The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic in (...) terms of appropriate matrix bundles and as semilattice-based logics, showing that the notion of consequence in these logics can be interpreted in terms of truth (or non-falsity) and meaningfulness (or meaninglessness) preservation. Finally, we use Płonka sums of matrices to investigate the pure variable inclusion companions of an arbitrary finitary logic. (shrink)

In the quantum logic approach, Bell inequalities in the sense of Pitowski are related with quasi hidden variables in the sense of Deliyannis. Some properties of hidden variables on effect algebras are discussed.

This paper will focus on a philosophically significant construction whose semantics brings together two important notions in Kit Fine’s philosophy, the notion of truthmaking and the notion of a variable embodiment, or its extension, namely what I call a ‘variable object’. This is the construction of definite NPs like 'the number of people that can fit into the bus', 'the book John needs to write', and 'the gifted mathematician John claims to be'. Such NPs are analysed as standing for variable (...) objects, which are part of the 'shallow', construction-driven ontology of natural language, yet are real. (shrink)

We propose to experimentally test non-deterministic time evolution in quantum mechanics by consecutive measurements of non-commuting observables on the same prepared state. While in the standard theory the measurement outcomes are uncorrelated, in a super-deterministic hidden variables theory the measurements would be correlated. We estimate that for macroscopic experiments the correlation time is too short to have been noticed yet, but that it may be possible with a suitably designed microscopic experiment to reach a parameter range where one would expect (...) a super-deterministic modification of quantum mechanics to become relevant. (shrink)

The practices of economists increase experimental reproducibility relative to those of selected psychologists but should not be universally adopted. Procedures criticized by Hertwig and Ortmann as producing variable data are valuable, instead, for generating questions. The procedure of choice should depend on the theoretical goal: measure a known factor or learn what factors are important and need to be measured.

The study aimed at identifying the personal variables and their effect in promoting job creation in Gaza Strip through business incubators. The researchers used the descriptive analytical approach to achieve the study objectives. The study population consisted of 92 of the pilot projects benefiting from the three business incubators in Gaza Strip (Palestinian Information Technology Incubator, UCAS Technology Incubator and Business and Technology Incubator). The study reached a number of results, the most important of which are the existence of statistically (...) significant differences on entrepreneurship attributed to each age as most of them are between the ages of 22-30, Gender for males, business incubator, scientific qualification for the specialties of information technology and engineering, and years of experience. Based on the findings, the researchers recommend focusing on university students in guiding them towards entrepreneurship and helping new graduates to start entrepreneurship. And to guide students to scientific disciplines that help them in entrepreneurship after graduation, whether starting a small business or self-employment, support females to entrepreneurship as most of the entrepreneurs are male, in addition to stimulating males as well. (shrink)

We examine a general class of variable-value population principles. Our particular focus is on the extent to which such principles can avoid the repugnant and sadistic conclusions. We show that if a mild limit property is imposed, avoidance of the repugnant conclusion implies the sadistic conclusion. This result generalizes earlier observations by showing that they apply to a substantially larger class of principles. Our second theorem states that, under the limit property, the axiom of mere addition also conflicts with avoidance (...) of the repugnant conclusion. This result is a consequence of a similar observation that appears in the earlier literature. (shrink)

The one-variable fragment of a first-order logic may be viewed as an “S5-like” modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have been obtained for special cases—notably, the modal counterparts $\mathrm {S5}$ and $\mathrm {MIPC}$ of the one-variable fragments of first-order classical logic and first-order intuitionistic logic, respectively—but a general approach, extending beyond first-order intermediate logics, has been lacking. To this end, a sufficient criterion is given in (...) this paper for the one-variable fragment of a semantically defined first-order logic—spanning families of intermediate, substructural, many-valued, and modal logics—to admit a certain natural axiomatization. More precisely, an axiomatization is obtained for the one-variable fragment of any first-order logic based on a variety of algebraic structures with a lattice reduct that has the superamalgamation property, using a generalized version of a functional representation theorem for monadic Heyting algebras due to Bezhanishvili and Harding. An alternative proof-theoretic strategy for obtaining such axiomatization results is also developed for first-order substructural logics that have a cut-free sequent calculus and admit a certain interpolation property. (shrink)

