A saturation property of structures obtained by forcing with a compact family of random variables

A method how to construct Boolean-valued models of some fragments of arithmetic was developed in Krajicek (2011), with the intended applications in bounded arithmetic and proof complexity. Such a model is formed by a family of random variables defined on a pseudo-finite sample space. We show that under a fairly natural condition on the family (called compactness in K.(2011)) the resulting structure has a property that is naturally interpreted as saturation for existential types. We also give an example showing that this cannot be extended to universal types.Comment: preprint February 201

On the Complexity of the Numerically Definite Syllogistic and Related Fragments

In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of some recently proposed proof-systems for these logics.Comment: 24 pages 1 figur

The Minnesota Species of Aeshna with Notes on their Habits and Distribution (Odonata: Aeshnidae)

Apart from the well-known green darner, Anax junius, the species of Aeshna are the most familiar Minnesota Aeshnidae. These species are remarkably uniform in appearance. The basic body color is brown with blue, green, or yellow stripes on the thorax and with marks of similar color on the abdomen. Usually the spots of male specimens are blue, whereas green of various shades appears on most females. The individual species are not readily discernible to the novice collector

Generalizing Tsirelson's bound on Bell inequalities using a min-max principle

Bounds on the norm of quantum operators associated with classical Bell-type inequalities can be derived from their maximal eigenvalues. This quantitative method enables detailed predictions of the maximal violations of Bell-type inequalities.Comment: 4 pages, 2 figures, RevTeX4, replaced with published versio

New optimal tests of quantum nonlocality

We explore correlation polytopes to derive a set of all Boole-Bell type conditions of possible classical experience which are both maximal and complete. These are compared with the respective quantum expressions for the Greenberger-Horne-Zeilinger (GHZ) case and for two particles with spin state measurements along three directions.Comment: 10 page

Testing the bounds on quantum probabilities

Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as criteria for the validity of quantum mechanics.Comment: 9 pages, Revte

How much contextuality?

The amount of contextuality is quantified in terms of the probability of the necessary violations of noncontextual assignments to counterfactual elements of physical reality.Comment: 5 pages, 3 figure

Bell inequalities as constraints on unmeasurable correlations

The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations described by tree graphs. This implies classical representability of any set of correlations , , , and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for the unmeasurable correlation associated to different choices for B. The same analysis applies to the Hardy model and to the "perfect correlations" discussed by Greenberger, Horne, Shimony and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical representation is the only basis for arguments about violations of locality and causality.Comment: Some modifications have been done in order to improve clarity of presentation and comparison with other approache

A Bio-Logical Theory of Animal Learning

This article provides the foundation for a new predictive theory of animal learning that is based upon a simple logical model. The knowledge of experimental subjects at a given time is described using logical equations. These logical equations are then used to predict a subject’s response when presented with a known or a previously unknown situation. This new theory suc- cessfully anticipates phenomena that existing theories predict, as well as phenomena that they cannot. It provides a theoretical account for phenomena that are beyond the domain of existing models, such as extinction and the detection of novelty, from which “external inhibition” can be explained. Examples of the methods applied to make predictions are given using previously published results. The present theory proposes a new way to envision the minimal functions of the nervous system, and provides possible new insights into the way that brains ultimately create and use knowledge about the world