Results for 'Trees Coucke'

977 found
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  1.  40
    Experiential Learning of Empathy in a Care-Ethics Lab.Linus Vanlaere, Trees Coucke & Chris Gastmans - 2010 - Nursing Ethics 17 (3):325-336.
    To generate empathy in the care of vulnerable older persons requires care providers to reflect critically on their care practices. Ethics education and training must provide them with tools to accomplish such critical reflection. It must also create a pedagogical context in which good care can be taught and cultivated. The care-ethics lab ‘sTimul’ originated in 2008 in Flanders with the stimulation of ethical reflection in care providers and care providers in training as its main goal. Also in 2008, sTimul (...)
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  2.  4
    Care-Givers’ Reflections on an Ethics Education Immersive Simulation Care Experience: A Series of Epiphanous Events.Ann Gallagher, Matthew Peacock, Magdalena Zasada, Trees Coucke, Anna Cox & Nele Janssens - forthcoming - Nursing Inquiry.
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  3.  21
    Appropriate Computer-Mediated Communication: An Australian Indigenous Information System Case Study. [REVIEW]Andrew Turk & Kathryn Trees - 1999 - AI and Society 13 (4):377-388.
    This article discusses ways to operationalise the concept of culturally appropriate computer-mediated communication, utilising information systems (IS) development methodologies and adopting a postmodern and postcolonial perspective. By way of illustration, it describes progress on the participative development of the Ieramugadu Cultural Information System. This project is designed to develop and evaluate innovative procedures for elicitation, analysis, storage and communication of indigenous cultural heritage information. It is investigating culturally appropriate IS design techniques, multimedia approaches and ways to ensure protection of secret/sacred (...)
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  4.  11
    Conjectures of Rado and Chang and Special Aronszajn Trees.Stevo Todorčević & Víctor Torres Pérez - 2012 - Mathematical Logic Quarterly 58 (4-5):342-347.
    We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.
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  5.  59
    A First-Order Axiomatization of the Theory of Finite Trees.Rolf Backofen, James Rogers & K. Vijay-Shanker - 1995 - Journal of Logic, Language and Information 4 (1):5-39.
    We provide first-order axioms for the theories of finite trees with bounded branching and finite trees with arbitrary (finite) branching. The signature is chosen to express, in a natural way, those properties of trees most relevant to linguistic theories. These axioms provide a foundation for results in linguistics that are based on reasoning formally about such properties. We include some observations on the expressive power of these theories relative to traditional language complexity classes.
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  6.  36
    Degrees of Rigidity for Souslin Trees.Gunter Fuchs & Joel David Hamkins - 2009 - Journal of Symbolic Logic 74 (2):423-454.
    We investigate various strong notions of rigidity for Souslin trees, separating them under ♢ into a hierarchy. Applying our methods to the automorphism tower problem in group theory, we show under ♢ that there is a group whose automorphism tower is highly malleable by forcing.
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  7.  12
    Kurepa Trees and Namba Forcing.Bernhard König & Yasuo Yoshinobu - 2012 - Journal of Symbolic Logic 77 (4):1281-1290.
    We show that strongly compact cardinals and MM are sensitive to $\lambda$-closed forcings for arbitrarily large $\lambda$. This is done by adding ‘regressive' $\lambda$-Kurepa trees in either case. We argue that the destruction of regressive Kurepa trees requires a non-standard application of MM. As a corollary, we find a consistent example of an $\omega_2$-closed poset that is not forcing equivalent to any $\omega_2$-directed-closed poset.
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  8.  46
    Classes and Theories of Trees Associated with a Class of Linear Orders.Valentin Goranko & Ruaan Kellerman - 2011 - Logic Journal of the IGPL 19 (1):217-232.
    Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of (...) in terms of the first-order theory of the generating class C, and indicate the problems obstructing such general results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees. (shrink)
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  9.  10
    A Question About Suslin Trees and the Weak Square Hierarchy.Ernest Schimmerling - 2005 - Notre Dame Journal of Formal Logic 46 (3):373-374.
    We present a question about Suslin trees and the weak square hierarchy which was contributed to the list of open problems of the BIRS workshop.
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  10.  28
    Finding Socially Best Spanning Trees.Andreas Darmann, Christian Klamler & Ulrich Pferschy - 2011 - Theory and Decision 70 (4):511-527.
