Search results for 'Model theory' (try it on Scholar)

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  1. A. Prestel (2011). Mathematical Logic and Model Theory: A Brief Introduction. Springer.score: 90.0
    Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic ...
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  2. Chen Chung Chang (1966). Continuous Model Theory. Princeton, Princeton University Press.score: 90.0
    CONTINUOUS MODEL THEORY CHAPTER I TOPOLOGICAL PRELIMINARIES. Notation Throughout the monograph our mathematical notation does not differ drastically from ...
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  3. Grigor Sargsyan (2013). Descriptive Inner Model Theory. Bulletin of Symbolic Logic 19 (1):1-55.score: 90.0
    The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas. There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture known as the Mouse Set Conjecture (MSC). One particular (...)
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  4. Greg Hjorth (1997). Some Applications of Coarse Inner Model Theory. Journal of Symbolic Logic 62 (2):337-365.score: 90.0
    The Martin-Steel coarse inner model theory is employed in obtaining new results in descriptive set theory. $\underset{\sim}{\Pi}$ determinacy implies that for every thin Σ 1 2 equivalence relation there is a Δ 1 3 real, N, over which every equivalence class is generic--and hence there is a good Δ 1 2 (N ♯ ) wellordering of the equivalence classes. Analogous results are obtained for Π 1 2 and Δ 1 2 quasilinear orderings and $\underset{\sim}{\Pi}^1_2$ determinacy is shown (...)
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  5. Gerald E. Sacks (1972). Saturated Model Theory. Reading, Mass.,W. A. Benjamin.score: 90.0
    This book contains the material for a first course in pure model theory with applications to differentially closed fields.
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  6. Thomas Macaulay Ferguson (2012). Notes on the Model Theory of DeMorgan Logics. Notre Dame Journal of Formal Logic 53 (1):113-132.score: 90.0
    We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical (...)
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  7. Iris Loeb (forthcoming). Uniting Model Theory and the Universalist Tradition of Logic: Carnap's Early Axiomatics. Synthese:1-19.score: 90.0
    We shift attention from the development of model theory for demarcated languages to the development of this theory for fragments of a language. Although it is often assumed that model theory for demarcated languages is not compatible with a universalist conception of logic, no one has denied that model theory for fragments of a language can be compatible with that conception. It thus seems unwarranted to ignore the universalist tradition in the search for (...)
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  8. Christian Wallmann (2013). A Shared Framework for Consequence Operations and Abstract Model Theory. Logica Universalis 7 (2):125-145.score: 87.0
    In this paper we develop an abstract theory of adequacy. In the same way as the theory of consequence operations is a general theory of logic, this theory of adequacy is a general theory of the interactions and connections between consequence operations and its sound and complete semantics. Addition of axioms for the connectives of propositional logic to the basic axioms of consequence operations yields a unifying framework for different systems of classical propositional logic. We (...)
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  9. Camilo Argoty (2013). The Model Theory of Modules of a C*-Algebra. Archive for Mathematical Logic 52 (5-6):525-541.score: 87.0
    We study the theory of a Hilbert space H as a module for a unital C*-algebra ${\mathcal{A}}$ from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are elementary equivalent to it. Also, we show that this theory has quantifier elimination and we characterize the model companion of the incomplete theory of all non-degenerate representations of ${\mathcal{A}}$ . Finally, we show (...)
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  10. Lauri Hella, Phokion G. Kolaitis & Kerkko Luosto (1996). Almost Everywhere Equivalence of Logics in Finite Model Theory. Bulletin of Symbolic Logic 2 (4):422-443.score: 84.0
    We introduce a new framework for classifying logics on finite structures and studying their expressive power. This framework is based on the concept of almost everywhere equivalence of logics, that is to say, two logics having the same expressive power on a class of asymptotic measure 1. More precisely, if L, L ′ are two logics and μ is an asymptotic measure on finite structures, then $\scr{L}\equiv _{\text{a.e.}}\scr{L}^{\prime}(\mu)$ means that there is a class C of finite structures with μ (C)=1 (...)
