An analogy between functional dependencies and implicational formulas of sentential logic has been discussed in the literature. We feel that a somewhat different connexion between dependency theory and sentential logic is suggested by the similarity between Armstrong's axioms for functional dependencies and Tarski's defining conditions for consequence relations, and we pursue aspects of this other analogy here for their theoretical interest. The analogy suggests, for example, a different semantic interpretation of consequence relations: instead of thinking ofB as (...) a consequence of a set of formulas {A1,...,A n} whenB is true on every assignment of truth-values on which eachA i is true, we can think of this relation as obtaining when every pair of truth-value assignments which give the same truth-values toA 1, the same truth-values toA 2,..., and the same truth-values toA n, also make the same assignment in respect ofB. We describe the former as the consequence relation inference-determined by the class of truth-value assignments (valuations) under consideration, and the latter as the consequence relation supervenience-determined by that class of assignments. Some comparisons will be made between these two notions. (shrink)

We consider a predicate logic Lfd where not all assignments of values to individual variables are possible. Some variables are functionally dependent on other variables. This makes sense if the models of logic are assumed to correspond to databases or states. We show that Lfd is undecidable but has a complete and sound sequent calculus formalisation.

The article studies properties of functional dependencies between strategies of players in Nash equilibria of multiplayer strategic games. The main focus is on the properties of functional dependencies in the context of a fixed dependency graph for payoff functions. A logical system describing properties of functional dependence for any given graph is proposed and is proven to be complete.

This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more concrete settings for dependence are discussed: (...) continuous dependence in topological models, linear dependence in vector spaces, and temporal dependence in dynamical systems and games. (shrink)

Two different types of functional dependencies are compared: dependencies that are functional due to the laws of nature and dependencies that are functional if all involved agents behave rationally. The first type of dependencies was axiomatized by Armstrong. This article gives a formal definition of the second type of functional dependencies in terms of strategic games and describes a sound and complete axiomatization of their properties. The axiomatization is significantly different from the Armstrong’s axioms.

In his ontological works Kurt Grelling tries to give a rigorous analysis of the foundations of the so-called Gestalt-psychology. Gestalten are peculiar emergent qualities, ontologically dependent on their foundations, but nonetheless non reducible to them. Grelling shows that this concept, as used in psychology and ontology, is often ambiguous. He distinguishes two important meanings in which the word “Gestalt” is used: Gestalten as structural aspects available to transposition and Gestalten as causally self-regulating wholes. Gestalten in the first meaning are, according (...) to Grelling, “equivalence classes of correspondences”, while Gestalten as self-regulating wholes have more to do with relations of ontological dependence. Grelling’s clarification of the concept of Gestalt is doubtless an excellent piece of philosophical analysis, but at the end of the day it turns out that his analysis captures at best only a part of intuitions traditionally connected with the notion of Gestalt. (shrink)

The cerebellum probably obeys the rules of sensorimotor integration common in the nervous system. One such a rule is formulated: the nervous system organizes spatial frames of reference for the sensorimotor apparatus and produces voluntary movements by shifting their origin points. We give examples of spatial frames of reference for different single- and multi-joint movements including locomotion and also illustrate that the process of motor development and learning may depend critically on the formation of appropriate frames of reference and the (...) organism's ability to manage them. We suggest that a solution to the problem of sensorimotor integration may not be trivial and may actually change the mental and experimental paradigms used in the understanding of the cerebellum and other brain structures, [HOUK et al.; SIMPSON et al.; SMITH; TIIACH]. (shrink)

To explore the number of latent variables underlying recognition of own- and other-race faces for Chinese observers, we conducted a study-recognition task where orientation, stimuli type, and duration were manipulated in the study phase and applied state trace analysis as a statistic method. Results showed that each state trace plot on each pair of stimuli types matched a single monotonic curve when stimuli type was set to state factor, but separate curves between face and non-face showed up when the state (...) factor was orientation. The results implied that at least two latent variables affected recognition performance in the inversion paradigm. Besides, the unidimensional structure between own- and other-race faces regardless of the state factor suggested that Chinese participants used the same recognition mechanism for unfamiliar own- and other-race faces in the inversion paradigm. (shrink)