Words sound slightly different each time they are said, both by the same talker and across talkers. Rather than hurting learning, lab studies suggest that talker variability helps infants learn similar sounding words. However, very little is known about how much variability infants hear within a single talker or across talkers in naturalistic input. Here, we quantified these types of talker variability for highly frequent words spoken to 44 infants, from naturalistic recordings sampled longitudinally over a year (...) of life (from 6 to 17 months). We used non‐contrastive acoustic measurements (e.g., mean pitch, duration, harmonics‐to‐noise ratio) and holistic measures of sound similarity (normalized acoustic distance) to quantify acoustic variability. We find three key results. First, pitch‐based variability was generally lower for infants' top talkers than across their other talkers, but overall acoustic distance is higher for tokens from the top talker versus the others. Second, the amount of acoustic variability infants heard could not be predicted from, and thus was not redundant with, other properties of the input such as the number of talkers or tokens, or proportion of speech from particular sources (e.g., women, children, electronics). Finally, we find that patterns of pitch‐based acoustic variability heard in naturalistic input were similar to those found with in‐lab stimuli that facilitated word learning. This large‐scale quantification of talker variability in infants' everyday input sets the stage for linking naturally occurring variability “in the wild” to early word learning. (shrink)

Working speed as a latent variable reflects a respondent’s efficiency to apply a specific skill, or a piece of knowledge to solve a problem. In this study, the common assumption of many response time models is relaxed in which respondents work with a constant speed across all test items. It is more likely that respondents work with different speed levels across items, in specific when these items measure different dimensions of ability in a multidimensional test. Multiple speed factors are used (...) to model the speed process by allowing speed to vary across different domains of ability. A joint model for multidimensional abilities and multifactor speed is proposed. Real response time data are analyzed with an exploratory factor analysis as an example to uncover the complex structure of working speed. The feasibility of the proposed model is examined using simulation data. An empirical example with responses and response times is presented to illustrate the proposed model’s applicability and rationality. (shrink)

In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We take cues from Franz Berto’s recent work on topic to show an alignment between families of variable sharing properties and responses to the topic transparency of relevant implication and negation. We then introduce and defend novel variable sharing properties stronger than strong depth relevance—which we call cn-relevance and lossless cn-relevance—showing that the properties are satisfied by the weak (...) relevant logics and , respectively. We argue that such properties address a sort of semantic lossiness of strong depth relevance. (shrink)

This paper explores some issues about the choice of variables for causal representation and explanation. Depending on which variables a researcher employs, many causal inference procedures and many treatments of causation will reach different conclusions about which causal relationships are present in some system of interest. The assumption of this paper is that some choices of variables are superior to other choices for the purpose of causal analysis. A number of possible criteria for variable choice are described and defended within (...) a broadly interventionist approach to causation. (shrink)

Incomplete penetrance and variable expressivity are non‐Mendelian phenomena resulting in the lack of correlation between genotype and phenotype. Not withstanding the diversity in mechanisms, differential expression of homologous alleles within cells manifests as variations in penetrance and expressivity of mutations between individuals of the same genotype. These phenomena are seen most often in dominantly inherited diseases, implying that they are sensitive to concentration of the gene product. In this framework and the advances in understanding the role of microRNA (miRNA) in (...) fine‐tuning gene expression at translational level, we propose miRNA‐mediated regulation as a mechanism for incomplete penetrance and variable expressivity. The presence of miRNA binding sites at 3′ UTR, co‐expression of target gene–miRNA pairs for genes showing incomplete penetrance and variable expressivity derived from available data lend support to our hypothesis. Single nucleotide polymorphisms in the miRNA target site facilitate the implied differential targeting of the transcripts from homologous alleles. (shrink)

We argue that some sign language loci (i.e. positions in signing space that realize discourse referents) are both formal variables and simplified representations of what they denote; in other words, they are simultaneously logical symbols and pictorial representations. We develop a 'formal semantics with iconicity' that accounts for their dual life; the key idea ('formal iconicity') is that some geometric properties of signs must be preserved by the interpretation function. We analyze in these terms three kinds of iconic effects in (...) American and French Sign Language (ASL and LSF): (i) structural iconicity, where relations of inclusion and complementation among loci are directly reflected in their denotations; (ii) locus-external iconicity, where the high or low position of a locus in signing space has a direct semantic reflex, akin to the semantic contribution of gender features of pronouns; and (iii) locus-internal iconicity, where different parts of a structured locus are targeted by different directional verbs, as was argued by Liddell and Kegl. The resulting semantics combines insights of two traditions that have been sharply divided by recent debates. In line with the 'formalist camp' (e.g. Lillo-Martin and Klima, Neidle, and Sandler and Lillo-Martin), our theory treats loci as variables, and develops an explicit formal analysis of their behavior. But we also incorporate insights of the 'iconic camp', which emphasized the role of iconic constraints in sign language in general and in pronominals in particular (e.g. Cuxac, Taub, Liddell). However, this synthesis is only possible if formal semantics makes provisions for iconic requirements at the very core of its interpretive procedure. (An Appendix discusses relevant data from Italian Sign Language [LIS].). (shrink)

Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux.