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  11. Erich Grädel, Phokion Kolaitis, Libkin G., Marx Leonid, Spencer Maarten, Vardi Joel, Y. Moshe, Yde Venema & Scott Weinstein (2007). Finite Model Theory and its Applications. Springer.score: 84.0
    This book gives a comprehensive overview of central themes of finite model theory – expressive power, descriptive complexity, and zero-one laws – together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, (...)
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  12. H. Jerome Keisler (1971). Model Theory for Infinitary Logic. Amsterdam,North-Holland Pub. Co..score: 75.0
    Provability, Computability and Reflection.
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  13. Dag Westerståhl (1976). Some Philosophical Aspects of Abstract Model Theory. Dissertation, University of Gothenburgscore: 75.0
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  14. Ayda I. Arruda, Newton C. A. Costdaa & R. Chuaqui (eds.) (1977). Non-Classical Logics, Model Theory, and Computability: Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976. [REVIEW] Sale Distributors for the U.S.A. And Canada, Elsevier/North-Holland.score: 75.0
  15. M. A. Dickmann (1975). Large Infinitary Languages: Model Theory. American Elsevier Pub. Co..score: 75.0
     
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  16. M. A. Dickmann (1970). Model Theory of Infinitary Languages. [Aarhus, Denmark,Universitet, Matematisk Institut].score: 75.0
     
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  17. Melvin Fitting (1969). Intuitionistic Logic, Model Theory and Forcing. Amsterdam, North-Holland Pub. Co..score: 75.0
  18. Ralph Kopperman (1972). Model Theory and its Applications. Boston,Allyn and Bacon.score: 75.0
     
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  19. W. A. J. Luxemburg (ed.) (1969). Applications of Model Theory to Algebra, Analysis, and Probability. New York, Holt, Rinehart and Winston.score: 75.0
     
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  20. Robert Mattison (1968). An Introduction to the Model Theory of First-Order Predicate Logic and a Related Temporal Logic. Santa Monica, Calif.,Rand Corp..score: 75.0
  21. Zbigniew Stachniak (1981). Introduction to Model Theory for Leśniewski's Ontology. Wydawnictwo Uniwersytetu Wrocłaskiego.score: 75.0
  22. Anja Matschuck (2011). Non-Local Correlations in Therapeutic Settings? A Qualitative Study on the Basis of Weak Quantum Theory and the Model of Pragmatic Information. Axiomathes 21 (2):249-261.score: 72.0
    Weak Quantum Theory (WQT) and the Model of Pragmatic Information (MPI) are two psychophysical concepts developed on the basis of quantum physics. The present study contributes to their empirical examination. The issue of the study is whether WQT and MPI can not only explain ‘psi’-phenomena theoretically but also prove to be consistent with the empirical phenomenology of extrasensory perception (ESP). From the main statements of both models, 33 deductions for psychic readings are derived. Psychic readings are defined as (...)
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  23. Matthias Aschenbrenner, Lou van den Dries & Joris van der Hoeven (2013). Toward a Model Theory for Transseries. Notre Dame Journal of Formal Logic 54 (3-4):279-310.score: 63.0
    The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.
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  24. Dirk Helbing (1996). A Stochastic Behavioral Model and a ?Microscopic? Foundation of Evolutionary Game Theory. Theory and Decision 40 (2):149-179.score: 63.0
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  25. David Pierce (2009). Model-Theory of Vector-Spaces Over Unspecified Fields. Archive for Mathematical Logic 48 (5):421-436.score: 63.0
    Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector spaces over algebraically closed fields (...)
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  26. Philip N. Johnson-Laird, Ruth M. J. Byrne & Vittorio Girotto (2009). The Mental Model Theory of Conditionals: A Reply to Guy Politzer. Topoi 28 (1):75-80.score: 62.0
    This paper replies to Politzer’s ( 2007 ) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the ‘paradoxes’ of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.