In ‘A modal theory of function’, I gave an argument against all existing theories of function and outlined a new theory. Karen Neander and Alex Rosenberg argue against both my negative and my positive claim. My aim here is not merely to defend my account from their objections, but to (a) very briefly point out that the new account of etiological function they propose in response to my criticism cannot avoid the circularity worry either and, more importantly, to (b) highlight, (...) and attempt to make precise, an important feature of my modal theory that may have been understated in the original paper – that function attributions depend on the explanatory project at hand. (shrink)

This paper briefly traces the evolution of the function concept until its modern set theoretic definition, and then investigates its relationship to the pre-formal notion of variable dependence. I shall argue that the common association of pre-formal dependence with the modern function concept is misconceived, and that two different notions of dependence are actually involved in the classic and the modern viewpoints, namely effective and functional dependence. The former contains the latter, and seems to conform more to our pre-formal (...) conception of dependence. The idea of effective dependence is further investigated in connection with the notions of function content and intensionality. Finally, the relevance of the distinction between the two kinds of dependence to mathematical practice is considered. (shrink)

The present paper discusses two interesting phenomena concerning phi-features on plural pronouns: plural pronouns that denote atomic individuals, and plural pronouns with more than one binder. A novel account of these two phenomena is proposed, according to which all occurrences of phi-features are both semantically and morphologically relevant. For such a ‘uniformly semantic account’ of phi-features, dependent plural pronouns constitute a theoretical challenge, while partial binding is more or less straightforwardly accounted for. In order to make sense of the semantic (...) effects of the phi-features on dependent plural pronouns, the following idea is pursued: the phi-features on a dependent plural pronoun reflect the range of values that the pronoun takes, rather than the particular value it denotes at a time. This idea is implemented in a compositional semantics by making use of choice functions. An appealing feature of the present account is that, unlike its predecessors, it accounts for dependent plural pronouns without c-commanding antecedents in essentially the same way as for those with c-commanding antecedents. It is also shown how this account of dependent plural pronouns can straightforwardly be augmented with set indices to account for partial binding. (shrink)

This commentary considers Merker's mesodiencephalic proposal in relation to quantitative measures of neural dynamics suggested to be relevant to consciousness. I suggest that even if critical neural mechanisms turn out to be subcortical, the functional utility of consciousness will depend on the rich conscious contents generated by continuous interaction of such mechanisms with a thalamocortical envelope. (Published Online May 1 2007).

Function-first epistemologists analyze epistemic concepts, norms, and practices by investigating their functions. According to the most prominent function-first account, the primary function of our concept of knowledge is identifying reliable informants. In this paper, I take for granted the function-first methodology to achieve three main goals: First, I argue against this prominent account: studying practices of knowledge attribution and denial related to epistemic dependence, coordination, and competition reveals that the primary function of our concept of knowledge is not identifying reliable (...) informants. Second, I recommend that function-firsters accept an alternative account: the primary function of our concept of knowledge is identifying those who have eliminated all relevant alternatives. Finally, I diagnose the error that has led function-firsters to their account: they base their investigation into the nature of knowledge on the situation of inquirers seeking informants, a situation that does not reflect the complexity of our epistemic condition. (shrink)

Schyns et al. make a strong case for context-dependent feature discovery. The features computed from specialized and diverse data-sets help to coordinate their activity by adapting so as to emphasize what is related across sets. Their perspective can be strengthened and extended by formal arguments for the contextual guidance of learning and processing and by neurobiological and psychological evidence of structures and processes that implement this guidance.

The three introductory questions posed by Hobson et al. point toward further investigations of cellular, circuit, and systems mechanisms involved in cognitive function that include the effect of CNS-state related modulatory systems on these mechanisms. [Hobson et al.].

Name der Zeitschrift: Semiotica Jahrgang: 2015 Heft: 203 Seiten: 9-37.

