A modular approach for item response theory modeling with the R package flirt

The new R package flirt is introduced for flexible item response theory (IRT) modeling of psychological, educational, and behavior assessment data. flirt integrates a generalized linear and nonlinear mixed modeling framework with graphical model theory. The graphical model framework allows for efficient maximum likelihood estimation. The key feature of flirt is its modular approach to facilitate convenient and flexible model specifications. Researchers can construct customized IRT models by simply selecting various modeling modules, such as parametric forms, number of dimensions, item and person covariates, person groups, link functions, etc. In this paper, we describe major features of flirt and provide examples to illustrate how flirt works in practice.     

Nice Embedding in Classical Logic

It is shown that a set of semi-recursive logics, including many fragments of CL (Classical Logic), can be embedded within CL in an interesting way. A logic belongs to the set iff it has a certain type of semantics, called nice semantics. The set includes many logics presented in the literature. The embedding reveals structural properties of the embedded logic. The embedding turns finite premise sets into finite premise sets. The partial decision methods for CL that are goal directed with respect to CL are turned into partial decision methods that are goal directed with respect to the embedded logics.     

Admissible Bases Via Stable Canonical Rules

We establish the dichotomy property for stable canonical multi-conclusionrules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics.     

Analytic Tableaux for all of <Emphasis Type="Italic">SIXTEEN</Emphasis><Subscript>3</Subscript>

In this paper we give an analytic tableau calculus P L _{1 6} for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ? _t , ? _f , ? _i , and ? under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment relations will in general require developing four tableaux, while proving that they are in the ? relation may require six.     

A Gentzen Calculus for Nothing but the Truth

In their paper Nothing but the Truth Andreas Pietz and Umberto Rivieccio present Exactly True Logic (ETL), an interesting variation upon the four-valued logic for first-degree entailment FDE that was given by Belnap and Dunn in the 1970s. Pietz & Rivieccio provide this logic with a Hilbert-style axiomatisation and write that finding a nice sequent calculus for the logic will presumably not be easy. But a sequent calculus can be given and in this paper we will show that a calculus for the Belnap-Dunn logic we have defined earlier can in fact be reused for the purpose of characterising ETL, provided a small alteration is made—initial assignments of signs to the sentences of a sequent to be proved must be different from those used for characterising FDE. While Pietz & Rivieccio define ETL on the language of classical propositional logic we also study its consequence relation on an extension of this language that is functionally complete for the underlying four truth values. On this extension the calculus gets a multiple-tree character—two proof trees may be needed to establish one proof.     

Gentzen-Style Sequent Calculus for Semi-intuitionistic Logic

The variety \({\mathcal{SH}}\) of semi-Heyting algebras was introduced by H. P. Sankappanavar (in: Proceedings of the 9th “Dr. Antonio A. R. Monteiro” Congress, Universidad Nacional del Sur, Bahía Blanca, 2008) [13] as an abstraction of the variety of Heyting algebras. Semi-Heyting algebras are the algebraic models for a logic HsH, known as semi-intuitionistic logic, which is equivalent to the one defined by a Hilbert style calculus in Cornejo (Studia Logica 98(1–2):9–25, 2011) [6]. In this article we introduce a Gentzen style sequent calculus GsH for the semi-intuitionistic logic whose associated logic GsH is the same as HsH. The advantage of this presentation of the logic is that we can prove a cut-elimination theorem for GsH that allows us to prove the decidability of the logic. As a direct consequence, we also obtain the decidability of the equational theory of semi-Heyting algebras.     

Automorphisms of the Lattice of Classical Modal Logics

In this paper we analyze the propositional extensions of the minimal classical modal logic system E, which form a lattice denoted as CExtE. Our method of analysis uses algebraic calculations with canonical forms, which are a generalization of the normal forms applicable to normal modal logics. As an application, we identify a group of automorphisms of CExtE that is isomorphic to the symmetric group S₄.     

Quantification in Some Non-normal Modal Logics

This paper offers a semantic study in multi-relational semantics of quantified N-Monotonic modal logics with varying domains with and without the identity symbol. We identify conditions on frames to characterise Barcan and Ghilardi schemata and present some related completeness results. The characterisation of Barcan schemata in multi-relational frames with varying domains shows the independence of BF and CBF from well-known propositional modal schemata, an independence that does not hold with constant domains. This fact was firstly suggested for classical modal systems by Stolpe (Logic Journal of the IGPL 11(5), 557–575, 2003), but unfortunately that work used only models and not frames.     