What I wish to propose in the present paper is a new form of “career induction” for ambitious young logicians. The basic problem is this: if we look at the n-variable fragments of relevant propositional logics, at what point does undecidability begin? Focus, to be definite, on the logic R. John Slaney showed that the 0-variable fragment of R (where we allow the sentential con- stants t and f) contains exactly 3088 non-equivalent propositions, and so is clearly decidable. In the (...) opposite direction, I claimed in my paper of 1984 that the five variable fragment of R is undecidable. The proof given there was sketchy (to put the matter charitably), and a close examination reveals that although the result claimed is true, the proof given is incorrect. In the present paper, I give a detailed and (I hope) correct proof that the four variable fragments of the principal relevant logics are undecidable. This leaves open the question of the decidability of the n-variable fragments for n = 1, 2, 3. At what point does undecidability set in? (shrink)

Variation in transcription is due in large part to variability in transcribers' theoretical and methodological commitments and goals. This reply addresses issues raised in the commentaries on the article `Variation in Transcription' concerning problems of representing different discourse genres in transcripts, the question of how research relationships shape the transcription process, the intellectual and institutional contexts in which transcription occurs and circulates, and the injunction to consider the practices as opposed to the products of transcription.

In this paper, I argue that the Tractatus classifies names into constant names and variable names. A variable name, via the application of the existential quantifier against the background of picturing, picks out and denotes an unspecified object from the range of objects of the form shown by the relevant variable. A constant name labels an object picked out from a scope of the existential quantifier. I also refute two types of attempts to argue that the Tractarian relation between a (...) name and its meaning is not realist, and to explain why it is more reasonable to hold that it is. (shrink)

El concepto de capital social ha sido abordado con gran interés en las últimas décadas por la sociología y las teorías del desarrollo en general. Todas las investigaciones tanto teóricas como aplicadas, reconocen en esta forma de capital la ayuda recíproca y la cooperación como sus componentes fundamentales. Este artículo tiene por objetivo, desarrollar una reflexión respecto a la importancia de la variable ideológica para la constitución y desarrollo de capital social. En este contexto, la literatura especializada concuerda en la (...) necesidad de que existan valores, creencias y normas a partir de las cuales se articulen las redes de relaciones recíprocas y cooperativas. Estos elementos constituyen ideologías que, desde nuestra perspectiva, aseguran la formación de capital social que refuerza desde las bases de la sociedad, el funcionamiento pleno de la democracia. (shrink)

Decision-making is a complex action requiring efficient information processing. Specifically, in movement in which performance efficiency depends on reaction time, e.g., open-loop controlled movements, these processes may play a crucial role. Information processing includes three distinct stages, stimulus identification, response selection, and response programming. Mainly, response selection may play a substantial contribution to the reaction time and appropriate decision making. The duration of this stage depends on the number of possible choices an individual has to “screen” to make a proper (...) decision. Given that reaction time is crucial in many sports, the possibilities of reducing it through practice are very tempting. The information processing and its relationship to the manner an individual is practicing are discussed. Especially the variability of practice issues will be explored. In variable practice conditions, an individual has to react to one or more stimuli and has to produce one of the many variations of the same movement or different movements they learned. One has to identify a stimulus appropriately and has to select a response optimally, i.e., choosing from as few choices as possible to reduce the reaction time. On the other hand, in constant practice conditions, an individual can be exposed to one or many stimuli. Still, there is only one variation of the movement that can be executed in the presence of a learned stimulus. Based on the information processing theory and the results of the research focusing on variability of practice, I discuss how the practice conditions may affect reaction time and, as a result, the decision-making process. I conceptually frame the possible implications of practice conditions on decision making related to information processing. In this review, a possible mechanism and relationship between practice conditions and decision-making are presented. Future research directions are presented. (shrink)

