Results for 'degree spectra of relations'

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  1. The Process of Doctoral Research Constraints and Opportunities.David Allen & National Conference on Doctoral Research in Management and Industrial Relations - 1982 - Health Services Management Unit, Dept. Of Social Administration, University of Manchester.
     
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  2.  17
    Realizing Levels of the Hyperarithmetic Hierarchy as Degree Spectra of Relations on Computable Structures.Walker M. White & Denis R. Hirschfeldt - 2002 - Notre Dame Journal of Formal Logic 43 (1):51-64.
    We construct a class of relations on computable structures whose degree spectra form natural classes of degrees. Given any computable ordinal and reducibility r stronger than or equal to m-reducibility, we show how to construct a structure with an intrinsically invariant relation whose degree spectrum consists of all nontrivial r-degrees. We extend this construction to show that can be replaced by either or.
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  3. Degree Spectra of Relations on Computable Structures in the Presence of Δ02 Isomorphisms.Denis R. Hirschfeldt - 2002 - Journal of Symbolic Logic 67 (2):697 - 720.
    We give some new examples of possible degree spectra of invariant relations on Δ 0 2 -categorical computable structures, which demonstrate that such spectra can be fairly complicated. On the other hand, we show that there are nontrivial restrictions on the sets of degrees that can be realized as degree spectra of such relations. In particular, we give a sufficient condition for a relation to have infinite degree spectrum that implies that every (...)
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  4.  2
    Degree Spectra of Relations on Structures of Finite Computable Dimension.Denis R. Hirschfeldt - 2002 - Annals of Pure and Applied Logic 115 (1-3):233-277.
    We show that for every computably enumerable degree a > 0 there is an intrinsically c.e. relation on the domain of a computable structure of computable dimension 2 whose degree spectrum is { 0 , a } , thus answering a question of Goncharov and Khoussainov 55–57). We also show that this theorem remains true with α -c.e. in place of c.e. for any α∈ω∪{ω} . A modification of the proof of this result similar to what was done (...)
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  5.  15
    Degree Spectra of Intrinsically C.E. Relations.Denis R. Hirschfeldt - 2001 - Journal of Symbolic Logic 66 (2):441-469.
    We show that for every c.e. degree a > 0 there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is {0, a}. This result can be extended in two directions. First we show that for every uniformly c.e. collection of sets S there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is the set of degrees of elements of S. Then we show that (...)
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  6.  13
    Computable Isomorphisms, Degree Spectra of Relations, and Scott Families.Bakhadyr Khoussainov & Richard A. Shore - 1998 - Annals of Pure and Applied Logic 93 (1-3):153-193.
    The spectrum of a relation on a computable structure is the set of Turing degrees of the image of R under all isomorphisms between and any other computable structure . The relation is intrinsically computably enumerable if its image under all such isomorphisms is c.e. We prove that any computable partially ordered set is isomorphic to the spectrum of an intrinsically c.e. relation on a computable structure. Moreover, the isomorphism can be constructed in such a way that the image of (...)
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  7.  11
    $\Pi _{1}^{0}$ Classes and Strong Degree Spectra of Relations.John Chisholm, Jennifer Chubb, Valentina S. Harizanov, Denis R. Hirschfeldt, Carl G. Jockusch, Timothy McNicholl & Sarah Pingrey - 2007 - Journal of Symbolic Logic 72 (3):1003 - 1018.
    We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear ordering. Countable $\Pi _{1}^{0}$ subsets of 2ω and Kolmogorov complexity play a major role in the proof.
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  8.  18
    Degree Spectra of Relations on Computable Structures.Denis R. Hirschfeldt - 2000 - Bulletin of Symbolic Logic 6 (2):197-212.
  9.  4
    Erratum to “Computable Isomorphisms, Degree Spectra of Relations, and Scott Families” [Ann. Pure Appl. Logic 93 153–193]. [REVIEW]Bakhadyr Khoussainov & Richard A. Shore - 1999 - Annals of Pure and Applied Logic 98 (1-3):297-298.
  10. Degree Spectra of Relations on Computable Structures in the Presence of Δ20 Isomorphisms.Denis Hirschfeldt - 2002 - Journal of Symbolic Logic 67 (2):697-720.