Obligation as Optimal Goal Satisfaction

Formalising deontic concepts, such as obligation, prohibition and permission, is normally carried out in a modal logic with a possible world semantics, in which some worlds are better than others. The main focus in these logics is on inferring logical consequences, for example inferring that the obligation O q is a logical consequence of the obligations O p and O (p → q). In this paper we propose a non-modal approach in which obligations are preferred ways of satisfying goals expressed in first-order logic. To say that p is obligatory, but may be violated, resulting in a less than ideal situation s, means that the task is to satisfy the goal p ∨ s, and that models in which p is true are preferred to models in which s is true. Whereas, in modal logic, the preference relation between possible worlds is part of the semantics of the logic, in this non-modal approach, the preference relation between first-order models is external to the logic. Although our main focus is on satisfying goals, we also formulate a notion of logical consequence, which is comparable to the notion of logical consequence in modal deontic logic. In this formalisation, an obligation O p is a logical consequence of goals G, when p is true in all best models of G. We show how this non-modal approach to the treatment of deontic concepts deals with problems of contrary-to-duty obligations and normative conflicts, and argue that the approach is useful for many other applications, including abductive explanations, defeasible reasoning, combinatorial optimisation, and reactive systems of the production system variety.     

A cage-based training,cognitive testing and enrichment system optimized for rhesus macaques in neuroscience research

In neurophysiological studies with awake non-human primates (NHP), it is typically necessary to train the animals over a prolonged period of time on a behavioral paradigm before the actual data collection takes place. Rhesus monkeys (Macaca mulatta) are the most widely used primate animal models in system neuroscience. Inspired by existing joystick- or touch-screen-based systems designed for a variety of monkey species, we built and successfully employed a stand-alone cage-based training and testing system for rhesus monkeys (eXperimental Behavioral Intrument, XBI). The XBI is mobile and easy to handle by both experts and non-experts; animals can work with only minimal physical restraints, yet the ergonomic design successfully encourages stereotypical postures with a consistent positioning of the head relative to the screen. The XBI allows computer-controlled training of the monkeys with a large variety of behavioral tasks and reward protocols typically used in systems and cognitive neuroscience research.     

On All Strong Kleene Generalizations of Classical Logic

By using the notions of exact truth (‘true and not false’) and exact falsity (‘false and not true’), one can give 16 distinct definitions of classical consequence. This paper studies the class of relations that results from these definitions in settings that are paracomplete, paraconsistent or both and that are governed by the (extended) Strong Kleene schema. Besides familiar logics such as Strong Kleene logic (K3), the Logic of Paradox (LP) and First Degree Entailment (FDE), the resulting class of all Strong Kleene generalizations of classical logic also contains a host of unfamiliar logics. We first study the members of our class semantically, after which we present a uniform sequent calculus (the SK calculus) that is sound and complete with respect to all of them. Two further sequent calculi (the \({{\bf SK}^\mathcal{P}}\) and \({\bf SK}^{\mathcal{N}}\) calculus) will be considered, which serve the same purpose and which are obtained by applying general methods (due to Baaz et al.) to construct sequent calculi for many-valued logics. Rules and proofs in the SK calculus are much simpler and shorter than those of the \({\bf SK}^{\mathcal{P}}\) and the \({\bf SK}^{\mathcal{N}}\) calculus, which is one of the reasons to prefer the SK calculus over the latter two. Besides favourably comparing the SK calculus to both the \({\bf SK}^{\mathcal{P}}\) and the \({\bf SK}^{\mathcal{N}}\) calculus, we also hint at its philosophical significance.     