Within a Complex Dynamic Systems Theory (CDST) framework, this longitudinal qualitative study explored the complex patterns and identified the degree of variability in three learners’ developmental process. Learners’ listening performance was tracked and examined every 6 weeks, followed by retrospective interviews and self-reflections every 7 weeks over the 43-month span. A series of CDST techniques were adopted for data analysis, including using min–max graphs to trace the minimum and maximum scores on the EFL learners’ listening developmental indices over time. (...) Monte-Carlo and Loess smoothing analyses were applied to gauge for degrees of variability. The results suggest that: (1) Min–max graphs and smoothed Loess curves depict flux developmental processes of learners’ L2 listening; (2) learners differed from each other in the degree of inter-individual variability in their listening developmental trajectory; and (3) occurrence of unanticipated patterns confirm that learners demonstrated personalized intra-individual variability within their unique listening developmental process. Results indicate that variability is a pattern characteristic of CDST both between and within individuals, and inform us about how Chinese EFL listeners’ language develops. We conclude by discussing the implications for researchers and practitioners who are concerned with learners’ developmental trajectories and unexpected changing patterns in the process of foreign language learning. (shrink)

Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables ‘x’ (...) and ‘y’ are synonymous, since sentences differing by the total, proper substitution of ‘x’ for ‘y’ always agree in meaning. We offer a precise interpretation of the challenge posed by (i) and (ii). We then develop some neglected passages of Tarski to show that his semantics for variables has the resources to resolve the antinomy without abandoning standard compositional semantics. (shrink)

A new theory to explain the emergence of firms and markets to carry out economic activity was presented in this author’s recent book . In this theory, called the Variability Approach,the multi-person firm emerges to carry out a production program, agreed upon during the preceding market period. This occurs when the participants in the program need to exchange among themselves additional information, additional to the information already exchanged during the preceding market period. The organization that emerges to facilitate the (...) required additional communication and to carry out the production program is called a multi-person firm. (shrink)

The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic in (...) terms of appropriate matrix bundles and as semilattice-based logics, showing that the notion of consequence in these logics can be interpreted in terms of truth (or non-falsity) and meaningfulness (or meaninglessness) preservation. Finally, we use Płonka sums of matrices to investigate the pure variable inclusion companions of an arbitrary finitary logic. -/- . (shrink)

Here I show that the one-variable fragment of several first-order relevant logics corresponds to certain S5ish extensions of the underlying propositional relevant logic. In particular, given a fairly standard translation between modal and one-variable languages and a permuting propositional relevant logic L, a formula $$\mathcal {A}$$ A of the one-variable fragment is a theorem of LQ (QL) iff its translation is a theorem of L5 (L.5). The proof is model-theoretic. In one direction, semantics based on the Mares-Goldblatt [15] semantics for (...) quantified L are transformed into ternary (plus two binary) relational semantics for S5-like extensions of L (for a general presentation, see Seki [26, 27]). In the other direction, a valuation is given for the full first-order relevant logic based on L into a model for a suitable S5 extension of L. I also discuss this work’s relation to finding a complete axiomatization of the constant domain, non-general frame ternary relational semantics for which RQ is incomplete [11]. (shrink)

There is surprising evidence that introspection of our phenomenal states varies greatly between individuals and within the same individual over time. This puts pressure on the notion that introspection gives reliable access to our own phenomenology: introspective unreliability would explain the variability, while assuming that the underlying phenomenology is stable. I appeal to a body of neurocomputational, Bayesian theory and neuroimaging findings to provide an alternative explanation of the evidence: though some limited testing conditions can cause introspection to be (...) unreliable, mostly it is our phenomenology itself that is variable. With this account of phenomenal variability, the occurrence of the surprising evidence can be explained while generally retaining introspective reliability. (shrink)

I introduce the notion of a ‘control variable’ which gives us a way of seeing how mental causation could be an unproblematic case of causation in general, rather than being some sui generis form of causation. Psychological variables may be the control variables for a system for which there are no physical control variables, even in a deterministic physical world. That explains how there can be psychological causation without physical causation, even in a deterministic physical world.

At 14 months, children appear to struggle to apply their fairly well-developed speech perception abilities to learning similar sounding words (e.g., bih/dih; Stager & Werker, 1997). However, variability in nonphonetic aspects of the training stimuli seems to aid word learning at this age. Extant theories of early word learning cannot account for this benefit of variability. We offer a simple explanation for this range of effects based on associative learning. Simulations suggest that if infants encode both noncontrastive information (...) (e.g., cues to speaker voice) and meaningful linguistic cues (e.g., place of articulation or voicing), then associative learning mechanisms predict these variability effects in early word learning. Crucially, this means that despite the importance of task variables in predicting performance, this body of work shows that phonological categories are still developing at this age, and that the structure of noninformative cues has critical influences on word learning abilities. (shrink)

Although skeptical of the prohibitive power of no-hidden-variables theorems, John Bell was himself responsible for the two most important ones. I describe some recent versions of the lesser known of the two (familiar to experts as the "Kochen-Specker theorem") which have transparently simple proofs. One of the new versions can be converted without additional analysis into a powerful form of the very much better known "Bell's Theorem," thereby clarifying the conceptual link between these two results of Bell.