    This article combines Social Choice Theory with Discrete Optimization. We assume that individuals have preferences over edges of a graph that need to be aggregated. The goal is to find a socially “best” spanning tree in the graph. As ranking all spanning trees is becoming infeasible even for small numbers of vertices and/or edges of a graph, our interest lies in finding algorithms that determine a socially “best” spanning tree in a simple manner. This problem is closely related to (...)
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  11.  55
    Game Trees For Decision Analysis.Prakash P. Shenoy - 1998 - Theory and Decision 44 (2):149-171.
    Game trees (or extensive-form games) were first defined by von Neumann and Morgenstern in 1944. In this paper we examine the use of game trees for representing Bayesian decision problems. We propose a method for solving game trees using local computation. This method is a special case of a method due to Wilson for computing equilibria in 2-person games. Game trees differ from decision trees in the representations of information constraints and uncertainty. We compare the (...)
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  12.  33
    Environmental Implications of the Erosion of Cultural Taboo Practices in Awka-South Local Government Area of Anambra State, Nigeria: 1. Forests, Trees, and Water Resource Preservation. [REVIEW]G. O. Anoliefo, O. S. Isikhuemhen & N. R. Ochije - 2003 - Journal of Agricultural and Environmental Ethics 16 (3):281-296.
    Cultural taboos and their sanctionshave helped to check abuse of the environmentat least among the local people. The disregardfor these traditional checks and balancesespecially among Christians has adverselyaffected their enforcement at this time. Theenvironment and culture preservation inAwka-South were investigated. The faithfulobservance of the traditional laws in the studyarea was attributed to the fact that Awka-Southarea had remained occupied by the same peoplefor centuries. The study showed that thepreserved forests and their shrines in Nibotown have largely remained intact. In Nisetown, (...)
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  13.  15
    Completely Metrisable Groups Acting on Trees.Christian Rosendal - 2011 - Journal of Symbolic Logic 76 (3):1005 - 1022.
    We consider actions of completely metrisable groups on simplicial trees in the context of the Bass—Serre theory. Our main result characterises continuity of the amplitude function corresponding to a given action. Under fairly mild conditions on a completely metrisable group G, namely, that the set of elements generating a non-discrete or finite subgroup is somewhere dense, we show that in any decomposition as a free product with amalgamation, G = A * C B, the amalgamated groups A, B and (...)
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  14.  13
    Club Degrees of Rigidity and Almost Kurepa Trees.Gunter Fuchs - 2013 - Archive for Mathematical Logic 52 (1-2):47-66.
    A highly rigid Souslin tree T is constructed such that forcing with T turns T into a Kurepa tree. Club versions of previously known degrees of rigidity are introduced, as follows: for a rigidity property P, a tree T is said to have property P on clubs if for every club set C (containing 0), the restriction of T to levels in C has property P. The relationships between these rigidity properties for Souslin trees are investigated, and some open (...)
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  15.  38
    Two-Sided Trees for Sentential Logic, Predicate Logic, and Sentential Modal Logic.Jesse Fitts & David Beisecker - 2019 - Teaching Philosophy 42 (1):41-56.
    This paper will present two contributions to teaching introductory logic. The first contribution is an alternative tree proof method that differs from the traditional one-sided tree method. The second contribution combines this tree system with an index system to produce a user-friendly tree method for sentential modal logic.
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  16. Action Trees and Moral Judgment.Joshua Knobe - 2010 - Topics in Cognitive Science 2 (3):555-578.
    It has sometimes been suggested that people represent the structure of action in terms of an action tree. A question now arises about the relationship between this action tree representation and people’s moral judgments. A natural hypothesis would be that people first construct a representation of the action tree and then go on to use this representation in making moral judgments. The present paper argues for a more complex view. Specifically, the paper reports a series of experimental studies that appear (...)
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  17. Combinatorics on Ideals and Forcing with Trees.Marcia J. Groszek - 1987 - Journal of Symbolic Logic 52 (3):582-593.
    Classes of forcings which add a real by forcing with branching conditions are examined, and conditions are found which guarantee that the generic real is of minimal degree over the ground model. An application is made to almost-disjoint coding via a real of minimal degree.
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  18.  25
    Analyzing Godel's T Via Expanded Head Reduction Trees.Arnold Beckmann & Andreas Weiermann - 2000 - Mathematical Logic Quarterly 46 (4):517-536.
