Physical activity is positively associated with college students' positive affect regardless of stressful life events during the COVID-19 pandemic

The study was designed to determine associations between physical activity (PA) and affect before and during COVID-19 stay-at-home orders and how change in PA predicted change in affect during this time. Before and during COVID-19 stay-at-home orders, college students (n = 107) completed assessments of PA, positive and negative affect, sleep quality, food insecurity, and stressful life events (during stay-at-home order only). Total minutes of PA was positively associated with positive affect before (B = 0.01, p < 0.01) and during (B = 0.01, p = 0.01) COVID-19 stay-at-home orders. Change in minutes of PA was positively associated with change in positive affect (B = 0.01, p = 0.01). Associations between PA and positive affect were not moderated by stressful life events. PA only predicted negative affect before COVID-19 stay-at-home orders (B = −0.003, p = 0.04). PA appears to enhance positive affect during a global pandemic. Findings have implications for PA as a tool for maintaining or enhancing mental health during a time of trauma and uncertainty.     

Grades of Probability Modality in the Law of Evidence

The paper presents an infinite hierarchy PR m [m = 1, 2, . . . ] of sound and complete axiomatic systems for modal logic with graded probabilistic modalities, which are to reflect what I have elsewhere called the Bolding-Ekelöf degrees of evidential strength as applied to the establishment of matters of fact in law-courts. Our present approach is seen to differ from earlier work by the author in that it treats the logic of these graded modalities not only from a semantical or model-theoretic viewpoint but from a prooftheoretical and axiomatic stance as well. A paramount feature of the approach is its use of so-called systematic frame constants as labels of diverse grades of probability. Apart from this novel feature our approach can be seen to go back to pioneering work by Lou Goble in 1970.     

Model Selection of Nested and Non-Nested Item Response Models Using Vuong Tests

Abstract

In this paper, we apply Vuong’s general approach of model selection to the comparison of nested and non-nested unidimensional and multidimensional item response theory (IRT) models. Vuong’s approach of model selection is useful because it allows for formal statistical tests of both nested and non-nested models. However, only the test of non-nested models has been applied in the context of IRT models to date. After summarizing the statistical theory underlying the tests, we investigate the performance of all three distinct Vuong tests in the context of IRT models using simulation studies and real data. In the non-nested case we observed that the tests can reliably distinguish between the graded response model and the generalized partial credit model. In the nested case, we observed that the tests typically perform as well as or sometimes better than the traditional likelihood ratio test. Based on these results, we argue that Vuong’s approach provides a useful set of tools for researchers and practitioners to effectively compare competing nested and non-nested IRT models.     

A geo-logical solution to the lottery paradox, with applications to conditional logic

We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams?? conditional logic and are exactly the rules that preserve a natural, logical structure over probabilistic credal states that we call probalogic. To motivate probalogic, we first expand classical logic to geo-logic, which fills the entire unit cube, and then we project the upper surfaces of the geo-logical cube onto the plane of probabilistic credal states by means of standard, linear perspective, which may be interpreted as an extension of the classical principle of indifference. Finally, we apply the geometrical/logical methods developed in the paper to prove a series of trivialization theorems against question-invariance as a constraint on acceptance rules and against rational monotonicity as an axiom of conditional logic in situations of uncertainty.     

A logical calculus for controlled monotonicity

In this paper we introduce a new deductive framework for analyzing processes displaying a kind of controlled monotonicity. In particular, we prove the cut-elimination theorem for a calculus involving series-parallel structures over partial orders which is built up from multi-level sequents, an interesting variant of Gentzen-style sequents. More broadly, our purpose is to provide a general, syntactical tool for grasping the combinatorics of non-monotonic processes.     

Bohrification of operator algebras and quantum logic

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families of projections indexed by a partially ordered set ${\mathcal{C}(A)}$ of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that ${\mathcal{C}(A)}$ consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Heyting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n × n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski?CMulvey) of the ??Bohrification?? ${\underline A}$ of A, which is a commutative Rickart C*-algebra in the topos of functors from ${\mathcal{C}A}$ to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns?CLakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hilbert space H and probability valuations on the internal Gelfand spectrum of ${\underline A}$ for A?=?B(H).     