This article reports an empirical investigation of the cognitive effort required to decide in multiattribute binary choice using a variation of the Additive Difference strategy. In contrast with other studies, this paper focuses on the effect of various context variables (rather than task variables) on cognitive effort. In order to select the context variables to be manipulated, we used the model proposed by Shugan (1980; J. Consumer Res. 75 (1980) 99). Our results indicate that there is a positive relationship between (...) the cognitive effort required to decide and the mean of the differences between the dimensions of the choice alternatives. We have also found an inverse relationship between cognitive effort and the variance of the differences between the dimensions of the choice alternatives. Finally, we have found that in negative correlation contexts the effort needed to decide is greater than in positive and null correlation contexts. (shrink)

Variability in the emotion regulation (ER) strategies one uses throughout daily life has been suggested to reflect adaptive ER ability and to act as a protective factor in mental health. Moreover, psychological inflexibility and persistent negative affect (or affective inertia) are key features of depression and other forms of mental illness and are often further exacerbated by rigid or overly passive regulatory behaviours. The current study investigated the hypothesis that ER variability might serve as a protective factor against (...) depressive symptoms and affective inertia. Using experience-sampling (N = 213), we tested whether two indictors of ER variability (between- and within-strategy SDs) were related to depressive symptoms and affective inertia. We found that people with higher between-strategy variability and within-strategy variability (specifically for reappraisal and distraction) reported fewer depressive symptoms. Both within- and between-strategy variability were negatively related to negative affective inertia. Between-strategy variability and negative affective inertia had unique effects on depression, when used as simultaneous predictors. Altogether, this study provides further evidence for the utility of ER as a factor buffering against depressive symptoms and particularly for the use of variable ER strategies. (shrink)

This article takes up a suggestion that the reason we cannot find certain hidden variable theories for quantum mechanics, as in Bell’s theorem, is that we require them to assign joint probability distributions on incompatible observables. These joint distributions are problematic because they are empirically meaningless on one standard interpretation of quantum mechanics. Some have proposed getting around this problem by using generalized probability spaces. I present a theorem to show a sense in which generalized probability spaces can’t serve as (...) hidden variable theories for quantum mechanics, so the proposal for getting around Bell’s theorem fails. 1 Introduction2 Bell’s Theorem and Classical Probability Spaces2.1 Bell’s derivation of the Bell inequalities2.2 Pitowsky’s derivation of the Bell inequalities3 Incompatible Observables4 Generalized Probability Spaces5 A ‘No-Go’ Theorem6 Conclusions. (shrink)

This paper demonstrates that the property of Replication Invariance, generally considered to be an innocuous requirement for the extension of fixed-population poverty comparisons to variable-population contexts, is incompatible with other plausible variable- and fixed-population axioms. This fact raises questions about what constitutes an appropriate headcount assessment of poverty, in terms of whether one should focus on the proportion, or the absolute numbers, of the population in poverty. This observation, in turn, has important implications for tracking poverty and setting targets for (...) its reduction or elimination. (shrink)

This work gives an extended presentation of the treatment of variable-binding operators adumbrated in [3:1993d]. Illustrative examples include elementary languages with quantifiers and lambda-equipped categorial languages. Some remarks are also offered to illustrate the philosophical import of the resulting picture. Particularly, a certain conception of logic emerges from the account: the view that logics are true theories in the model-theoretic sense, i.e. the result of selecting a certain class of models as the only “admissible” interpretation structures (for a given language).

