Results for 'Finite, The'

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  1. The Finite, the Infinite, and the Absolute.George Frederick James Temple - 1964 - [Southampton]University of Southampton.
     
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  2.  16
    Not Wholly Finite: The Dual Aspect of Finite Modes in Spinoza.Noa Shein - 2018 - Philosophia 46 (2):433-451.
    Spinoza’s bold claim that there exists only a single infinite substance entails that finite things pose a deep challenge: How can Spinoza account for their finitude and their plurality? Taking finite bodies as a test case for finite modes in general I articulate the necessary conditions for the existence of finite things. The key to my argument is the recognition that Spinoza’s account of finite bodies reflects both Cartesian and Hobbesian influences. This recognition leads to the surprising realization there must (...)
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  3.  23
    Finite Subjects in the Ethics: Spinoza on Indexical Knowledge, the First Person and the Individuality of Human Minds.Ursula Renz - 2013 - Renz, Ursula . Finite Subjects in the Ethics: Spinoza on Indexical Knowledge, the First Person and the Individuality of Human Minds. Oxford: Oxford University Press.
    This chapter suggests a new interpretation of Spinoza’s concept of mind claiming that the goal of the equation of the human mind with the idea of the body is not to solve the mind-body problem, but rather to show how we can, within the framework of Spinoza’s rationalism, conceive of finite minds as irreducibly distinguishable individuals. To support this view, the chapter discusses the passage from E2p11 to E2p13 against the background of three preliminaries, i.e. the notion of a union (...)
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  4.  22
    The Finite Model Property for Semilinear Substructural Logics.San-Min Wang - 2013 - Mathematical Logic Quarterly 59 (4-5):268-273.
  5. The Finite Values Property.E. Howarth & J. B. Paris - 2016 - In C. Beierle, C. Brewka & M. Thimm (eds.), Computational Models of Rationality, Essays Dedicated to Gabriele Kern-Isberner on the Occasion of her 60th Birthday. London, UK: College Publications. pp. 316-331.
    We argue that the simplicity condition on a probability function on sentences of a predicate language L that it takes only finitely many values on the sentences of any finite sublanguage of L can be viewed as rational. We then go on to investigate consequences of this condition, linking it to the model theoretic notion of quantifier elimination.
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  6.  13
    Beyond the Finite: The Sublime in Art and Science.Iain Boyd Whyte (ed.) - 2010 - Oxford University Press.
    Science is continually faced with describing that which is beyond. This book, through contributions from nine prominent scholars, tackles that challenge.
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  7.  57
    Jamesian Finite Theism and the Problems of Suffering.Walter Scott Stepanenko - 2018 - European Journal for Philosophy of Religion 10 (4):1.
    William James advocated a form of finite theism, motivated by epistemological and moral concerns with scholastic theism and pantheism. In this article, I elaborate James’s case for finite theism and his strategy for dealing with these concerns, which I dub the problems of suffering. I contend that James is at the very least implicitly aware that the problem of suffering is not so much one generic problem but a family of related problems. I argue that one of James’s great contributions (...)
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  8.  23
    Crossing the Finite Provinces of Meaning. Experience and Metaphor.Gerd Sebald - 2011 - Human Studies 34 (4):341-352.
    Schutz’s references to literature and arts in his theoretical works are manifold. But literature and theory are both a certain kind of a finite province of meaning, that means they are not easily accessible from the paramount reality of everyday life. Now there is another kind of referring to literature: metaphorizing it. Using it, as may be said with Lakoff and Johnson, to understand and to experience one kind of thing in terms of another. Literally metapherein means “to carry over”. (...)
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  9.  13
    Resistance to Pragmatic Tendencies in the World of Working in the Religious Finite Province of Meaning.Michael D. Barber - 2017 - Human Studies 40 (4):565-588.
    This essay describes some of the basic pragmatic tendencies at work in the world of working and then shows how the finite provinces of meaning of theoretical contemplation and literature act against those pragmatic tendencies. This analysis prepares the way to see how the religious province of meaning in a similar but also distinctive way acts back against these pragmatic tendencies. These three finite provinces of meaning make it possible to see the world from another center of orientation than that (...)
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  10. A Normal Modal Calculus Between T and S4 Without the Finite Model Property.David Makinson - 1969 - Journal of Symbolic Logic 34 (1):35-38.
    The first example of an intuitively meaningful propositional logic without the finite model property, and still the simplest one in the literature. The question of its decidability appears still to be open.
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  11.  23
    Conway–Kochen and the Finite Precision Loophole.Ronnie Hermens - 2014 - Foundations of Physics 44 (10):1038-1048.