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  27. Joël Combase (2011). A Silver-Like Perfect Set Theorem with an Application to Borel Model Theory. Notre Dame Journal of Formal Logic 52 (4):415-429.score: 62.0
    A number of results have been obtained concerning Borel structures starting with Silver and Friedman followed by Harrington, Shelah, Marker, and Louveau. Friedman also initiated the model theory of Borel (in fact totally Borel) structures. By this we mean the study of the class of Borel models of a given first-order theory. The subject was further investigated by Steinhorn. The present work is meant to go further in this direction. It is based on the assumption that the (...)
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  28. Shawn Hedman (2004). A First Course in Logic: An Introduction to Model Theory, Proof Theory, Computability, and Complexity. Oxford University Press.score: 60.0
    The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability (...), and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course. (shrink)
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  29. Karl-Georg Niebergall (2002). Structuralism, Model Theory and Reduction. Synthese 130 (1):135 - 162.score: 60.0
    In this paper, the (possible) role of model theory forstructuralism and structuralist definitions of ``reduction'' arediscussed. Whereas it is somewhat undecisive with respect tothe first point – discussing some pro's and con's ofthe model theoretic approach when compared with a syntacticand a structuralist one – it emphasizes that severalstructuralist definitions of ``reducibility'' do not providegenerally acceptable explications of ``reducibility''. This claimrests on some mathematical results proved in this paper.
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  30. Albert Newen & Tobias Schlicht (2009). Understanding Other Minds: A Criticism of Goldman's Simulation Theory and an Outline of the Person Model Theory. Grazer Philosophische Studien 79 (1):209-242.score: 60.0
    What exactly do we do when we try to make sense of other people e.g. by ascribing mental states like beliefs and desires to them? After a short criticism of Theory-Theory, Interaction Theory and the Narrative Theory of understanding others as well as an extended criticism of the Simulation Theory in Goldman's recent version (2006), we suggest an alternative approach: the Person Model Theory . Person models are the basis for our ability to (...)
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  31. Peter Milne (1999). Tarski, Truth and Model Theory. Proceedings of the Aristotelian Society 99 (2):141–167.score: 60.0
    As Wilfrid Hodges has observed, there is no mention of the notion truth-in-a-model in Tarski's article 'The Concept of Truth in Formalized Languages'; nor does truth make many appearances in his papers on model theory from the early 1950s. In later papers from the same decade, however, this reticence is cast aside. Why should Tarski, who defined truth for formalized languages and pretty much founded model theory, have been so reluctant to speak of truth in (...)
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  32. Elias H. Alves (1984). Paraconsistent Logic and Model Theory. Studia Logica 43 (1-2):17 - 32.score: 60.0
    The object of this paper is to show how one is able to construct a paraconsistent theory of models that reflects much of the classical one. In other words the aim is to demonstrate that there is a very smooth and natural transition from the model theory of classical logic to that of certain categories of paraconsistent logic. To this end we take an extension of da Costa''sC 1 = (obtained by adding the axiom A A) and (...)
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  33. Jaroslav Peregrin (1997). Language and its Models: Is Model Theory a Theory of Semantics? Nordic Journal of Philosophical Logic 2 (1):1-23.score: 60.0
    Tarskian model theory is almost universally understood as a formal counterpart of the preformal notion of semantics, of the “linkage between words and things”. The wide-spread opinion is that to account for the semantics of natural language is to furnish its settheoretic interpretation in a suitable model structure; as exemplified by Montague 1974.
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  34. Josh Weisberg (2003). Being All That We Can Be: A Critical Review of Thomas Metzinger's Being No One: The Self-Model Theory of Subjectivity. Journal of Consciousness Studies 10 (11):89-96.score: 60.0
    Some theorists approach the Gordian knot of consciousness by proclaiming its inherent tangle and mystery. Others draw out the sword of reduction and cut the knot to pieces. Philosopher Thomas Metzinger, in his important new book, Being No One: The Self-Model Theory of Subjectivity,1 instead attempts to disentangle the knot one careful strand at a time. The result is an extensive and complex work containing almost 700 pages of philosophical analysis, phenomenological reflection, and scientific data. The text offers (...)