The basic idea of rule-utilitarianism is that right action should be defined in terms of what would be required by rules which would maximize either actual or expected utility if those rules gained general acceptance, or perhaps general compliance. Rule-utilitarians face a dilemma. They must characterize 'general acceptance' either as 100% acceptance, or as something less. On the first horn of the dilemma, rule-utilitarianism in vulnerable to the charge of utopianism; on the second, it is open to the charge of (...) arbitrariness and lack of philosophical depth. I press this objection, and develop and defend an alternative version of rule-utilitarianism which can evade the dilemma. I call this new version 'variable-rate rule-utilitarianism'. (shrink)

Bell’s inequality is an empirical constrain on theories with hidden variables, which EPR argued are needed to explain observed perfect correlations if keeping locality. One way to deal with the empirical violation of Bell’s inequality is by openly embracing nonlocality, in a theory like the pilot-wave theory. Nonetheless, recent proposals have revived the possibility that one can avoid nonlocality by resorting to superdeterministic theories. These are local hidden variables theories which violate statistical independence which is one assumption of Bell’s inequality. (...) In this paper I compare and contrast these two hidden variable strategies: the pilot-wave theory and superdeterminism. I show that even if the former is nonlocal and the other is not, both are contextual. Nonetheless, in contrast with the pilot-wave theory, superdeterminist contextuality makes it impossible to test the theory (which therefore becomes unfalsifiable and unconfirmable) and renders the theory uninformative (measurement results tell us nothing about the system). It is questionable therefore whether a theory with these features is worth its costs. (shrink)

To relax the apparent tension between nonlocal hidden variables and relativity, we propose that the observable proper time is not the same quantity as the usual proper-time parameter appearing in local relativistic equations. Instead, the two proper times are related by a nonlocal rescaling parameter proportional to |ψ|2, so that they coincide in the classical limit. In this way particle trajectories may obey local relativistic equations of motion in a manner consistent with the appearance of nonlocal quantum correlations. To illustrate (...) the main idea, we first present two simple toy models of local particle trajectories with nonlocal time, which reproduce some nonlocal quantum phenomena. After that, we present a realistic theory with a capacity to reproduce all predictions of quantum theory. (shrink)

It is a classical result of Mortimer that $L^2$ , first-order logic with two variables, is decidable for satisfiability. We show that going beyond $L^2$ by adding any one of the following leads to an undecidable logic:– very weak forms of recursion, viz.¶(i) transitive closure operations¶(ii) (restricted) monadic fixed-point operations¶– weak access to cardinalities, through the Härtig (or equicardinality) quantifier¶– a choice construct known as Hilbert's $\epsilon$ -operator.In fact all these extensions of $L^2$ prove to be undecidable both for satisfiability, (...) and for satisfiability in finite structures. Moreover most of them are hard for $\Sigma^1_1$ , the first level of the analytical hierachy, and thus have a much higher degree of undecidability than first-order logic. (shrink)

Investigation of Indigenous concepts and their meanings is highly inspirational for contemporary science because these concepts represent adaptive solutions in various environmental and social milieus. Past research has shown that conceptualizations of consciousness can vary widely between cultural groups from different geographical regions. The present study explores variability among a few of the thousands of Indigenous cultural understandings of consciousness. Indigenous concepts of consciousness are often relational and inseparable from environmental and religious concepts. Furthermore, this exploration of variability (...) reveals the layers with which some Indigenous peoples understand their conscious experience of the world. Surprisingly, Indigenous understandings of global consciousness was found not to be in opposition to local consciousness. The final concluding section of this study discusses the usability of Indigenous concepts and meanings for recent scientific debates. (shrink)

The enormous scale of the available information and products on the Internet has necessitated the development of algorithms that intermediate between options and human users. These algorithms attempt to provide the user with relevant information. In doing so, the algorithms may incur potential negative consequences stemming from the need to select items about which it is uncertain to obtain information about users versus the need to select items about which it is certain to secure high ratings. This tension is an (...) instance of the exploration–exploitation trade‐off in the context of recommender systems. Because humans are in this interaction loop, the long‐term trade‐off behavior depends on human variability. Our goal is to characterize the trade‐off behavior as a function of human variability fundamental to such human–algorithm interaction. To tackle the characterization, we first introduce a unifying model that smoothly transitions between active learning and recommending relevant information. The unifying model gives us access to a continuum of algorithms along the exploration–exploitation trade‐off. We then present two experiments to measure the trade‐off behavior under two very different levels of human variability. The experimental results inform a thorough simulation study in which we modeled and varied human variability systematically over a wide rage. The main result is that exploration–exploitation trade‐off grows in severity as human variability increases, but there exists a regime of low variability where algorithms balanced in exploration and exploitation can largely overcome the trade‐off. (shrink)

We study model theory of random variables using finitary integral logic. We prove definability of some probability concepts such as having F as distribution function, independence and martingale property. We then deduce Kolmogorov's existence theorem from the compactness theorem.