A sequent calculus for a logic of contingencies

We introduce a sequent calculus that is sound and complete with respect to propositional contingencies, i.e., formulas which are neither provable nor refutable. Like many other sequent and natural deduction proof systems, this calculus possesses cut elimination and the subformula property and has a simple proof search mechanism.     

Determining individual preschoolers' preferences in a group arrangement

This study sought to determine the accuracy of an assessment format in which selection outcomes were delayed and probabilistic; these are unavoidable features of an assessment designed to determine preferences of multiple children simultaneously. During the single arrangement, preference hierarchies were established by having a child repeatedly select from among several foods and by sequentially restricting preferred items from the array. After being taught the associations between colored cards and the same food items, group assessments were conducted with 3 children simultaneously, in which each child chose a card and all children received the food correlated with a randomly selected card from those that had just been selected. The group assessment appeared to be accurate and perhaps more efficient for determining preferences; thus, we posit that this arrangement is suitable for determining context preferences of multiple children simultaneously.     

Asymptotic Densities in Logic and Type Theory

This paper presents a systematic approach for obtaining results from the area of quantitative investigations in logic and type theory. We investigate the proportion between tautologies (inhabited types) of a given length n against the number of all formulas (types) of length n. We investigate an asymptotic behavior of this fraction. Furthermore, we characterize the relation between number of premises of implicational formula (type) and the asymptotic probability of finding such formula among the all ones. We also deal with a distribution of these asymptotic probabilities. Using the same approach we also prove that the probability that randomly chosen fourth order type (or type of the order not greater than 4), which admits decidable lambda definability problem, is zero. Presented by Jacek Malinowski     

Base-rate neglect as a function of base rates in probabilistic contingency learning

When humans predict criterion events based on probabilistic predictors, they often lend excessive weight to the predictor and insufficient weight to the base rate of the criterion event. In an operant analysis, using a matching-to-sample paradigm, Goodie and Fantino (1996) showed that humans exhibit base-rate neglect when predictors are associated with criterion events through physical similarity. In partial replications of their studies, we demonstrated similar effects when the predictors resembled the criterion events in terms of similarly skewed base rates. Participants' predictions were biased toward the more (or less) frequent criterion event following the more (or less) frequent predictor. This finding adds to the growing evidence for pseudocontingencies (Fiedler & Freytag, 2004), a framework that stresses base-rate influences on contingency learning.     

Chunk and Permeate,a Paraconsistent Inference Strategy. Part I: The Infinitesimal Calculus

In this paper we introduce a paraconsistent reasoning strategy, Chunk and Permeate. In this, information is broken up into chunks, and a limited amount of information is allowed to flow between chunks. We start by giving an abstract characterisation of the strategy. It is then applied to model the reasoning employed in the original infinitesimal calculus. The paper next establishes some results concerning the legitimacy of reasoning of this kind – specifically concerning the preservation of the consistency of each chunk – and concludes with some other possible applications and technical questions.     

Statistics of Intuitionistic versus Classical Logics

For the given logical calculus we investigate the proportion of the number of true formulas of a certain length n to the number of all formulas of such length. We are especially interested in asymptotic behavior of this fraction when n tends to infinity. If the limit exists it is represented by a real number between 0 and 1 which we may call the density of truth for the investigated logic. In this paper we apply this approach to the intuitionistic logic of one variable with implication and negation. The result is obtained by reducing the problem to the same one of Dummett's intermediate linear logic of one variable (see [2]). Actually, this paper shows the exact density of intuitionistic logic and demonstrates that it covers a substantial part (more than 93%) of classical prepositional calculus. Despite using strictly mathematical means to solve all discussed problems, this paper in fact, may have a philosophical impact on understanding how much the phenomenon of truth is sporadic or frequent in random mathematics sentences.     

Evolution, Behavior Principles, And Developmental Systems: A Review Of Gottlieb’s Synthesizing Nature-nurture: Prenatal Roots Of Instinctive Behavior.

Gottlieb's developmental psychobiology book provides a base for reexamining the place of the experimental analysis of behavior in the life sciences. His experimental program demonstrating the critical function of the environment in the development of a species‐typical behavior helped force an acceptance of probabilistic epigenesis, the acknowledgment that the developmental genome‐environment system is fully interactional. (Indeed, nature vs. nurture is deader than a doornail.) The repercussions for evolutionary biology and the roles and categorizations of genes, behavior, and environment in behavior‐environment relations are explored in light of current knowledge, including specific implications for the experimental analysis of behavior.     

Measuring Probabilistic Reasoning: The Construction of a New Scale Applying Item Response Theory

Probabilistic reasoning skills are important in various contexts. The aim of the present study was to develop a new instrument (the Probabilistic Reasoning Scale – PRS) to accurately measure low levels of probabilistic reasoning ability in order to identify people with difficulties in this domain. Item response theory was applied to construct the scale, and to investigate differential item functioning (i.e., whether the items were invariant) across genders, educational levels, and languages. Additionally, we tested the validity of the scale by investigating the relationships between the PRS and several other measures. The results revealed that the items had a low level of difficulty. Nonetheless, the discriminative measures showed that the items can discriminate between individuals with different trait levels, and the test information function showed that the scale accurately assesses low levels of probabilistic reasoning ability. Additionally, through investigating differential item functioning, the measurement equivalence of the scale at the item level was confirmed for gender, educational status, and language (i.e., Italian and English). Concerning validity, the results showed the expected correlations with numerical skills, math‐related attitudes, statistics achievement, IQ, reasoning skills, and risky choices both in the Italian and British samples. In conclusion, the PRS is an ideal instrument for identifying individuals who struggle with basic probabilistic reasoning, and who could be targeted by specific interventions. Copyright © 2017 John Wiley & Sons, Ltd.     

Gentzen-Type Methods for Bilattice Negation

A general Gentzen-style framework for handling both bilattice (or strong) negation and usual negation is introduced based on the characterization of negation by a modal-like operator. This framework is regarded as an extension, generalization or re- finement of not only bilattice logics and logics with strong negation, but also traditional logics including classical logic LK, classical modal logic S4 and classical linear logic CL. Cut-elimination theorems are proved for a variety of proposed sequent calculi including CLS (a conservative extension of CL) and CLS_cw (a conservative extension of some bilattice logics, LK and S4). Completeness theorems are given for these calculi with respect to phase semantics, for SLK (a conservative extension and fragment of LK and CLS_cw, respectively) with respect to a classical-like semantics, and for SS4 (a conservative extension and fragment of S4 and CLScw, respectively) with respect to a Kripke-type semantics. The proposed framework allows for an embedding of the proposed calculi into LK, S4 and CL.     

Utility independence of multiattribute utility theory is equivalent to standard sequence invariance of conjoint measurement

Utility independence is a central condition in multiattribute utility theory, where attributes of outcomes are aggregated in the context of risk. The aggregation of attributes in the absence of risk is studied in conjoint measurement. In conjoint measurement, standard sequences have been widely used to empirically measure and test utility functions, and to theoretically analyze them. This paper shows that utility independence and standard sequences are closely related: utility independence is equivalent to a standard sequence invariance condition when applied to risk. This simple relation between two widely used conditions in adjacent fields of research is surprising and useful. It facilitates the testing of utility independence because standard sequences are flexible and can avoid cancelation biases that affect direct tests of utility independence. Extensions of our results to nonexpected utility models can now be provided easily. We discuss applications to the measurement of quality-adjusted life-years (QALY) in the health domain.