  11.  18
    Spectra of Structures and Relations.Valentina S. Harizanov & Russel G. Miller - 2007 - Journal of Symbolic Logic 72 (1):324 - 348.
    We consider embeddings of structures which preserve spectra: if g: M → S with S computable, then M should have the same Turing degree spectrum (as a structure) that g(M) has (as a relation on S). We show that the computable dense linear order L is universal for all countable linear orders under this notion of embedding, and we establish a similar result for the computable random graph G. Such structures are said to be spectrally universal. We use (...)
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  12.  2
    New Degree Spectra of Abelian Groups.Alexander G. Melnikov - 2017 - Notre Dame Journal of Formal Logic 58 (4):507-525.
    We show that for every computable ordinal of the form β=δ+2n+1>1, where δ is zero or a limit ordinal and n∈ω, there exists a torsion-free abelian group having an X-computable copy if and only if X is nonlowβ.
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  13.  14
    The Degree Spectra of Homogeneous Models.Karen Lange - 2008 - Journal of Symbolic Logic 73 (3):1009-1028.
    Much previous study has been done on the degree spectra of prime models of a complete atomic decidable theory. Here we study the analogous questions for homogeneous models. We say a countable model A has a d-basis if the types realized in A are all computable and the Turing degree d can list $\Delta _{0}^{0}$ -indices for all types realized in A. We say A has a d-decidable copy if there exists a model B ≅ A such (...)
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  14.  6
    Some Effects of Ash–Nerode and Other Decidability Conditions on Degree Spectra.Valentina S. Harizanov - 1991 - Annals of Pure and Applied Logic 55 (1):51-65.
    With every new recursive relation R on a recursive model , we consider the images of R under all isomorphisms from to other recursive models. We call the set of Turing degrees of these images the degree spectrum of R on , and say that R is intrinsically r.e. if all the images are r.e. C. Ash and A. Nerode introduce an extra decidability condition on , expressed in terms of R. Assuming this decidability condition, they prove that R (...)
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  15.  4
    Degree Spectra of Real Closed Fields.Russell Miller & Victor Ocasio González - 2019 - Archive for Mathematical Logic 58 (3-4):387-411.
    Several researchers have recently established that for every Turing degree \, the real closed field of all \-computable real numbers has spectrum \. We investigate the spectra of real closed fields further, focusing first on subfields of the field \ of computable real numbers, then on archimedean real closed fields more generally, and finally on non-archimedean real closed fields. For each noncomputable, computably enumerable set C, we produce a real closed C-computable subfield of \ with no computable copy. (...)
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  16.  23
    Spaces of Orders and Their Turing Degree Spectra.Malgorzata A. Dabkowska, Mieczyslaw K. Dabkowski, Valentina S. Harizanov & Amir A. Togha - 2010 - Annals of Pure and Applied Logic 161 (9):1134-1143.
    We investigate computability theoretic and topological properties of spaces of orders on computable orderable groups. A left order on a group G is a linear order of the domain of G, which is left-invariant under the group operation. Right orders and bi-orders are defined similarly. In particular, we study groups for which the spaces of left orders are homeomorphic to the Cantor set, and their Turing degree spectra contain certain upper cones of degrees. Our approach unifies and extends (...)
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  17.  12
    Degree Spectra and Computable Dimensions in Algebraic Structures.Denis R. Hirschfeldt, Bakhadyr Khoussainov, Richard A. Shore & Arkadii M. Slinko - 2002 - Annals of Pure and Applied Logic 115 (1-3):71-113.
    Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in the given (...)
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  18.  16
    Degree Spectra of Prime Models.Barbara F. Csima - 2004 - Journal of Symbolic Logic 69 (2):430 - 442.
    We consider the Turing degrees of prime models of complete decidable theories. In particular we show that every complete decidable atomic theory has a prime model whose elementary diagram is low. We combine the construction used in the proof with other constructions to show that complete decidable atomic theories have low prime models with added properties. If we have a complete decidable atomic theory with all types of the theory computable, we show that for every degree d with 0 (...)