    Inspired from Buchholz' ordinal analysis of ID1 and Beckmann's analysis of the simple typed λ-calculus we classify the derivation lengths for Gödel's system T in the λ-formulation.
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  19.  19
    Automorphism Group Actions on Trees.A. Ivanov & R. Kossak - 2004 - Mathematical Logic Quarterly 50 (1):71.
    We study the situation when the automorphism group of a recursively saturated structure acts on an ℝ-tree. The cases of and models of Peano Arithmetic are central in the paper.
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  20.  23
    Trees and Spaces as Emotion and Norm Laden Components of Local Ecosystems in Nyamaropa Communal Land, Nyanga District, Zimbabwe.Alois Mandondo - 1997 - Agriculture and Human Values 14 (4):353-372.
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  21.  10
    Trees and Keislers Problem.Ali Enayat - 2001 - Archive for Mathematical Logic 40 (4):273-276.
    We give a new negative solution to Keisler's problem regarding Skolem functions and elementary extensions. In contrast to existing ad hoc solutions due to Payne, Knight, and Lachlan, our solution uses well-known models.
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  22.  40
    Projecting the Trees but Ignoring the Forest: A Brief Critique of Alfredo Pereira Jr.'s Target Essay.Gregory Michael Nixon - 2018 - Trans/Form/Ação 41 (s1):269-292.
    Pereira’s “The Projective Theory of Consciousness” is an experimental statement, drawing on many diverse sources, exploring how consciousness might be produced by a projective mechanism that results both in private selves and an experienced world. Unfortunately, pulling together so many unrelated sources and methods means none gets full attention. Furthermore, it seems to me that the uncomfortable breadth of this paper unnecessarily complicates his project; in fact it may hide what it seeks to reveal. If this conglomeration of diverse sources (...)
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  23. Finite Trees and the Necessary Use of Large Cardinals.Harvey Friedman - manuscript
    We introduce insertion domains that support the placement of new, higher, vertices into finite trees. We prove that every nonincreasing insertion domain has an element with simple structural properties in the style of classical Ramsey theory. This result is proved using standard large cardinal axioms that go well beyond the usual axioms for mathematics. We also establish that this result cannot be proved without these large cardinal axioms. We also introduce insertion rules that specify the placement of new, higher, (...)
     
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  24. On the Existence of Indiscernible Trees.Kota Takeuchi & Akito Tsuboi - 2012 - Annals of Pure and Applied Logic 163 (12):1891-1902.
    We introduce several concepts concerning the indiscernibility of trees. A tree is by definition an ordered set such that, for any a∈O, the initial segment {b∈O:b (...)
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  25.  8
    Perfect Trees and Elementary Embeddings.Sy-David Friedman & Katherine Thompson - 2008 - Journal of Symbolic Logic 73 (3):906-918.
    An important technique in large cardinal set theory is that of extending an elementary embedding j: M → N between inner models to an elementary embedding j*: M[G] → N[G*] between generic extensions of them. This technique is crucial both in the study of large cardinal preservation and of internal consistency. In easy cases, such as when forcing to make the GCH hold while preserving a measurable cardinal (via a reverse Easton iteration of α-Cohen forcing for successor cardinals α), the (...)
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  26. Peacocke's Trees.Boyd Millar - 2010 - Synthese 174 (3):445-461.
    In Sense and Content , Christopher Peacocke points out that two equally-sized trees at different distances from the perceiver are normally represented to be the same size, despite the fact that in a certain sense the nearer tree looks bigger ; he concludes on the basis of this observation that visual experiences possess irreducibly phenomenal properties. This argument has received the most attention of all of Peacocke’s arguments for separatism—the view that the intentional and phenomenal properties of experiences are (...)
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  27.  28
    Socratic Trees.Dorota Leszczyńska-Jasion, Mariusz Urbański & Andrzej Wiśniewski - 2013 - Studia Logica 101 (5):959-986.
    The method of Socratic proofs (SP-method) simulates the solving of logical problem by pure questioning. An outcome of an application of the SP-method is a sequence of questions, called a Socratic transformation. Our aim is to give a method of translation of Socratic transformations into trees. We address this issue both conceptually and by providing certain algorithms. We show that the trees which correspond to successful Socratic transformations—that is, to Socratic proofs—may be regarded, after a slight modification, as (...)
