The importance of mathematics in the context of the scientific and technological development of humanity is determined by the possibility of creating mathematical models of the objects studied under the different branches of Science and Technology. The arithmetisation process that took place during the nineteenth century consisted of the quest to discover a new mathematical reality in which the validity of logic would stand as something essential and central. Nevertheless, in contrast to this process, the development of mathematical analysis within (...) a framework that largely involves intuition and geometry is a fact that cannot go unnoticed amongst the mathematics community, as we shall show in this paper through the research made by Bernhard Riemann on complex variables. (shrink)

The satisfiability and finite satisfiability problems for the two-variable fragment of first-order logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are coded succinctly.

Throughout the development of finite model theory, the fragments of first-order logic with only finitely many variables have played a central role. This survey gives an introduction to the theory of finite variable logics and reports on recent progress in the area.For each k ≥ 1 we let Lk be the fragment of first-order logic consisting of all formulas with at most k variables. The logics Lk are the simplest finite-variable logics. Later, we are going to consider infinitary (...) variants and extensions by so-called counting quantifiers.Finite variable logics have mostly been studied on finite structures. Like the whole area of finite model theory, they have interesting model theoretic, complexity theoretic, and combinatorial aspects. For finite structures, first-order logic is often too expressive, since each finite structure can be characterized up to isomorphism by a single first-order sentence, and each class of finite structures that is closed under isomorphism can be characterized by a first-order theory. The finite variable fragments seem to be promising candidates with the right balance between expressive power and weakness for a model theory of finite structures. This may have motivated Poizat [67] to collect some basic model theoretic properties of the Lk. Around the same time Immerman [45] showed that important complexity classes such as polynomial time or polynomial space can be characterized as collections of all classes of finite structures definable by uniform sequences of first-order formulas with a fixed number of variables and varying quantifier-depth. (shrink)

This commentary addresses the complexities of representation in sociolinguistic transcripts, considering the meaning potentials of different representational choices at the level of both ideology and identity. It considers the kinds of authenticity and evidence that are indexed by simplified versus more detailed transcripts, suggesting that a simplified transcript may give more direct access to elements of the original speaker's voice. Second, it discusses the role of transcripts as scholarly texts, and questions their use as sociolinguistic records suitable for reinterpretation by (...) scholars who do not have access to the original recordings. Third, it emphasizes that the use of non-standard orthographies is an unreliable source of data on sociolinguistic variation, because few authors use non-standard forms in consistent and principled ways. Fourth, it proposes that translations may take different forms depending on whether they are efforts to be `faithful' to `authentic' speech in the target versus the source language. Finally, it reflects on the act of transcription as part of professional practice and identity among linguists. (shrink)

Relational complexity theory has important virtues, but the present model omits key aspects and evidence. In contrast, skill theory specifies (1) a detailed series of developmental changes in relational complexity from birth to age 30, (2) processes of interaction of content and structure that produce variability in complexity, (3) the role of cortical development, and (4) empirical criteria for complexity levels, including developmental discontinuities. Many findings support these specifications.

The main result of the present paper is that the variable-free fragment of logic K*, the logic with a single K-style modality and its “reflexive and transitive closure,” is EXPTIMEcomplete. It is then shown that this immediately gives EXPTIME-completeness of variable-free fragments of a number of known EXPTIME-complete logics. Our proof contains a general idea of how to construct a polynomial-time reduction of a propositional logic to its n-variable—and even, in the cases of K*, PDL, CTL, ATL, and some others, (...) variable-free—fragments. Complexity of countermodels for such fragments is considered. (shrink)

The unreduced many-body interaction problem solution, absent in usual science framework, reveals a new quality of emerging multiple, equally real but mutually incompatible system configurations, or “realisations”, giving rise to the universal concept of dynamic complexity and chaoticity. Their imitation by a single, “average” realisation or trajectory in usual theory (corresponding to postulated “exact” or perturbative problem solutions) is a rough simplification of reality underlying all stagnating and emerging problems of conventional (unitary) science, often in the form of missing, or (...) “dark”, entities and “hidden variables”. We show how the application of unreduced interaction problem solution and the ensuing concept of dynamic complexity provides the desired causally complete and intrinsically unified solutions to respective unitary science problems in the entire range of complexity levels, from elementary particles and cosmology to emergent consciousness and modern development crisis, implying real, essential and urgently needed progress. (shrink)