The ciliated protozoan, Paramecium, broadcasts the activity of its individual ion channel classes through its swimming behaviour. This fact has made it possible to isolate mutants with defective ion currents, simply by selecting individuals with abnormal swimming patterns. At least four of Paramecium's ion currents are activated by rising intracellular calcium concentration, including two K+ currents and a Na+ current. A variety of cell lines with defects in these Ca2+‐dependent currents have been isolated: in several cases, the defects have been (...) traced to mutations in the structural gene for calmodulin. Sequence analysis of calmodulins from these and other Ca2+ ‐dependent ion‐current mutants may enable a detailed mapping of putative channel interaction domains on the surface of the calmodulin molecule. (shrink)

There are a limited number of neuroimaging investigations into motor control of the lumbopelvic musculature. Most investigation examining motor control of the lumbopelvic musculature utilize transcranial magnetic stimulation and focus primarily on the motor cortex. This has resulted in a dearth of knowledge as it relates to how other regions of the brain activate during lumbopelvic movement. Additionally, task-based functional connectivity during lumbopelvic movements has not been well elucidated. Therefore, we used functional magnetic resonance imaging to examine brain (...) activation and ROI-to-ROI task-based functional connectivity in 19 healthy individuals during the performance of three lumbopelvic movements: modified bilateral bridge, left unilateral bridge, and right unilateral bridge. The whole brain analysis found robust, bilateral activation within the motor regions of the brain during the bilateral bridge task, and contralateral activation of the motor regions during unilateral bridging tasks. Furthermore, the ROI-to-ROI analysis demonstrated significant connectivity of a motor network that included the supplemental motor area, bilateral precentral gyrus, and bilateral cerebellum regardless of the motor task performed. These data suggest that while whole brain activation reveals unique patterns of activation across the three tasks, functional connectivity is very similar. As motor control of the lumbopelvic area is of high interest to those studying low back pain, this study can provide a comparison for future research into potential connectivity changes that occur in individuals with LBP. (shrink)

There is an under-appreciated tradition of genealogical explanation that is centrally concerned with social functions. I shall refer to it as the tradition of pragmatic genealogy. It runs from David Hume (T, 3.2.2) and the early Friedrich Nietzsche (TL) through E. J. Craig (1990, 1993) to Bernard Williams (2002) and Miranda Fricker (2007). These pragmatic genealogists start out with a description of an avowedly fictional “state of nature” and end up ascribing social functions to particular building blocks of our practices (...) – such as the fact that we use a certain concept, or live by a certain virtue – which we did not necessarily expect to have such a function at all. That the seemingly archaic device of a fictional state-of-nature story should be a helpful way to get at the functions of our actual practices must seem a mystifying proposal, however; I shall therefore endeavor to demystify it in what follows. My aim in this chapter is twofold. First, by delineating the framework of pragmatic genealogy and contrasting it with superficially similar methods, I argue that pragmatic genealogies are best interpreted as dynamic models whose point is to reveal the function – and non-coincidentally often the social function – of certain practices. Second, by buttressing this framework with something it notably lacks, namely an account of the type of functionality it operates with, I argue that both the type of functional commitment and the depth of factual obligation incurred by a pragmatic genealogy depend on what we use the method for: the dynamic models of pragmatic genealogy can be used merely as heuristic devices helping us spot functional patterns, or more ambitiously as arguments grounding our ascriptions of functionality to actual practices, or even more ambitiously as bases for functional explanations of the resilience or the persistence of practices. By bringing these distinctions into view, we gain the ability to distinguish strengths and weaknesses of the method’s application from strengths and weaknesses of the method itself. (shrink)

Representations are not only used in our folk-psychological explanations of behaviour, but are also fruitfully postulated, for example, in cognitive science. The mainstream view in cognitive science maintains that our mind is a representational system. This popular view requires an understanding of the nature of the entities they are postulating. Teleosemantic theories face this challenge, unpacking the normativity in the relation of representation by appealing to the teleological function of the representing state. It has been argued that, if intentionality is (...) to be explained in teleological terms, then the function of a state cannot depend on its phylogenetical history, given the metaphysical possibility of a duplicate of an intentional being that lacks an evolutionary history. In this paper, I present a method to produce, according to our current knowledge in genetic engineering, human-like individuals who are not the product of natural selection in the required sense. This variation will be used to shed light on the main replies that have been offered in the literature to the Swampman thought experiment. I argue that these replies are not satisfactory: representations should better not depend on natural selection. I conclude that a non-etiological notion of function is to be preferred for characterizing the relation of representation. (shrink)