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  19.  24
    Degree Spectra of the Successor Relation of Computable Linear Orderings.Jennifer Chubb, Andrey Frolov & Valentina Harizanov - 2009 - Archive for Mathematical Logic 48 (1):7-13.
    We establish that for every computably enumerable (c.e.) Turing degree b the upper cone of c.e. Turing degrees determined by b is the degree spectrum of the successor relation of some computable linear ordering. This follows from our main result, that for a large class of linear orderings the degree spectrum of the successor relation is closed upward in the c.e. Turing degrees.
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  20.  3
    Turing Degree Spectra of Differentially Closed Fields.David Marker & Russell Miller - 2017 - Journal of Symbolic Logic 82 (1):1-25.
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  21.  12
    Weak Truth Table Degrees of Structures.David R. Belanger - 2015 - Notre Dame Journal of Formal Logic 56 (2):263-285.
    We study the weak truth table degree spectra of first-order relational structures. We prove a dichotomy among the possible wtt degree spectra along the lines of Knight’s upward-closure theorem for Turing degree spectra. We prove new results contrasting the wtt degree spectra of finite- and infinite-signature structures. We show that, as a method of defining classes of reals, the wtt degree spectrum is, except for some trivial cases, strictly more expressive than (...)
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    Degree Spectra and Immunity Properties.Barbara F. Csima & Iskander S. Kalimullin - 2010 - Mathematical Logic Quarterly 56 (1):67-77.
    We analyze the degree spectra of structures in which different types of immunity conditions are encoded. In particular, we give an example of a structure whose degree spectrum coincides with the hyperimmune degrees. As a corollary, this shows the existence of an almost computable structure of which the complement of the degree spectrum is uncountable.
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  23.  54
    The Spectra of Soundless Voices and Audible Thoughts: Towards an Integrative Model of Auditory Verbal Hallucinations and Thought Insertion.Clara S. Humpston & Matthew R. Broome - 2016 - Review of Philosophy and Psychology 7 (3):611-629.
    Patients with psychotic disorders experience a range of reality distortions. These often include auditory-verbal hallucinations, and thought insertion to a lesser degree; however, their mechanisms and relationships between each other remain largely elusive. Here we attempt to establish a integrative model drawing from the phenomenology of both AVHs and TI and argue that they in fact can be seen as ‘spectra’ of experiences with varying degrees of agency and ownership, with ‘silent and internal own thoughts’ on one extreme (...)
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  24.  13
    The Continuous Spectra of Quantum Operators.Boris Leaf - 1982 - Foundations of Physics 12 (6):583-606.
    The linear vector space for the quantum description of a physical system is formulated as the intersection of the domains of Hermiticity of the observables characterizing the system. It is shown that on a continuous interval of its spectrum every Hermitian operator on a Hilbert space of one degree of freedom is a generalized coordinate with a conjugate generalized momentum. Every continuous spectral interval of a Hermitian operator is the limit of a discrete spectrum in the same interval. This (...)
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    Categoricity Spectra for Polymodal Algebras.Nikolay Bazhenov - 2016 - Studia Logica 104 (6):1083-1097.
    We investigate effective categoricity for polymodal algebras. We prove that the class of polymodal algebras is complete with respect to degree spectra of nontrivial structures, effective dimensions, expansion by constants, and degree spectra of relations. In particular, this implies that every categoricity spectrum is the categoricity spectrum of a polymodal algebra.
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  26.  13
    Computability of Fraïssé Limits.Barbara F. Csima, Valentina S. Harizanov, Russell Miller & Antonio Montalbán - 2011 - Journal of Symbolic Logic 76 (1):66 - 93.
    Fraïssé studied countable structures S through analysis of the age of S i.e., the set of all finitely generated substructures of S. We investigate the effectiveness of his analysis, considering effectively presented lists of finitely generated structures and asking when such a list is the age of a computable structure. We focus particularly on the Fraïssé limit. We also show that degree spectra of relations on a sufficiently nice Fraïssé limit are always upward closed unless the relation (...)
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  27.  6
    Turing Degrees of Hypersimple Relations on Computable Structures.Valentina S. Harizanov - 2003 - Annals of Pure and Applied Logic 121 (2-3):209-226.