Drawing on a corpus of telephone conversational data, this study examines a collection of self-deprecations in Korean conversations. Detailed analyses of self-deprecations in larger fragments than minimal adjacency pair sequences illustrate the multifaceted nature of self-deprecation. Self-deprecation entails not only deprecatory assessments, but complaint or trouble talk about one’s shortcomings, reenactment of experiences or moments that support the deprecation, and discussion of how to remedy problems. The study further shows that self-deprecation is not a solitary but an interactionally organized practice. (...) The speaker’s repeated self-deprecations elicit a series of different responses from the recipient, such as positive reframing, downgrading the deprecator’s problem, and recommending solutions to the deprecator’s problem. Many instances of self-deprecation suggest that it can be an important resource for building motivation, responsibility, and a sense of affiliation and solidarity with other social members. (shrink)

Caplan & Waters's model differentiating levels of processing and the role of working memory is important and likely right. However, their claim rests on a lack of correlation between working memory and structural complexity. We examine sources of variability in these measures that remain unaccounted for (by anyone), variability that muddies a straightforward claim that the lack of correlation is cleanly established.

Fundamental analytic, algebraic, and geometric properties of generalized Hamiltonian (Birkhoffian) theory are compared with the properties of a covering unitary phase-space formulation based on complex variables of the form (p+iq). Technical advantages in the unitary phase-space formulation are illustrated by a detailed discussion of the one-dimensional extended damped harmonic oscillator. One advantage is the ability to fully describe nonconservative constraint forces within a globally conservative system. Another advantage is that wider classes of gauge transformations are available to simplify (...) the construction of smooth solution manifolds. (shrink)

This paper investigates three morphosyntactic alternations in Estonian – those between the exterior locative cases allative, adessive and ablative and the corresponding postpositionspeale‘onto’,peal‘on’ andpealt‘off’. Based on the Complexity Principle (e.g., Rohdenburg, Günter. 2002. Processing complexity and the variable use of prepositions in English. In Hubert Cuyckens & Günter Radden (eds.),Perspectives on prepositions, 79–100. Tübingen: Niemeyer), we expect cognitively more complex constructions to use more explicit (i.e., morphologically more substantial) marking by means of a postposition. Further, we expect variation to (...) be conditioned similarly in all three semantic categories. For each of the three alternations, a random sample of the two outcomes (case vs. postposition) from the Estonian National Corpus is used, resulting in 3,000 data points. Using properties of the Landmark phrase as independent variables in Bayesian mixed-effects logistic regression models, we predict the choice of postpositions over case-marked realisations. Of the patterns found, only the frequency-related one supports our complexity-related hypothesis. We conclude that the Complexity Principle, in its general form, has little explanatory power for the Estonian constructions at hand and, in particular, that the derived principle of ‘analytic support’ is not generally applicable. We show, however, that the grammatical knowledge of Estonian exterior locative cases and the corresponding postpositions is regulated by our three factors in a relatively uniform way. (shrink)

It is shown in this article that many positions that are usually considered incompatible or antagonistic can be synthesized into a unified framework, creating a model of transpersonal development based around plurality and complexity. The model focuses on evolutionary developmental biology as well as around psychological theories. A large degree of variability in the nature of transpersonal experience in the life cycle is to be expected, due to differences in both the “timing of onset” of transpersonal characteristics and the “length (...) of developmental period.” Numerous developmental patterns are identified, using the work of some prominent transpersonal theorists. (shrink)