Coherent Odds and Subjective Probability

A well-known Dutch book, due to de Finetti, shows how violations of the additivity law of probability theory (Pr(A∪B)=Pr(A)+Pr(B)−Pr(A∩B)) open the door to a sequence of bets leading to a sure loss. In this paper we show that in a market environment, when bookies act strategically, it may well be optimal for them to post incoherent (nonadditive) odds. This is true even when the bookie's own preferences are expected utility, provided she plays against at least two nonexpected utility bettors.     

Replacement in Logic

We study a range of issues connected with the idea of replacing one formula by another in a fixed (linguistic) context. The replacement core of a consequence relation ? is the relation holding between a set of formulas {A ₁, ..., A _m , ...} and a formula B when for every context C(·), we have C(A ₁), ..., C(A _m ), ...???C(B). Section 1 looks at some differences between which inferences are lost on passing to the replacement cores of the classical and intuitionistic consequence relations. For example, we find that while the inference from A and B to $A \land B$ , sanctioned by both these initial consequence relations, is retained on passage to the replacement core in the classical case, it is lost in the intuitionistic case. Further discussion of these two (and some other) logics occupies Sections 3 and 4. Section 2 looks at the m?=?1 case, describing A as replaceable by B according to ? when B is a consequence of A by the replacement core of ?, and inquiring as to which choices of ? render this induced replaceability relation symmetric. Section 5 investigates further conceptual refinements— such as a contrast between horizontal and vertical replaceability—suggested by some work of R. B. Angell and R. Harrop (and a comment on the latter by T. J. Smiley) in the 1950s and 1960s. Appendix 1 examines a related aspect of term-for-term replacement in connection with identity in predicate logic. Appendix 2 is a repository for proofs which would otherwise clutter up Section 3.     

Representing parametric order constraints in multi-trial applications of multinomial processing tree models

Binary multinomial processing tree (MPT) models parameterize the multinomial distribution over a set of J categories, such that each of its parameters, θ₁,θ₂,…,θ_S, is functionally independent and free to vary in the interval [0,1]. This paper analyzes binary MPT models subject to parametric order-constraints of the form 0?θ_s?θ_t?1. Such constraints arise naturally in multi-trial learning and memory paradigms, where some parameters representing cognitive processes would naturally be expected to be non-decreasing over learning trials or non-increasing over forgetting trials. The paper considers the case of one or more, non-overlapping linear orders of parametric constraints. Several ways to reparameterize the model to reflect the constraints are presented, and for each it is shown how to construct a new binary MPT that has the same number of parameters and is statistically equivalent to the original model with the order constraints. The results both extend the mathematical analysis of the MPT class as well as offering an approach to order restricted inference at the level of the entire class. An empirical example of this approach is provided.     

Noticing and responding in a discrimination based on a distinguishing element

In learning a successive go/no-go discrimination between a positive display consisting of the elements A and B, and negative display consisting of A-alone, pigeons first trained to peck A shift to pecking the distinguishing B element. In order to learn whether or not the shift to B is facilitated by B's function as a signal of the reinforcer, apart from the direct reinforcement of B responses, six arrangements of the elements with respect to the food reinforcer were used. Discrete trials were terminated by a single peck or after 4 sec. The A and B elements were dots of different color. The most critical comparison was between two groups, both of which received no reinforcement for a response directed to B. In one case, B signaled the reinforcer: An A response was reinforced when B was present but not when A appeared alone. In the other, B signaled the absence of a reinforcer: An A response was nonreinforced when B was present, while the response to A-alone was reinforced. During training and in extinction many more reponses were made to B when it signaled the reinforcer than when it signaled its absence. It is concluded that in a discrimination between AB positive and A negative the shift from pecking A to pecking B is facilitated by B's role as a signal for the reinforcer even on trials in which the peck is not made to B. Results from certain other groups showed that, unless pecks shifted to B within the positive display, pecks to A continued on the negative, A-alone trials as well as on the positive AB trials.     

