A Liouville function is an analytic function H : C → C with a Taylor series ∑ ∞ n=1 xn/an such the an’s form a “very fast growing” sequence of integers. In this paper we exhibit the complete first-order theory of the complex field expanded with H .

Two complexity problems in algebraic logic are surveyed: the satisfaction problem and the network satisfaction problem. Various complexity results are collected here and some new ones are derived. Many examples are given. The network satisfaction problem for most cylindric algebras of dimension four or more is shown to be intractable. Complexity is tied-in with the expressivity of a relation al...

We introduce and consider the problem of effectively organizing a population of workers of varying abilities. We assume that arriving tasks for the workforce are homogeneous, and that each is characterized by an unknown and onedimensional difficulty value x ∈ [0, 1]. Each worker i is characterized by their ability wi ∈ [0, 1], and can solve the task if and only if x ≤ wi. If a worker is unable ...

OBJECTIVE Children can be the only persons present in an emergency situation. Aim of the study was to evaluate the effects of a first aid course for 4-5-year-old kindergarten children given by a first aid instructor and kindergarten teachers. METHODS A mixed methods approach using both quantitative and qualitative methods was used to investigate the effects of teaching first aid in the kinder...

scan is an algorithm for reducing existential second-order logic formulae to equivalent simpler formulae, often first-order logic formulae. It is provably impossible for such a reduction to first-order logic to be successful for every second-order logic formula which has an equivalent first-order formula. In this paper we show that scan successfully computes the first-order equivalents of all S...

We introduce depth-first search with dynamic decomposition for counting the solutions of a binary CSP completely. In particular, we use the method for computing the number of minimal energy structures for model proteins.

The behavioural semantics of specifications with higher-order logical formulae as axioms is analyzed. A characterization of behavioural abstraction via behavioural satisfaction of formulae in which the equality symbol is interpreted as indistinguishability, which is due to Reichel and was recently generalized to the case of first-order logic by Bidoit et al, is further generalized to this case....

Pre anc* to which not far short of 500 children of J wSCh?01 or school age were referred last year. jn as dissatisfied with the task of acting merely Ca a first aid capacity relegated to picking up has es, anc* t^s' I trust healthy, dissatisfaction SlJ encouraged me to put forward here some hafesti?ns not only as to where things appear to as t6 ?one wrong but also, with less certainty, j0 how t...

BACKGROUND There is limited evidence indicating that laypersons trained in first aid provide better help, but do not help more often than untrained laypersons. This study investigated the effect of conventional first aid training versus conventional training plus supplementary training aimed at decreasing barriers to helping. METHODS The authors conducted a randomised controlled trial. After ...

Distributed representations (such as those based on embed-dings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We present a model theory/semantics for first order logic based on vectors of reals. We describe the model theory , discuss some interesting properties of such ...