Modal dependence logic was introduced recently by Väänänen. It enhances the basic modal language by an operator = (). For propositional variables p 1, . . . , p n , = (p 1, . . . , p n-1, p n ) intuitively states that the value of p n is determined by those of p 1, . . . , p n-1. Sevenster (J. Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for (...) nondeterministic exponential time.In this paper we consider fragments of modal dependence logic obtained by restricting the set of allowed propositional connectives. We show that satisfiability for poor man’s dependence logic, the language consisting of formulas built from literals and dependence atoms using ${\wedge, \square, \lozenge}$ (i. e., disallowing disjunction), remains NEXPTIME-complete. If we only allow monotone formulas (without negation, but with disjunction), the complexity drops to PSPACE-completeness.We also extend Väänänen’s language by allowing classical disjunction besides dependence disjunction and show that the satisfiability problem remains NEXPTIME-complete. If we then disallow both negation and dependence disjunction, satisfiability is complete for the second level of the polynomial hierarchy. Additionally we consider the restriction of modal dependence logic where the length of each single dependence atom is bounded by a number that is fixed for the whole logic. We show that the satisfiability problem for this bounded arity dependence logic is PSPACE-complete and that the complexity drops to the third level of the polynomial hierarchy if we then disallow disjunction.In this way we completely classify the computational complexity of the satisfiability problem for all restrictions of propositional and dependence operators considered by Väänänen and Sevenster. (shrink)

This paper is motivated by the desire to formulate a relativistically covariant hidden-variable particle trajectory interpretation of the quantum theory of the vector field that is formulated in such a way as to allow the inclusion of gravity. We present a methodology for calculating the flows of rest energy and a conserved density for the massive vector field using the time-like eigenvectors and eigenvalues of the stress-energy-momentum tensor. Such flows may be used to define particle trajectories which follow the flow. (...) This work extends our previous work which used a similar procedure for the scalar field. The massive, spin-one, complex vector field is discussed in detail and the flows of energy-momentum are illustrated in a simple example of standing waves in a plane. (shrink)

Network Analysis is considered as a new method that challenges Latent Variable models in inferring psychological attributes. With Network Analysis, psychological attributes are derived from a complex system of components without the need to call on any latent variables. But the ontological status of psychological attributes is not adequately defined with Network Analysis, because a psychological attribute is both a complex system and a property emerging from this complex system. The aim of this article is to (...) reappraise the legitimacy of latent variable models by engaging in an ontological and epistemological discussion on psychological attributes. Psychological attributes relate to the mental equilibrium of individuals embedded in their social interactions, as robust attractors within complex dynamic processes with emergent properties, distinct from physical entities located in precise areas of the brain. Latent variables thus possess legitimacy, because the emergent properties can be conceptualized and analyzed on the sole basis of their manifestations, without exploring the upstream complex system. However, in opposition with the usual Latent Variable models, this article is in favor of the integration of a dynamic system of manifestations. Latent Variables models and Network Analysis thus appear as complementary approaches. New approaches combining Latent Network Models and Network Residuals are certainly a promising new way to infer psychological attributes, placing psychological attributes in an inter-subjective dynamic approach. Pragmatism-realism appears as the epistemological framework required if we are to use latent variables as representations of psychological attributes. (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)

Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions have universal aesthetic appeal. Perceptual and aesthetic responses to visual complexity have been more varied with findings suggesting both linear (Forsythe et al., 2011) and curvilinear (...) (Berlyne, 1970) relationships. Individual differences have been found to account for many of the differences we see in aesthetic responses but some, such as culture, have received little attention within the fractal and complexity research fields. This 2-study paper aims to test preference responses to fractal dimension and visual complexity, using a large cohort (N=443) of participants from around the world to allow universality claims to be tested. It explores the extent to which age, culture and gender can predict our preferences for fractally complex patterns. Following exploratory analysis that found strong correlations between fractal dimension and visual complexity, a series of linear mixed-effect models were implemented to explore if each of the individual variables could predict preference. The first tested a linear complexity model (likelihood of selecting the more complex image from the pair of images) and the second a mid-range fractal dimension model (likelihood of selecting an image within mid-range). Results show that individual differences can reliably predict preferences for complexity across culture, gender and age. However, in fitting with current findings the mid-range models show greater consistency in preference not mediated by gender, age or culture. This paper supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying preference but also highlights the fragility of universal claims by demonstrating individual differences in preference for the interrelated concept of visual complexity. This highlights a current stalemate in the field of empirical aesthetics. (shrink)