    Recently Cator and Landsman made a comparison between Bell’s Theorem and Conway and Kochen’s Strong Free Will Theorem. Their overall conclusion was that the latter is stronger in that it uses fewer assumptions, but also that it has two shortcomings. Firstly, no experimental test of the Conway–Kochen Theorem has been performed thus far, and, secondly, because the Conway–Kochen Theorem is strongly connected to the Kochen–Specker Theorem it may be susceptible to the finite precision loophole of Meyer, Kent and Clifton. In (...)
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  12.  36
    How to Take Advantage of the Blur Between the Finite and the Infinite.Pierre Cartier - 2012 - Logica Universalis 6 (1-2):217-226.
    In this paper is presented and discussed the notion of true finite by opposition to the notion of theoretical finite. Examples from mathematics and physics are given. Fermat’s infinite descent principle is challenged.
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  13. The Concept of Truth in a Finite Universe.Panu Raatikainen - 2000 - Journal of Philosophical Logic 29 (6):617-633.
    The prospects and limitations of defining truth in a finite model in the same language whose truth one is considering are thoroughly examined. It is shown that in contradistinction to Tarski's undefinability theorem for arithmetic, it is in a definite sense possible in this case to define truth in the very language whose truth is in question.
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  14. Acosmism or Weak Individuals?: Hegel, Spinoza, and the Reality of the Finite.Yitzhak Y. Melamed - 2010 - Journal of the History of Philosophy 48 (1):pp. 77-92.
    Like many of his contemporaries, Hegel considered Spinoza a modern reviver of ancient Eleatic monism, in whose system “all determinate content is swallowed up as radically null and void”. This characterization of Spinoza as denying the reality of the world of finite things had a lasting influence on the perception of Spinoza in the two centuries that followed. In this article, I take these claims of Hegel to task and evaluate their validity. Although Hegel’s official argument for the unreality of (...)
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  15.  31
    Incompleteness in the Finite Domain.Pavel Pudlák - 2017 - Bulletin of Symbolic Logic 23 (4):405-441.
    Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond NP ≠ coNP. These conjectures formally connect computational complexity with the difficulty of proving some sentences, which means that high computational complexity of a problem associated with a sentence implies that the sentence is not provable in a weak theory, or requires a long proof. Another reason for putting forward these conjectures is that some results in proof complexity seem to be (...)
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  16.  34
    Finite Identification From the Viewpoint of Epistemic Update.Cédric Dégremont & Nina Gierasimczuk - 2011 - Information And Computation 209 (3):383-396.
    Formal learning theory constitutes an attempt to describe and explain the phenomenon of learning, in particular of language acquisition. The considerations in this domain are also applicable in philosophy of science, where it can be interpreted as a description of the process of scientific inquiry. The theory focuses on various properties of the process of hypothesis change over time. Treating conjectures as informational states, we link the process of conjecture-change to epistemic update. We reconstruct and analyze the temporal aspect of (...)
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  17.  25
    On the Finite Model Property of Intuitionistic Modal Logics Over MIPC.Takahito Aoto & Hiroyuki Shirasu - 1999 - Mathematical Logic Quarterly 45 (4):435-448.
    MIPC is a well-known intuitionistic modal logic of Prior and Bull . It is shown that every normal intuitionistic modal logic L over MIPC has the finite model property whenever L is Kripke-complete and universal.
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  18.  32
    Disquotationalism, Minimalism, and the Finite Minimal Theory.Jay Newhard - 2004 - Canadian Journal of Philosophy 34 (1):61 - 86.
    Recently, Paul Horwich has developed the minimalist theory of truth, according to which the truth predicate does not express a substantive property, though it may be used as a grammatical expedient. Minimalism shares these claims with Quine’s disquotationalism; it differs from disquotationalism primarily in holding that truth-bearers are propositions, rather than sentences. Despite potential ontological worries, allowing that propositions bear truth gives Horwich a prima facie response to several important objections to disquotationalism. In section I of this paper, disquotationalism is (...)
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  19.  25
    Elementary Properties of the Finite Ranks.Anuj Dawar, Kees Doets, Steven Lindell & Scott Weinstein - 1998 - Mathematical Logic Quarterly 44 (3):349-353.
    This note investigates the class of finite initial segments of the cumulative hierarchy of pure sets. We show that this class is first-order definable over the class of finite directed graphs and that this class admits a first-order definable global linear order. We apply this last result to show that FO = FO.
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  20.  9
    The Finite Model Property for Knotted Extensions of Propositional Linear Logic.C. J. van Alten - 2005 - Journal of Symbolic Logic 70 (1):84-98.