A representation theorem for finite random scale systems

This paper investigates necessary and sufficient conditions on choice probabilities P_a,B (of picking an element a in an offered set B), for the existence of random variables U_a, satisfying the equation P_a,B = $\text{P}${U_a = max {U_b | b ∈ B}} for all nonempty finite subsets B in a fixed set A, and all a ∈ B. A complete solution to this representation problem is obtained in the case where A is finite. The proof of the representation theorem provides an algorithm to construct the random variables U_a, up to some uniqueness properties. Investigation of these uniqueness properties show that an important part of the ordinal structure of the underlying random variables can be recovered.     

Using Multidimensional Grief Theory to Explore the Effects of Deployment, Reintegration, and Death on Military Youth and Families

To date, the US military has made major strides in acknowledging and therapeutically addressing trauma and post-traumatic stress disorder (PTSD) in service members and their families. However, given the nature of warfare and high rates of losses sustained by both military members (e.g., deaths of fellow unit members) and military families (e.g., loss of a young parent who served in the military), as well as the ongoing threat of loss that military families face during deployment, we propose that a similar focus on grief is also needed to properly understand and address many of the challenges encountered by bereaved service members, spouses, and children. In this article, we describe a newly developed theory of grief (multidimensional grief theory) and apply it to the task of exploring major features of military-related experiences during the phases of deployment, reintegration, and the aftermath of combat death—especially as they impact children. We also describe implications for designing preventive interventions during each phase and conclude with recommended avenues for future research. Primary aims are to illustrate: (1) the indispensable role of theory in guiding efforts to describe, explain, predict, prevent, and treat maladaptive grief in military service members, children, and families; (2) the relevance of multidimensional grief theory for addressing both losses due to physical death as well as losses brought about by extended physical separations to which military children and families are exposed during and after deployment; and (3) a focus on military-related grief as a much-needed complement to an already-established focus on military-related PTSD.     

Rough approximation of pairwise comparisons described by multi‐attribute stochastic dominance

Given a finite set A of actions evaluated by a set of attributes, preferential information is considered in the form of a pairwise comparison table including pairs of actions from subset B⊂A described by stochastic dominance relations on particular attributes and a total order on the decision attribute. Using a rough sets approach for the analysis of the subset of preference relations, a set of decision rules is obtained, and these are applied to a set A\B of potential actions. The rough sets approach of looking for the reduction of the set of attributes gives us the possibility of operating on a multi‐attribute stochastic dominance for a reduced number of attributes. Copyright © 1999 John Wiley & Sons, Ltd.     

Defining reward value by cross-modal scaling

Researchers in comparative psychology often use different food rewards in their studies, with food values defined by a pre-experimental preference test. While this technique rank orders food values, it provides limited information about value differences because preferences may reflect not only value differences, but also the degree to which one good may “substitute” for another (e.g., one food may substitute well for another food, but neither substitutes well for water). We propose scaling the value of food pairs by a third food that is less substitutable for either food offered in preference tests (cross-modal scaling). Here, Cebus monkeys chose between four pairwise alternatives: fruits A versus B; cereal amount X versus fruit A and cereal amount Y versus fruit B where X and Y were adjusted to produce indifference between each cereal amount and each fruit; and cereal amounts X versus Y. When choice was between perfect substitutes (different cereal amounts), preferences were nearly absolute; so too when choice was between close substitutes (fruits); however, when choice was between fruits and cereal amounts, preferences were more modest and less likely due to substitutability. These results suggest that scaling between-good value differences in terms of a third, less-substitutable good may be better than simple preference tests in defining between-good value differences.     