A new etiological model is proposed for schizophrenia that combines variability‐enhancing nonspecific factors acting during development with more specific risk factors. This model is better suited than the current etiological models of schizophrenia, based on the risk factors paradigm, for predicting and/or explaining several important findings about schizophrenia: high co‐morbidity rates, low specificity of many risk factors, and persistence in the population of the associated genetic polymorphisms. Compared with similar models, e.g., de‐canalization, common psychopathology factor, sexual‐selection, or differential sensitivity to (...) the environment, this proposal is more general and integrative. Recently developed research methods have proven the existence of genetic and environmental factors that enhance developmental variability. Applying such methods to newly collected or already available data can allow for testing the hypotheses upon which this model is built. If validated, this model may change the understanding of the etiology of schizophrenia, the research models, and preventionbrk paradigms. (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)

This paper considers the impact of complexity theory on the way in which we see propositions corresponding to the reality that they describe, and our concept of truth in that context. A contingently associated idea is the atomistic expectation that we can reduce language to primitive units of meaning, and tie those in with agreed units of experience. If we see both language and the reality that it describes and explains as complex, this position becomes difficult to maintain. Complexity (...) theory, with its emphasis on non‐linear and dynamic interactions between multiple variables, within indeterminate and transient systems, supports the case for a connectionist and holistic analysis. Theories are more likely to be under‐determined by evidence and open to interpretation, with the potential for ‘certainties’ weakened. If educational situations are complex, then the drive towards specific and focused research findings that will support policy and practice, and the associated notion of control, is illusory. Rather than providing evidence for prescription, research is thus understood as descriptive and explanatory, within a range of interpretative possibilities. Action takes place within a necessarily incomplete and constantly changing situation, more appropriately understood in terms of survival than control. (shrink)

In the paper we consider complexity of intuitionistic propositional logic and its natural fragments such as implicative fragment, finite-variable fragments, and some others. Most facts we mention here are known and obtained by logicians from different countries and in different time since 1920s; we present these results together to see the whole picture.

According to a mainstream position in contemporary cognitive science and philosophy, the use of abstract compositional concepts is amongst the most characteristic indicators of meaningful deliberative thought in an organism or agent. In this article, we show how the ability to develop and utilise abstract conceptual structures can be achieved by a particular kind of learning agent. More specifically, we provide and motivate a concrete operational definition of what it means for these agents to be in possession of abstract concepts, (...) before presenting an explicit example of a minimal architecture that supports this capability. We then proceed to demonstrate how the existence of abstract conceptual structures can be operationally useful in the process of employing previously acquired knowledge in the face of new experiences, thereby vindicating the natural conjecture that the cognitive functions of abstraction and generalisation are closely related. (shrink)

Extending new verbs is important in becoming a productive speaker of a language. Prior results show children have difficulty extending verbs when they have seen events with varied agents. This study further examines the impact of variability on verb learning and asks whether variability interacts with event complexity or differs by language. Children in the United States, China, Korea, and Singapore learned verbs linked to simple and complex events. Sets of events included one or three agents, and children were (...) asked to extend the verb at test. Children learning verbs linked to simple movements performed similarly across conditions. However, children learning verbs linked to events with multiple objects were less successful if those events were enacted by multiple agents. A follow-up study rules out an influence of event order. Overall, similar patterns of results emerged across languages, suggesting common cognitive processes support children's verb learning. (shrink)

We provide a Kripke semantics for a STIT logic with the "next" operator. As the atemporal group STIT is undecidable and unaxiomatizable, we are interested in strict fragments of atemporal group STIT. First we prove that the satisfiability problem of a formula of the fragment made up of individual coalitions plus the grand coalition is also NEXPTIME-complete. We then generalize this result to a fragment where coalitions are in a given lattice. We also prove that if we restrict the language (...) to nested coalitions the satisfiability problem is NP-complete if the number of agents is fixed and PSPACE-complete if the number of agents is variable. Finally we embed individual STIT with the "next" operator into a fragment of atemporal group STIT. (shrink)

The aim of this work is to study complex ecological models exhibiting simple dynamics. We consider large scale systems which can be decomposed into weakly coupled subsystems. Perturbation Theory is used in order to get a reduced set of differential equations governing slow time varying global variables. As examples, we study the influence of the individual behaviour of animals in competition and predator-prey models. The animals are assumed to do many activities all day long such as searching for (...) food of different types. The degree of competition as well as the predation pressure are dependent upon these activities. Preys are more vulnerable when doing some activities during which they are very exposed to predators attacks rather than for others during which they are hidden. We study the effect of a change in the average individual behaviour of the animals on interspecific relationships. Computer simulations of the whole sets of equations are compared to simulations of the reduced sets of equations. (shrink)