Early Feeding,Child Behaviour and Parenting as Correlates of Problem Eating

Mealtimes are a common source of stress for families. Examining factors related to problem eating may provide markers by which to identify families requiring assistance and salient targets for treatment. The current study investigated parenting practices and cognitions, generalisation of child behavioural issues, and early feeding history as they relate to problem eating in typically developing young children. We compared a community sample of 105 parents of 1.5–6-year-old children via survey and observation with 96 parents seeking treatment for their child’s problem eating. History of problems with breastfeeding, χ²(1)?=?3.88, p?=?.049, and the transition to solids, χ²(1)?=?7.27, p?=?.007, were more common among problem eaters than comparisons. Problem eaters had a greater number of problem behaviours outside of mealtimes, F(1181)?=?10.88, p?=?.001, though not more frequently than comparisons and not to clinical levels, F(1181)?=?1.81, p?=?.181. Parents of problem eaters reported more unhelpful mealtime parenting strategies, F(1155)?=?22.59, p?<?.001, yet general parenting style was similar by group, F(1187)?=?0.42, p?=?.527. Parents’ cognitions about mealtimes, F(1155)?=?119.81, p?<?.001, including mealtime-specific self-efficacy, F(1155)?=?171.30, p?<?.001, were poorer amongst problem eaters, and were the only factors to predict problem eating in the total sample. General parenting self-efficacy was poorer in parents of problem eaters (Behaviour: F(1187)?=?42.36, p?<?.001; Setting: F(1187)?=?10.64, p?=?.001). Evidence of feeding issues in infancy may support early detection of and intervention for later problem eating. The significance of broader child behaviour is less clear. Parent factors, particularly those specific to mealtimes, and cognitive in nature (including mealtime parenting self-efficacy) clearly differentiated the groups, and represent important targets for intervention.     

Handling Inconsistencies in the Early Calculus

The early calculus is a popular example of an inconsistent but fruitful scientific theory. This paper is concerned with the formalisation of reasoning processes based on this inconsistent theory. First it is shown how a formal reconstruction in terms of a sub-classical negation leads to triviality. This is followed by the evaluation of the chunk and permeate mechanism (C&P) proposed by Brown and Priest in (Journal of Philosophical Logic, 33(4), 379–388, 2004) to obtain a non-trivial formalisation of the early infinitesimal calculus. Different shortcomings of this application of C&P as an explication of inconsistency tolerant reasoning are pointed out, both conceptual and technical. To remedy these shortcomings, an adaptive logic is proposed that allows for conditional permeations of formulas under the assumption of consistency preservation. First the adaptive logic is defined and explained and thereafter it is demonstrated how this adaptive logic remedies the defects C&P suffered from.     

Learning multiple rules simultaneously: Affixes are more salient than reduplications

Language learners encounter numerous opportunities to learn regularities, but need to decide which of these regularities to learn, because some are not productive in their native language. Here, we present an account of rule learning based on perceptual and memory primitives (Endress, Dehaene-Lambertz, & Mehler, Cognition, 105(3), 577–614, 2007; Endress, Nespor, & Mehler, Trends in Cognitive Sciences, 13(8), 348–353, 2009), suggesting that learners preferentially learn regularities that are more salient to them, and that the pattern of salience reflects the frequency of language features across languages. We contrast this view with previous artificial grammar learning research, which suggests that infants “choose” the regularities they learn based on rational, Bayesian criteria (Frank & Tenenbaum, Cognition, 120(3), 360–371, 2013; Gerken, Cognition, 98(3)B67–B74, 2006, Cognition, 115(2), 362–366, 2010). In our experiments, adult participants listened to syllable strings starting with a syllable reduplication and always ending with the same “affix” syllable, or to syllable strings starting with this “affix” syllable and ending with the “reduplication”. Both affixation and reduplication are frequently used for morphological marking across languages. We find three crucial results. First, participants learned both regularities simultaneously. Second, affixation regularities seemed easier to learn than reduplication regularities. Third, regularities in sequence offsets were easier to learn than regularities at sequence onsets. We show that these results are inconsistent with previous Bayesian rule learning models, but mesh well with the perceptual or memory primitives view. Further, we show that the pattern of salience revealed in our experiments reflects the distribution of regularities across languages. Ease of acquisition might thus be one determinant of the frequency of regularities across languages.     

Understanding Negation Implicationally in the Relevant Logic R

A star-free relational semantics for relevant logic is presented together with a sound and complete sequent proof theory (display calculus). It is an extension of the dualist approach to negation regarded as modality, according to which de Morgan negation in relevant logic is better understood as the confusion of two negative modalities. The present work shows a way to define them in terms of implication and a new connective, co-implication, which is modeled by respective ternary relations. The defined negations are confused by a special constraint on ternary relation, called the generalized star postulate, which implies definability of the Routley star in the frame. The resultant logic is shown to be equivalent to the well-known relevant logic R. Thus it can be seen as a reconstruction of R in the dualist framework.     