    Let be an infinite computable structure, and let R be an additional computable relation on its domain A. The syntactic notion of formal hypersimplicity of R on , first introduced and studied by Hird, is analogous to the computability-theoretic notion of hypersimplicity of R on A, given the definability of certain effective sequences of relations on A. Assuming that R is formally hypersimple on , we give general sufficient conditions for the existence of a computable isomorphic copy of on (...)
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    Turing Degrees of Certain Isomorphic Images of Computable Relations.Valentina S. Harizanov - 1998 - Annals of Pure and Applied Logic 93 (1-3):103-113.
    A model is computable if its domain is a computable set and its relations and functions are uniformly computable. Let be a computable model and let R be an extra relation on the domain of . That is, R is not named in the language of . We define to be the set of Turing degrees of the images f under all isomorphisms f from to computable models. We investigate conditions on and R which are sufficient and necessary for (...)
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  29.  5
    Homomorphisms and Quotients of Degree Structures.Burkhard Englert, Manuel Lerman & Kevin Wald - 2003 - Annals of Pure and Applied Logic 123 (1-3):193-233.
    We investigate homomorphisms of degree structures with various relations, functions and constants. Our main emphasis is on pseudolattices, i.e., partially ordered sets with a join operation and relations simulating the meet operation. We show that there are no finite quotients of the pseudolattice of degrees or of the pseudolattice of degrees 0′, but that many finite distributive lattices are pseudolattice quotients of the pseudolattice of computably enumerable degrees.
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  30.  14
    Number Word Constructions, Degree Semantics and the Metaphysics of Degrees.Brendan Balcerak Jackson & Doris Penka - 2017 - Linguistics and Philosophy 40 (4):347-372.
    A central question for ontology is the question of whether numbers really exist. But it seems easy to answer this question in the affirmative. The truth of a sentence like ‘Seven students came to the party’ can be established simply by looking around at the party and counting students. A trivial paraphrase of is ‘The number of students who came to the party is seven’. But appears to entail the existence of a number, and so it seems that we must (...)
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  31.  15
    Computable Isomorphisms of Boolean Algebras with Operators.Bakhadyr Khoussainov & Tomasz Kowalski - 2012 - Studia Logica 100 (3):481-496.
    In this paper we investigate computable isomorphisms of Boolean algebras with operators (BAOs). We prove that there are examples of polymodal Boolean algebras with finitely many computable isomorphism types. We provide an example of a polymodal BAO such that it has exactly one computable isomorphism type but whose expansions by a constant have more than one computable isomorphism type. We also prove a general result showing that BAOs are complete with respect to the degree spectra of structures, computable (...)
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  32.  10
    "Modernism" Versus "Traditionalism" in Bourgeois Studies of International Relations.S. A. Petrovskii & L. A. Petrovskaia - 1975 - Russian Studies in Philosophy 14 (2):69-96.
    Implementation of the Peace Program propounded by the Twenty-Fourth Congress of the CPSU is substantially furthered by the struggle against bourgeois ideology in a field directly related to interpretation of the principal problems of contemporary foreign policy - the field of the theory of international relations. Naturally, the success of this struggle depends in large degree on the depth and care with which one analyzes the conditions and tendencies characteristic of bourgeois studies of international politics.
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  33.  5
    Polish-Russian Economic Relations Under the Conditions of System Transformation.Paweł Bożyk - 2011 - International Studies. Interdisciplinary Political and Cultural Journal 13 (1):19-26.
    Polish-Russian Economic Relations Under the Conditions of System Transformation The rapid economic transformation in Central and Eastern Europe, modelled on Western economies and based, in some aspects, on neoliberal principles, has found the region's countries to a bigger or lesser degree unprepared. The resulting economic recession, especially in Russia, has had an adverse effect on mutual trade between Poland and Russia. In order to improve economic relations with Russia and increase the trade volume, Poland, remaining within the (...)
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  34.  3
    Employers' satisfaction over the fulfillment of the social task of graduates of wide access master degree courses.Zoila del Socorro López Díaz - 2017 - Humanidades Médicas 17 (2):338-353.