     
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  35. William Demopoulos (2008). Some Remarks on the Bearing of Model Theory on the Theory of Theories. Synthese 164 (3):359 - 383.score: 60.0
    The present paper offers some remarks on the significance of first order model theory for our understanding of theories, and more generally, for our understanding of the “structuralist” accounts of the nature of theoretical knowledge that we associate with Russell, Ramsey and Carnap. What is unique about the presentation is the prominence it assigns to Craig’s Interpolation Lemma, some of its corollaries, and the manner of their demonstration. They form the underlying logical basis of the analysis.
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  36. Stephen Read (1997). Completeness and Categoricity: Frege, Gödel and Model Theory. History and Philosophy of Logic 18 (2):79-93.score: 60.0
    Frege?s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such as arithmetic and set theory. As such, it was seen to fail by Gödel?s incompleteness theorem of 1931. It is argued, however, that this is to impose a later interpretation on the word ?complete? it is clear from Dedekind?s writings that at least as good as interpretation of completeness is categoricity. Whereas few interesting first-order mathematical theories are categorical (...)
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  37. Yannis Stephanou (2000). Model Theory and Validity. Synthese 123 (2):165-193.score: 60.0
    Take a formula of first-order logic which is a logical consequence of some other formulae according to model theory, and in all those formulae replace schematic letters with English expressions. Is the argument resulting from the replacement valid in the sense that the premisses could not have been true without the conclusion also being true? Can we reason from the model-theoretic concept of logical consequence to the modal concept of validity? Yes, if the model theory (...)
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  38. William Demopoulos (1994). Frege, Hilbert, and the Conceptual Structure of Model Theory. History and Philosophy of Logic 15 (2):211-225.score: 60.0
    This paper attempts to confine the preconceptions that prevented Frege from appreciating Hilbert?s Grundlagen der Geometrie to two: (i) Frege?s reliance on what, following Wilfrid Hodges, I call a Frege?Peano language, and (ii) Frege?s view that the sense of an expression wholly determines its reference.I argue that these two preconceptions prevented Frege from achieving the conceptual structure of model theory, whereas Hilbert, at least in his practice, was quite close to the model?theoretic point of view.Moreover, the issues (...)
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  39. Giangiacomo Gerla & Virginia Vaccaro (1984). Modal Logic and Model Theory. Studia Logica 43 (3):203 - 216.score: 60.0
    We propose a first order modal logic, theQS4E-logic, obtained by adding to the well-known first order modal logicQS4 arigidity axiom schemas:A → □A, whereA denotes a basic formula. In this logic, thepossibility entails the possibility of extending a given classical first order model. This allows us to express some important concepts of classical model theory, such as existential completeness and the state of being infinitely generic, that are not expressibile in classical first order logic. Since they can (...)
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  40. Jouko Väänänen (2008). The Craig Interpolation Theorem in Abstract Model Theory. Synthese 164 (3):401 - 420.score: 60.0
    The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics (...)
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  41. Wim Veldman & Frank Waaldijk (1996). Some Elementary Results in Intutionistic Model Theory. Journal of Symbolic Logic 61 (3):745-767.score: 60.0
    We establish constructive refinements of several well-known theorems in elementary model theory. The additive group of the real numbers may be embedded elementarily into the additive group of pairs of real numbers, constructively as well as classically.
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  42. Jean-Baptiste Van der Henst (2002). Mental Model Theory Versus the Inference Rule Approach in Relational Reasoning. Thinking and Reasoning 8 (3):193 – 203.score: 60.0
    Researchers currently working on relational reasoning typically argue that mental model theory (MMT) is a better account than the inference rule approach (IRA). They predict and observe that determinate (or one-model) problems are easier than indeterminate (or two-model) problems, whereas according to them, IRA should lead to the opposite prediction. However, the predictions attributed to IRA are based on a mistaken argument. The IRA is generally presented in such a way that inference rules only deal with (...)