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  28.  15
    Aronszajn Trees and the Successors of a Singular Cardinal.Spencer Unger - 2013 - Archive for Mathematical Logic 52 (5-6):483-496.
    From large cardinals we obtain the consistency of the existence of a singular cardinal κ of cofinality ω at which the Singular Cardinals Hypothesis fails, there is a bad scale at κ and κ ++ has the tree property. In particular this model has no special κ +-trees.
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  29.  22
    Should Trees Have Standing?: Law, Morality, and the Environment.Christopher D. Stone - 2010 - Oup Usa.
    Originally published in 1972, Should Trees Have Standing? was a rallying point for the then burgeoning environmental movement, launching a worldwide debate on the basic nature of legal rights that reached the U.S. Supreme Court. Now, in the 35th anniversary edition of this remarkably influential book, Christopher D. Stone updates his original thesis and explores the impact his ideas have had on the courts, the academy, and society as a whole. At the heart of the book is an eminently (...)
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  30.  11
    Conjectures of Rado and Chang and Special Aronszajn Trees.Stevo Todorcevic & Víctor Torres Pérez - 2012 - Mathematical Logic Quarterly 58 (4):342-347.
    We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.
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  31.  27
    Aronszajn Trees, Square Principles, and Stationary Reflection.Chris Lambie-Hanson - 2017 - Mathematical Logic Quarterly 63 (3-4):265-281.
    We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of math formula introduced by Brodsky and Rinot for the purpose of constructing κ-Souslin trees. Answering a question of Rinot, we prove that the weaker of these strengthenings is compatible with stationary reflection at κ but the stronger is not. We then prove that, if μ is a singular cardinal, math formula implies the existence of a special math formula-tree with a cf-ascent (...)
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  32.  13
    Aronszajn Trees on ℵ2 and ℵ3.Uri Abraham - 1983 - Annals of Pure and Applied Logic 24 (3):213-230.
    Assuming the existence of a supercompact cardinal and a weakly compact cardinal above it, we provide a generic extension where there are no Aronszajn trees of height ω 2 or ω 3 . On the other hand we show that some large cardinal assumptions are necessary for such a consistency result.
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  33.  74
    The Prior Probabilities of Phylogenetic Trees.Joel D. Velasco - 2008 - Biology and Philosophy 23 (4):455-473.
    Bayesian methods have become among the most popular methods in phylogenetics, but theoretical opposition to this methodology remains. After providing an introduction to Bayesian theory in this context, I attempt to tackle the problem mentioned most often in the literature: the “problem of the priors”—how to assign prior probabilities to tree hypotheses. I first argue that a recent objection—that an appropriate assignment of priors is impossible—is based on a misunderstanding of what ignorance and bias are. I then consider different methods (...)
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  34.  76
    PDL for Ordered Trees.Loredana Afanasiev, Patrick Blackburn, Ioanna Dimitriou, Bertrand Gaiffe, Evan Goris, Maarten Marx & Maarten de Rijke - 2005 - Journal of Applied Non-Classical Logics 15 (2):115-135.
    This paper is about a special version of PDL, proposed by Marcus Kracht, for reasoning about sibling ordered trees. It has four basic programs corresponding to the child, parent, left- and right-sibling relations in such trees. The original motivation for this language is rooted in the field of model-theoretic syntax. Motivated by recent developments in the area of semi-structured data, and, especially, in the field of query languages for XML documents, we revisit the language. This renewed interest comes (...)
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  35.  17
    A Calculus for Belnap's Logic in Which Each Proof Consists of Two Trees.Stefan Wintein & Reinhard Muskens - 2012 - Logique Et Analyse 220:643-656.
    In this paper we introduce a Gentzen calculus for (a functionally complete variant of) Belnap's logic in which establishing the provability of a sequent in general requires \emph{two} proof trees, one establishing that whenever all premises are true some conclusion is true and one that guarantees the falsity of at least one premise if all conclusions are false. The calculus can also be put to use in proving that one statement \emph{necessarily approximates} another, where necessary approximation is a natural (...)
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  36.  34
    Classes of Ulm Type and Coding Rank-Homogeneous Trees in Other Structures.E. Fokina, J. F. Knight, A. Melnikov, S. M. Quinn & C. Safranski - 2011 - Journal of Symbolic Logic 76 (3):846 - 869.