    Las relaciones entre el mundo de la educación y el trabajo tienen objetivos diversos, relacionados con la pertinencia, la formación recibida, el ejercicio profesional, la eficiencia universitaria y la repercusión social; de manera que resulta valiosa la información sobre el cumplimiento del encargo social del profesional, al tiempo que se convierte en instrumento de gestión universitaria. Objetivo: determinar la satisfacción alcanzada por el cumplimento del encargo social de egresados de maestrías ejecutadas en la Facultad de Ciencias Médicas "Manuel Fajardo". Métodos: (...)
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  35.  22
    Burqas in Back Alleys: Street Art, Hijab, and the Reterritorialization of Public Space.John A. Sweeney - 2011 - Continent 1 (4):253-278.
    continent. 1.4 (2011): 253—278. A Sense of French Politics Politics itself is not the exercise of power or struggle for power. Politics is first of all the configuration of a space as political, the framing of a specific sphere of experience, the setting of objects posed as "common" and of subjects to whom the capacity is recognized to designate these objects and discuss about them.(1) On April 14, 2011, France implemented its controversial ban of the niqab and burqa , commonly (...)
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  36.  40
    Representability of Ordinal Relations on a Set of Conditional Events.Giulianella Coletti & Barbara Vantaggi - 2006 - Theory and Decision 60 (2-3):137-174.
  37.  18
    Towards a Model of Corporate and Social Stakeholder Engagement: Analyzing the Relations Between a French Mutual Bank and Its Members. [REVIEW]Carine Girard & André Sobczak - 2012 - Journal of Business Ethics 107 (2):215-225.
    The aim of this article is to develop a new classification of stakeholders based on the concept of corporate and social engagement. Engagement is analyzed as an organizational learning process between the managers of an organization and its stakeholders. It is a necessary condition to improve the organization’s impact on its economic, social, and natural environment. Applied to the membership of a French mutual bank in order to identify the members’ varying levels of engagement, this new mapping technique may help (...)
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  38. Three Sources of Vagueness in Degree Constructions.Galit W. Sassoon - 2009 - In Arndt Riester & Torgrim Solstad (eds.), Proceedings of Sinn Und Bedeutung 13. pp. 469--483.
    This paper presents a novel semantic analysis of unit names and gradable adjectives, inspired by measurement theory (Krantz et al 1971). Based on measurement theory's typology of measures, I claim that different predicates are associated with different types of measures whose special characteristics, together with features of the relations denoted by unit names, explain the puzzling limited distribution of measure phrases.
     
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  39.  6
    Hyperarithmetical Relations in Expansions of Recursive Structures.Alan D. Vlach - 1994 - Annals of Pure and Applied Logic 66 (2):163-196.
    Let be a model of a theory T. Depending on wether is decidable or recursive, and on whether T is strongly minimal or -minimal, we find conditions on which guarantee that every infinite independent subset of is not recursively enumerable. For each of the same four cases we also find conditions on which guarantee that every infinite independent subset of has Turing degree 0'. More generally, let be a recursive -structure, R a relation symbol not in , ψ a (...)
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  40.  10
    Uncountable Degree Spectra.Valentina S. Harizanov - 1991 - Annals of Pure and Applied Logic 54 (3):255-263.
    We consider a recursive model and an additional recursive relation R on its domain, such that there are uncountably many different images of R under isomorphisms from to some recursive model isomorphic to . We study properties of the set of Turing degrees of all these isomorphic images of R on the domain of.
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  41.  64
    The Metaphysics of Relations, Edited by Anna Marmodoro and David Yates. [REVIEW]Rognvaldur Ingthorsson - 2017 - Disputatio 9 (44):123–130.
    The Metaphysics of Relations is an anthology of thirteen original papers plus an introduction, addressing the philosophical issue of relations from a contemporary and historical perspective. The result is a remarkably coherent whole, where the different papers shed light on each other even though very few of them explicitly address interconnections. As a consequence, the book works really well as an introduction to the philosophical issue on relations, while the individual papers represent cutting edge research on the (...)