Approximating Cartesian Closed Categories in NF-Style Set Theories

I criticize, but uphold the conclusion of, an argument by McLarty to the effect that New Foundations style set theories don’t form a suitable foundation for category theory. McLarty’s argument is from the fact that Set and Cat are not Cartesian closed in NF-style set theories. I point out that these categories do still have a property approximating Cartesian closure, making McLarty’s argument not conclusive. After considering and attempting to address other problems with developing category theory in NF-style set theories, I conclude that NF-style set theories are not a good foundation for category theory, because of numerous limitations introduced by their stratification restrictions.     

The importance of meta-ethics in engineering education

Our shared moral framework is negotiated as part of the social contract. Some elements of that framework are established (tell the truth under oath), but other elements lack an overlapping consensus (just when can an individual lie to protect his or her privacy?). The tidy bits of our accepted moral framework have been codified, becoming the subject of legal rather than ethical consideration. Those elements remaining in the realm of ethics seem fragmented and inconsistent.Yet, our engineering students will need to navigate the broken ground of this complex moral landscape. A minimalist approach would leave our students with formulated dogma—principles of right and wrong such as the National Society for Professional Engineers (NSPE) Code of Ethics for Engineers—but without any insight into the genesis of these principles. A slightly deeper, micro-ethics approach would teach our students to solve ethical problems by applying heuristics—giving our students a rational process to manipulate ethical dilemmas using the same principles simply referenced a priori by dogma. A macro-ethics approach—helping students to inductively construct a posteriori principles from case studies—goes beyond the simple statement or manipulation of principles, but falls short of linking personal moral principles to the larger, social context. Ultimately, it is this social context that requires both the application of ethical principles, and the negotiation of moral values—from an understanding of meta-ethics.The approaches to engineering ethics instruction (dogma, heuristics, case studies, and meta-ethics) can be associated with stages of moral development. If we leave our students with only a dogmatic reaction to ethical dilemmas, they will be dependent on the ethical decisions of others (a denial of their fundamental potential for moral autonomy). Heuristics offers a tool to deal independently with moral questions, but a tool that too frequently reduces to casuistry when rigidly applied to “simplified” dilemmas. Case studies, while providing a context for engineering ethics, can encourage the premature analysis of specific moral conduct rather than the development of broad moral principles—stifling our students’ facility with meta-ethics. Clearly, if a moral sense is developmental, ethics instruction should lead our students from lower to higher stages of moral development.     

Proofs,pictures, and Euclid

Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs in the Elements in particular, the received view is that Euclid’s reliance on geometric diagrams undermines his efforts to develop a gap-free deductive theory. The central difficulty concerns the generality of the theory. How can inferences made from a particular diagrams license general mathematical results? After surveying the history behind the received view, this essay provides a contrary analysis by introducing a formal account of Euclid’s proofs, termed Eu. Eu solves the puzzle of generality surrounding Euclid’s arguments. It specifies what diagrams Euclid’s diagrams are, in a precise formal sense, and defines generality-preserving proof rules in terms of them. After the central principles behind the formalization are laid out, its implications with respect to the question of what does and does not constitute a genuine picture proof are explored.     

Normal Modal Logics Determined by Aligned Clusters

We consider the family of logics from NExt(KTB) which are determined by linear frames with reflexive and symmetric relation of accessibility. The condition of linearity in such frames was first defined in the paper [9]. We prove that the cardinality of the logics under consideration is uncountably infinite.     

A Bayesian approach to estimating variance components within a multivariate generalizability theory framework

In many behavioral research areas, multivariate generalizability theory (mG theory) has been typically used to investigate the reliability of certain multidimensional assessments. However, traditional mG-theory estimation—namely, using frequentist approaches—has limits, leading researchers to fail to take full advantage of the information that mG theory can offer regarding the reliability of measurements. Alternatively, Bayesian methods provide more information than frequentist approaches can offer. This article presents instructional guidelines on how to implement mG-theory analyses in a Bayesian framework; in particular, BUGS code is presented to fit commonly seen designs from mG theory, including single-facet designs, two-facet crossed designs, and two-facet nested designs. In addition to concrete examples that are closely related to the selected designs and the corresponding BUGS code, a simulated dataset is provided to demonstrate the utility and advantages of the Bayesian approach. This article is intended to serve as a tutorial reference for applied researchers and methodologists conducting mG-theory studies.