We formulate the problem of permuting a matrix to block angular form as the combinatorial minimization of an objective function. We motivate the use of simulated annealing (SA) as an optimization tool. We then introduce a heuristic temperature dependent penalty function in the simulated annealing cost function, to be used instead of the real objective function being minimized. Finally we show that this temperature dependent penalty function version of simulated annealing consistently outperforms the standard simulated annealing approach, producing, with smaller (...) running times, better solutions. We believe that the use of a temperature dependent penalty function may be useful in developing SA algorithms for other combinatorial problems. -/- . (shrink)

The Expected Shortfall or Conditional Value-at-Risk (CVaR) has been playing the role of main risk measure in the recent years and paving the way for an enormous number of applications in risk management due to its very intuitive form and important coherence properties. This work aims to explore this measure as a probability-dependent utility functional, introducing an alternative view point for its Choquet Expected Utility representation. Within this point of view, its main preference properties will be characterized and its (...) utility representation provided through local utilities with an explicit dependence on the assessed revenue’s distribution (quantile) function. Then, an intuitive interpretation for the related probability dependence and the piecewise form of such utility will be introduced on an investment pricing context, in which a CVaR maximizer agent will behave in a relativistic way based on his previous estimates of the probability function. Finally, such functional will be extended to incorporate a larger range of risk-averse attitudes and its main properties and implications will be illustrated through examples, such as the so-called Allais Paradox. (shrink)

This paper describes and defends the view that minimal chemical life essentially involves the chemical integration of three chemical functionalities: containment, metabolism, and program (Rasmussen et al. in Protocells: bridging nonliving and living matter, 2009a ). This view is illustrated and explained with the help of CMP and Rasmussen diagrams (Rasmussen et al. In: Rasmussen et al. (eds.) in Protocells: bridging nonliving and living matter, 71–100, 2009b ), both of which represent the key chemical functional dependencies among containment, metabolism, (...) and program. The CMP model of minimal chemical life gains some support from the broad view of life as open-ended evolution, which I have defended elsewhere (Bedau in The philosophy of artificial life, 1996 ; Bedau in Artificial Life, 4:125–140, 1998 ). Further support comes from the natural way the CMP model resolves the puzzle about whether life is a matter of degree. (shrink)

Which function is computed by a Turing machine will depend on how the symbols it manipulates are interpreted. Further, by invoking bizarre systems of notation it is easy to define Turing machines that compute textbook examples of uncomputable functions, such as the solution to the decision problem for first-order logic. Thus, the distinction between computable and uncomputable functions depends on the system of notation used. This raises the question: which systems of notation are the relevant ones for determining whether a (...) function is computable? These are the acceptable notations. I argue for a use criterion of acceptability: the acceptable notations for a domain of objects D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {D}}$$\end{document} are the notations that we can use for the usual D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {D}}$$\end{document}-activities. Acceptable notations for natural numbers are ones that we can count with. Acceptable notations for logical formulas are the ones that we can use in inference and logical analysis. And so on. This criterion makes computability a relative notion—whether a function is computable depends on which notations are acceptable, which is relative to our interests and abilities. I argue that this is not a problem, however, since there is independent reason for taking the extension of computable function to be relative to contingent facts. Similarly, the fact that the use criterion makes a mathematical distinction depend on practical concerns is also not a problem because it dovetails with similar phenomena in other areas of computability theory, namely the roles of notation in computation over real numbers and of Extended Church’s Thesis in complexity theory. (shrink)

After presenting Kripke’s criticism to Frege’s ideas on context dependence of thoughts, I present two recent attempts of considering cognitive aspects of context dependent expressions inside a truth conditional pragmatics or semantics: Recanati’s non-descriptive modes of presentation (MOPs) and Kaplan’s ways of having in mind (WHIMs). After analysing the two attempts and verifying which answers they should give to the problem discussed by Kripke, I suggest a possible interpretation of these attempts: to insert a procedural or algorithmic level in semantic (...) representations of indexicals. That a function may be computed by different procedures might suggest new possibilities of integrating contextual cognitive aspects in model theoretic semantic. (shrink)