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  43. Tracey McGrail (2000). The Model Theory of Differential Fields with Finitely Many Commuting Derivations. Journal of Symbolic Logic 65 (2):885-913.score: 60.0
    In this paper we set out the basic model theory of differential fields of characteristic 0, which have finitely many commuting derivations. We give axioms for the theory of differentially closed differential fields with m derivations and show that this theory is ω-stable, model complete, and quantifier-eliminable, and that it admits elimination of imaginaries. We give a characterization of forking and compute the rank of this theory to be ω m + 1.
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  44. Mike Prest, Vera Puninskaya & Alexandra Ralph (2004). Some Model Theory of Sheaves of Modules. Journal of Symbolic Logic 69 (4):1187 - 1199.score: 60.0
    We explore some topics in the model theory of sheaves of modules. First we describe the formal language that we use. Then we present some examples of sheaves obtained from quivers. These, and other examples, will serve as illustrations and as counterexamples. Then we investigate the notion of strong minimality from model theory to see what it means in this context. We also look briefly at the relation between global, local and pointwise versions of properties related (...)
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  45. Georg Schiemer & Erich H. Reck (2013). Logic in the 1930s: Type Theory and Model Theory. Bulletin of Symbolic Logic 19 (4):433-472.score: 60.0
    In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style of Principia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early (...)
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  46. Françoise Delon & Rafel Farré (1996). Some Model Theory for Almost Real Closed Fields. Journal of Symbolic Logic 61 (4):1121-1152.score: 60.0
    We study the model theory of fields k carrying a henselian valuation with real closed residue field. We give a criteria for elementary equivalence and elementary inclusion of such fields involving the value group of a not necessarily definable valuation. This allows us to translate theories of such fields to theories of ordered abelian groups, and we study the properties of this translation. We also characterize the first-order definable convex subgroups of a given ordered abelian group and prove (...)
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  47. Philip N. Johnson-Laird (1994). A Model Theory of Induction. International Studies in the Philosophy of Science 8 (1):5 – 29.score: 60.0
    Abstract Theories of induction in psychology and artificial intelligence assume that the process leads from observation and knowledge to the formulation of linguistic conjectures. This paper proposes instead that the process yields mental models of phenomena. It uses this hypothesis to distinguish between deduction, induction, and creative forms of thought. It shows how models could underlie inductions about specific matters. In the domain of linguistic conjectures, there are many possible inductive generalizations of a conjecture. In the domain of models, however, (...)
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  48. Arthur M. Jacobs & Jonathan Grainger (1999). Modeling a Theory Without a Model Theory, or, Computational Modeling “After Feyerabend”. Behavioral and Brain Sciences 22 (1):46-47.score: 60.0
    Levelt et al. attempt to “model their theory” with WEAVER++. Modeling theories requires a model theory. The time is ripe for a methodology for building, testing, and evaluating computational models. We propose a tentative, five-step framework for tackling this problem, within which we discuss the potential strengths and weaknesses of Levelt et al.'s modeling approach.
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  49. Ravi Rajani & Mike Prest (2009). Pure-Injectivity and Model Theory for G-Sets. Journal of Symbolic Logic 74 (2):474-488.score: 60.0
    In the model theory of modules the Ziegler spectrum, the space of indecomposable pure-injective modules, has played a key role. We investigate the possibility of defining a similar space in the context of G-sets where G is a group.
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  50. Sam S. Rakover (1997). Can Psychology Provide a Coherent Account of Human Behavior? A Proposed Multiexplanation-Model Theory. Behavior and Philosophy 25 (1):43 - 76.score: 60.0
    Human behavior cannot be understood by using only models of explanation utilized in the natural sciences. Multiple models of explanation, which are not consistent with, or reducible to each other, are required and are in fact used in psychology to explain human actions. This situation, called "Multiexplanation," could cause a problem of developing a justified correspondence between psychological phenomena and multiple models of explanation. Unless this problem is solved, the explanatory capability of a psychological theory seems inconsistent and ad (...)
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