Controlled languages are regimented fragments of natural languagedesigned to make the processing of natural language more efficient andreliable. This paper defines a controlled language, E2V, whose principalgrammatical resources include determiners, relative clauses, reflexivesand pronouns. We provide a formal syntax and semantics for E2V, in whichanaphoric ambiguities are resolved in a linguistically natural way. Weshow that the expressive power of E2V is equal to that of thetwo-variable fragment of first-order logic. It follows that the problemof determining the satisfiability of a set (...) of E2V sentences is NEXPTIMEcomplete. We show that E2V can be extended in various ways withoutcompromising these complexity results; however, relaxing our policy onanaphora resolution renders the satisfiability problem for E2Vundecidable. Finally, we argue that our results have a bearing on thebroader philosophical issue of the relationship between natural andformal languages. (shrink)

Fixed-rate versions of rule-consequentialism and rule-utilitarianism evaluate rules in terms of the expected net value of one particular level of social acceptance, but one far enough below 100% social acceptance to make salient the complexities created by partial compliance. Variable-rate versions of rule-consequentialism and rule-utilitarianism instead evaluate rules in terms of their expected net value at all different levels of social acceptance. Brad Hooker has advocated a fixed-rate version. Michael Ridge has argued that the variable-rate version is better. The debate (...) continues here. Of particular interest is the difference between the implications of Hooker's and Ridge's rules about doing good for others. (shrink)

Background: Heart rate variability (HRV) has been considered as a measure of heart-brain interaction and autonomic modulation, and it is modified by cognitive and attentional tasks. In cognitive tasks, HRV was reduced in participants who achieved worse results. This could indicate the possibility of HRV predicting cognitive performance, but this association is still unclear in a high cognitive load sport such as chess Objective: To analyse modifications on HRV and subjective perception of stress, difficulty and complexity in different chess problem (...) tasks. Design: HRV was assessed at baseline. During the chess problems, HRV was also monitored, and immediately after chess problems the subjective stress, difficulty and complexity were also registered. Method: A total of 16 male chess players, age: 35.19 (13.44) and ELO: 1927.69 (167.78) were analysed while six chess problem solving tasks with different level of difficulty were conducted (two low level, two medium level and two high level chess problems). Participants were classified according to their results into two groups: high performance or low performance. Results: Friedman test showed a significant effect of tasks in HRV indexes and perceived difficulty, stress and complexity in both high and low performance groups. A decrease in HRV was observed in both groups when chess problems difficulty increased. In addition, HRV was significantly higher in the high performance group than in the low performance group during chess problems. Conclusions: An increase in autonomic modulation was observed to meet the cognitive demands of the problems, being higher while the difficulty of the tasks increased. Non-linear HRV indexes seem to be more reactive to tasks difficulty, being an interesting and useful tool in chess training. (shrink)

A crucial question for artificial cognition systems is what meaning is and how it arises. In pursuit of that question, this paper extends earlier work in which we show that emergence of simple signaling in biologically inspired models using arrays of locally interactive agents. Communities of "communicators" develop in an environment of wandering food sources and predators using any of a variety of mechanisms: imitation of successful neighbors, localized genetic algorithms and partial neural net training on successful neighbors. Here we (...) focus on environmental variability, comparing results for environments with (a) constant resources, (b) random resources, and (c) cycles of "boom and bust." In both simple and complex models across all three mechanisms of strategy change, the emergence of communication is strongly favored by cycles of "boom and bust." These results are particularly intriguing given the importance of environmental variability in fields as diverse as psychology, ecology and cultural anthropology. (shrink)

Language processing changes with the knowledge and use of two languages. The advantage of being bilingual comes at the expense of increased processing demands and processing costs. I suggest considering bilingual complexity including these demands and costs. The proposed model claims effortless monolingual processing. By integrating individual and situational variability, the model would lose its idealistic touch, even for monolinguals.

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a (...) Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)