A characterization of the concept of independence in knowledge structures

In knowledge space theory a knowledge structure provides a deterministic representation of the implications among the items in a given set Q. Concrete procedures for the efficient assessment of knowledge by means of a knowledge structure have been proposed by Doignon and Falmagne [Falmagne, J.-C., & Doignon, J.-P. (1988a). A class of stochastic procedures for the assessment of knowledge. British Journal of Mathematical and Statistical Psychology, 41, 1-23; Falmagne, J.-C., & Doignon, J.-P. (1988b). A markovian procedure for assessing the state of a system. Journal of Mathematical Psychology, 32, 232-258]. The primitive idea at the core of such procedures is that the (correct or wrong) answers of a student to a subset A⊆Q of items could be inferred from the answers to a subset B⊆Q of items that were previously presented to that student. Since B provides information about A, from the viewpoint of the teacher these two subsets are not independent. This idea of dependence vs. independence is formalized in this paper in terms of an independence relation on the power set of Q. A nice characterization of this relation allows to express an arbitrary knowledge structure as the combination of a number of substructures each of which is independent of each other. An algorithm is then proposed which checks for independence in a knowledge structure and decomposes this last into a collection of independent substructures.     

Interpolation in Extensions of First-Order Logic

We prove a generalization of Maehara’s lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig’s interpolation property. As a corollary, we obtain a direct proof of interpolation for (classical and intuitionistic) first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, (strict) partial and linear orders, and various intuitionistic order theories such as apartness and positive partial and linear orders.

     

Consequences of schematism

In his (2001a) and in some related papers, Tim Crane has maintained that intentional objects are schematic entities, in the sense that, insofar as being an intentional object is not a genuine metaphysical category, qua objects of thought intentional objects have no particular nature. This approach to intentionalia is the metaphysical counterpart of the later Husserl's ontological approach to the same entities, according to which qua objects of thought intentionalia are indifferent to existence. But to buy a metaphysically deflationary approach does not mean to buy an ontologically deflationary approach, according to which we have to accept all the intentional objects there apparently are. Being metaphysically deflationary on intentionalia rather means that from the ontological point of view one must really allow only for those intentionalia for which one is entitled to say that there are such things; typically, for which an ontological proof is available. From metaphysical schematism plus conditional, or partial, ontological committment to intentionalia, further interesting consequences follow. First, this theoretical combination allows one to deal with the ‘too-many entities’ problem (may one fail to accept an ontological proof for an entity of a given kind if she thinks that the entity we would have to be committed to is an entity of another kind?). Second, it allows one to deal with the ‘genuinely true report’ problem (how is it that if we exercise mindreading with respect to a somehow deluded person, we want our reports to come out as really, not merely fictionally, true?).     

Parts and differences

Part/whole is said in many ways: the leg is part of the table, the subset is part of the set, rectangularity is part of squareness, and so on. Do the various flavors of part/whole have anything in common? They may be partial orders, but so are lots of non-mereological relations. I propose an “upward difference transmission” principle: x is part of y if and only if x cannot change in specified respects while y stays the same in those respects.     

On two types of deviation from the matching law: bias and undermatching

Data on choice generally conform closely to an equation of the form: log(B₁/B₂)=a log(r₁/r₂+log k, where B₁ and B₂ are the frequencies of responding at Alternatives 1 and 2, r₁ and r₂ are the obtained reinforcement from Alternatives 1 and 2, and a and k are empirical constants. When a and k equal one, this equation is equivalent to the matching relation: B₁/B₂=r₁/r₂. Two types of deviation from matching can occur with this formulation: a and k not equal to one. In some experiments, a systematically falls short of one. This deviation is undermatching. The reasons for undermatching are obscure at present. Some evidence suggests, however, that factors favoring discrimination also favor matching. Matching (a=1) may represent the norm in choice when discrimination is maximal. When k differs from one, its magnitude indicates the degree of bias in choice. The generalized matching law predicts that bias should take this form (adding a constant proportion of responding to the favored alternative). Data from a variety of experiments indicate that it generally does.