functions ft _ k*.f: ku.*:U-{*}, we have (X*.f) o (ku.*) = ku f: U- U. *I- U for every f E U. Composing with o

Univvz... ty o6 ULicechx. Let NNIL (No Nestings of Implication to the Left) be the fragment of IpL (intuitionistic propositional logic) in which the antecedent of any implication is always prime. The following strong interpolation theorem is proved: if IpL}-A+B and A or B is in NNIL, then there is an interpolant I in KNIT The proof consists in constructing I from a proof of A+B in a sequent calculus system by means of a variant of a method devised by K. Schutte. This settles a question posed by A.

as UtAech.t ty I, r n tpri n- er es No. 29 Department of Philosophy

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It is always annoying to read what someone else has to say about one's papers. The writer-- usually a reviewer-- inevitably picks out some small point of tangential interest and expands on it. Such is what I intend to do to McAloon 1975 here: McAloon prefaces his paper with an abstract which does not even mention the result on which I, perversely enough, wish to focus. This result, as is so subtly hinted in the title of the present note, is the uniqueness of a certain kind of Rosser sentence for ZF. Rosser's original sentence is easily described. Let Prov(x,y) express "x proves y (or, more precisely: the derivation coded by x proves the formula coded by y "). The Rosser sentence is then any sentence (p provably satisfying cp

This paper can best be viewed as a portrait in miniature of a fascinating structure: a. descending hierarchy of reflection principles. Ascending hierarchies of reflection principles are amply studied, e.g. in Feferman's great paper Transfinite Recursive Progressions of Axiomatic Theories (Feferman[l962]). The problem adressed in the study of ascending hierarchies is: what is the a

Depa. tmeht- o j--Ph:.foph y ty a3 4eeh Uvu.velmj a-ftovcc:ngen- D:---Hoeh.zema Depantmen;s o Phyzia and Phita4vphy

$os, * soy x,71 ly`y Department of Philosophy University of UtrechtApplications of constructive logic to sheaf constructions in toposes Paper corresponding to the talk delivered at