    The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian p-groups, the class of Abelian torsion groups, and the special class of "rank-homogeneous" trees. We consider these conditions as a possible definition of what it means for a class of structures to have "Ulm type". The result says that there can be no Turing computable embedding of a class not of Ulm type into one of Ulm type. We (...)
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  37.  57
    Constraining Prior Probabilities of Phylogenetic Trees.Bengt Autzen - 2011 - Biology and Philosophy 26 (4):567-581.
    Although Bayesian methods are widely used in phylogenetic systematics today, the foundations of this methodology are still debated among both biologists and philosophers. The Bayesian approach to phylogenetic inference requires the assignment of prior probabilities to phylogenetic trees. As in other applications of Bayesian epistemology, the question of whether there is an objective way to assign these prior probabilities is a contested issue. This paper discusses the strategy of constraining the prior probabilities of phylogenetic trees by means of (...)
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  38.  32
    Computable Trees of Scott Rank [Image] , and Computable Approximation.Wesley Calvert, Julia F. Knight & Jessica Millar - 2006 - Journal of Symbolic Logic 71 (1):283 - 298.
    Makkai [10] produced an arithmetical structure of Scott rank $\omega _{1}^{\mathit{CK}}$. In [9]. Makkai's example is made computable. Here we show that there are computable trees of Scott rank $\omega _{1}^{\mathit{CK}}$. We introduce a notion of "rank homogeneity". In rank homogeneous trees, orbits of tuples can be understood relatively easily. By using these trees, we avoid the need to pass to the more complicated "group trees" of [10] and [9]. Using the same kind of trees, (...)
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  39.  61
    Ramsey’s Theorem for Trees: The Polarized Tree Theorem and Notions of Stability. [REVIEW]Damir D. Dzhafarov, Jeffry L. Hirst & Tamara J. Lakins - 2010 - Archive for Mathematical Logic 49 (3):399-415.
    We formulate a polarized version of Ramsey’s theorem for trees. For those exponents greater than 2, both the reverse mathematics and the computability theory associated with this theorem parallel that of its linear analog. For pairs, the situation is more complex. In particular, there are many reasonable notions of stability in the tree setting, complicating the analysis of the related results.
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  40.  21
    Computable Categoricity of Trees of Finite Height.Steffen Lempp, Charles McCoy, Russell Miller & Reed Solomon - 2005 - Journal of Symbolic Logic 70 (1):151-215.
    We characterize the structure of computably categorical trees of finite height, and prove that our criterion is both necessary and sufficient. Intuitively, the characterization is easiest to express in terms of isomorphisms of (possibly infinite) trees, but in fact it is equivalent to a Σ03-condition. We show that all trees which are not computably categorical have computable dimension ω. Finally, we prove that for every n≥ 1 in ω, there exists a computable tree of finite height which (...)
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  41. Analytic Cut Trees.Carlo Cellucci - 2000 - Logic Journal of the IGPL 8 (6):733-750.
    It has been maintained by Smullyan that the importance of cut-free proofs does not stem from cut elimination per se but rather from the fact that they satisfy the subformula property. In accordance with such a viewpoint in this paper we introduce analytic cut trees, a system from which cuts cannot be eliminated but satisfying the subformula property. Like tableaux analytic cut trees are a refutation system but unlike tableaux they have a single inference rule and several branch (...)
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  42.  21
    Linguistics, Logic and Finite Trees.Patrick Blackburn & Wilfried Meyer-Viol - 1994 - Logic Journal of the IGPL 2 (1):3-29.
    A modal logic is developed to deal with finite ordered binary trees a they are used in linguistics. A modal language is introduced with operators for the ‘mother of’, ‘first daughter of’ and ‘second daughter of’ relations together with their transitive reflexive closures. The relevant class of tree models is defined and three linguistic applications of this language are discussed: context free grammars, command relations, and trees decorated with feature structures. An axiomatic proof system is given for which (...)
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  43.  5
    Indiscernibles, EM-Types, and Ramsey Classes of Trees.Lynn Scow - 2015 - Notre Dame Journal of Formal Logic 56 (3):429-447.