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  42.  10
    Categoricity Spectra for Rigid Structures.Ekaterina Fokina, Andrey Frolov & Iskander Kalimullin - 2016 - Notre Dame Journal of Formal Logic 57 (1):45-57.
    For a computable structure $\mathcal {M}$, the categoricity spectrum is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable copies of $\mathcal {M}$. If the spectrum has a least degree, this degree is called the degree of categoricity of $\mathcal {M}$. In this paper we investigate spectra of categoricity for computable rigid structures. In particular, we give examples of rigid structures without degrees of categoricity.
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  43.  9
    Computability and Uncountable Linear Orders II: Degree Spectra.Noam Greenberg, Asher M. Kach, Steffen Lempp & Daniel D. Turetsky - 2015 - Journal of Symbolic Logic 80 (1):145-178.
  44. Robot Rights? Towards a Social-Relational Justification of Moral Consideration.Mark Coeckelbergh - 2010 - Ethics and Information Technology 12 (3):209-221.
    Should we grant rights to artificially intelligent robots? Most current and near-future robots do not meet the hard criteria set by deontological and utilitarian theory. Virtue ethics can avoid this problem with its indirect approach. However, both direct and indirect arguments for moral consideration rest on ontological features of entities, an approach which incurs several problems. In response to these difficulties, this paper taps into a different conceptual resource in order to be able to grant some degree of moral (...)
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  45. The Degree of Epistemic Justification and the Conjunction Fallacy.Tomoji Shogenji - 2012 - Synthese 184 (1):29-48.
    This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and I (...)
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  46.  22
    On All Strong Kleene Generalizations of Classical Logic.Stefan Wintein - 2016 - Studia Logica 104 (3):503-545.
    By using the notions of exact truth and exact falsity, one can give 16 distinct definitions of classical consequence. This paper studies the class of relations that results from these definitions in settings that are paracomplete, paraconsistent or both and that are governed by the Strong Kleene schema. Besides familiar logics such as Strong Kleene logic, the Logic of Paradox and First Degree Entailment, the resulting class of all Strong Kleene generalizations of classical logic also contains a host (...)
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  47. Introduction: The Metaphysics of Relations (with Anna Marmodoro).David Yates - 2016 - In Anna Marmodoro & David Yates (eds.), The Metaphysics of Relations. Oxford University Press. pp. 1-18.
    An introduction to our edited volume, The Metaphysics of Relations, covering a range of issues including the problem of order, the ontological status of relations, reasons for ancient scepticism about relational properties, and two ways of drawing the distinction between internal and external relations.
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  48.  11
    Reconstruction of Binary Relations From Their Restrictions of Cardinality 2, 3, 4 and (N ‐ 1) I.Gérard Lopez & Claire Rauzy - 1992 - Mathematical Logic Quarterly 38 (1):27-37.
    We shall prove here that any binary relation on a base E with cardinality n > 6 is reconstructible from its restrictions of cardinality 2, 3, 4 and . This proof needs results of part I of this paper where we characterize any pair of relations R, R' which are 2-, 3- and 4-hypomorphic. As a corollary we obtain that any binary relation is -reconstructible.
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  49.  18
    Composable Relations Induced in Networks of Aligned Ontologies: A Category Theoretic Approach.Seremeti Lambrini & Kameas Achilles - 2015 - Axiomathes 25 (3):285-311.
    A network of aligned ontologies is a distributed system, whose components are interacting and interoperating, the result of this interaction being, either the extension of local assertions, which are valid within each individual ontology, to global assertions holding between remote ontology syntactic entities through a network path, or to local assertions holding between local entities of an ontology, but induced by remote ontologies, through a cycle in the network. The mechanism for achieving this interaction is the composition of relations. (...)
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  50.  29
    Determining the Degree of Reality of Language.Jesús Gerardo Martínez del Castillo - 2015 - International Journal of Language and Linguistics 3 (6-1):31-38.
    Speakers live language, that is, they intuit, create, acquire, perform, speak and say, interpret, use, evaluate and, even, speak of language. The real language is the language lived by speakers. On the contrary linguists, who at the same time are speakers and linguists, study language as something manifesting of front of them. In order to study language it is necessary to determine the degree of reality of the thing called language as the reality lived and used by speakers.
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