    The author has previously shown that for a certain class of structures $\mathcal {I}$, $\mathcal {I}$-indexed indiscernible sets have the modeling property just in case the age of $\mathcal {I}$ is a Ramsey class. We expand this known class of structures from ordered structures in a finite relational language to ordered, locally finite structures which isolate quantifier-free types by way of quantifier-free formulas. This result is applied to give new proofs that certain classes of trees are Ramsey. To aid (...)
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  44.  88
    Talking About Trees and Truth-Conditions.Reinhard Muskens - 2001 - Journal of Logic, Language and Information 10 (4):417-455.
    We present Logical Description Grammar (LDG), a model ofgrammar and the syntax-semantics interface based on descriptions inelementary logic. A description may simultaneously describe the syntacticstructure and the semantics of a natural language expression, i.e., thedescribing logic talks about the trees and about the truth-conditionsof the language described. Logical Description Grammars offer a naturalway of dealing with underspecification in natural language syntax andsemantics. If a logical description (up to isomorphism) has exactly onetree plus truth-conditions as a model, it completely specifies (...)
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  45.  22
    Trees and Π 1 1 -Subsets of Ω1 Ω 1.Alan Mekler & Jouko Vaananen - 1993 - Journal of Symbolic Logic 58 (3):1052 - 1070.
    We study descriptive set theory in the space ω1 ω 1 by letting trees with no uncountable branches play a similar role as countable ordinals in traditional descriptive set theory. By using such trees, we get, for example, a covering property for the class of Π 1 1 -sets of ω1 ω 1 . We call a family U of trees universal for a class V of trees if $\mathscr{U} \subseteq \mathscr{V}$ and every tree in V (...)
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  46.  44
    Peach Trees, Gravity and God: Mechanism in Locke.Marleen Rozemond & Gideon Yaffe - 2004 - British Journal for the History of Philosophy 12 (3):387 – 412.
    Locke claimed that God superadded various powers to matter, including motion, the perfections of peach trees and elephants, gravity, and that he could superadd thought. Various interpreters have discussed the question whether Locke's claims about superaddition are in tension with his commitment to mechanistic explanation. This literature assumes that for Locke mechanistic explanation involves deducibility. We argue that this is an inaccurate interpretation and that mechanistic explanation involves a different type of intelligibility for Locke.
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  47.  25
    On Intermediate Predicate Logics of Some Finite Kripke Frames, I. Levelwise Uniform Trees.Dmitrij Skvortsov - 2004 - Studia Logica 77 (3):295 - 323.
    An intermediate predicate logic L is called finite iff it is characterized by a finite partially ordered set M, i.e., iff L is the logic of the class of all predicate Kripke frames based on M. In this paper we study axiomatizability of logics of this kind. Namely, we consider logics characterized by finite trees M of a certain type (levelwise uniform trees) and establish the finite axiomatizability criterion for this case.
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  48.  12
    Trees and Ehrenfeucht–Fraı̈ssé Games.Stevo Todorčević & Jouko Väänänen - 1999 - Annals of Pure and Applied Logic 100 (1-3):69-97.
    Trees are natural generalizations of ordinals and this is especially apparent when one tries to find an uncountable analogue of the concept of the Scott-rank of a countable structure. The purpose of this paper is to introduce new methods in the study of an ordering between trees whose analogue is the usual ordering between ordinals. For example, one of the methods is the tree-analogue of the successor operation on the ordinals.
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  49.  15
    Finding Paths Through Narrow and Wide Trees.Stephen Binns & Bjørn Kjos-Hanssen - 2009 - Journal of Symbolic Logic 74 (1):349-360.
    We consider two axioms of second-order arithmetic. These axioms assert, in two different ways, that infinite but narrow binary trees always have infinite paths. We show that both axioms are strictly weaker than Weak König's Lemma, and incomparable in strength to the dual statement (WWKL) that wide binary trees have paths.
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  50.  55
    Partial Proof Trees as Building Blocks for a Categorial Grammar.Aravind K. Joshi & Seth Kulick - 1997 - Linguistics and Philosophy 20 (6):637-667.
    We describe a categorial system (PPTS) based on partial proof trees(PPTs) as the building blocks of the system. The PPTs are obtained byunfolding the arguments of the type that would be associated with a lexicalitem in a simple categorial grammar. The PPTs are the basic types in thesystem and a derivation proceeds by combining PPTs together. We describe theconstruction of the finite set of basic PPTs and the operations forcombining them. PPTS can be viewed as a categorial system incorporating (...)
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