    The logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule: γ, xn → y / γ, xm → y. It is proved that the class of algebraic models for such a logic has the finite embeddability property, meaning that every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. It follows that each such logic has the finite model property (...)
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  21.  6
    Abelian‐by‐G Groups, for G Finite, From the Model Theoretic Point of View.Annalisa Marcja & Carlo Toffalori - 1994 - Mathematical Logic Quarterly 40 (1):125-131.
    Let G be a finite group. We prove that the theory af abelian-by-G groups is decidable if and only if the theory of modules over the group ring ℤ[G] is decidable. Then we study some model theoretic questions about abelian-by-G groups, in particular we show that their class is elementary when the order of G is squarefree.
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  22.  8
    Bimodal Logics with a “Weakly Connected” Component Without the Finite Model Property.Agi Kurucz - 2017 - Notre Dame Journal of Formal Logic 58 (2):287-299.
    There are two known general results on the finite model property of commutators [L0,L1]. If L is finitely axiomatizable by modal formulas having universal Horn first-order correspondents, then both [L,K] and [L,S5] are determined by classes of frames that admit filtration, and so they have the fmp. On the negative side, if both L0 and L1 are determined by transitive frames and have frames of arbitrarily large depth, then [L0,L1] does not have the fmp. In this paper we show that (...)
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  23.  5
    A Normal Modal Calculus Between T and S4 Without the Finite Model Property.David Makinson - 1971 - Journal of Symbolic Logic 36 (4):692-692.
    The first example of an intuitively meaningful propositional logic without the finite model property, and still the simplest one in the literature. The question of its decidability appears still to be open.
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  24. The Finite Cutset Property.J.‐M. Brochet - 1993 - Mathematical Logic Quarterly 39 (1):158-164.
    A cutset of H is a subset of ∪ H which meets every element of H.H has the finite cutset property if every cutset of H contains a finite one. We study this notion, and in particular how it is related to the compactness of H for the natural topology. MSC: 04A20, 54D30.
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  25. Almost Ideal: Computational Epistemology and the Limits of Rationality for Finite Reasoners.Danilo Fraga Dantas - 2016 - Dissertation, University of California, Davis
    The notion of an ideal reasoner has several uses in epistemology. Often, ideal reasoners are used as a parameter of (maximum) rationality for finite reasoners (e.g. humans). However, the notion of an ideal reasoner is normally construed in such a high degree of idealization (e.g. infinite/unbounded memory) that this use is unadvised. In this dissertation, I investigate the conditions under which an ideal reasoner may be used as a parameter of rationality for finite reasoners. In addition, I present and justify (...)
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  26. The Presentation of the Infinite in the Finite' : The Place of God in Post-Kantian Philosophy.Stephen Mulhall - 2007 - In Brian Leiter & Michael Rosen (eds.), The Oxford Handbook of Continental Philosophy. Oxford University Press.
     
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  27. Spinoza on Negation, Mind-Dependence and the Reality of the Finite.Karolina Hübner - 2015 - In Yitzhak Melamed (ed.), The Young Spinoza: A Metaphysician in the Making. pp. 221-37.
    The article explores the idea that according to Spinoza finite thought and substantial thought represent reality in different ways. It challenges “acosmic” readings of Spinoza's metaphysics, put forth by readers like Hegel, according to which only an infinite, undifferentiated substance genuinely exists, and all representations of finite things are illusory. Such representations essentially involve negation with respect to a more general kind. The article shows that several common responses to the charge of acosmism fail. It then argues that we must (...)
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  28.  5
    The Logic of Informational Independence and Finite Models.G. Sandu - 1997 - Logic Journal of the IGPL 5 (1):79-95.
    In this paper we relax the assumption that the logical constants of ordinary first-order logic be linearly ordered. As a consequence, we shall have formulas involving not only partially ordered quantifiers, but also partially ordered connectives. The resulting language, called the language of informational independence will be given an interpretation in terms of games of imperfect information. The II-logic will be seen to have some interesting properties: It is very natural to define in this logic two negations, weak negation as (...)
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  29. On the Ethics of the Finite. The Referential Nature of the Sublime in Kant.O. Briese - 1996 - Kant-Studien 87 (3):325-347.
  30.  28
    Between the Infinite and the Finite: God, Hegel and Disagreement.Anthony Joseph Carroll - 2019 - European Journal for Philosophy of Religion 11 (3):95-113.
    In this article, I consider the importance of philosophy in the dialogue between religious believers and non-believers. I begin by arguing that a new epistemology of epistemic peer disagreement is required if the dialogue is to progress. Rather than viewing the differences between the positions as due to a deficit of understanding, I argue that differences result from the existential anchoring of such enquiries in life projects and the under-determination of interpretations by experience. I then explore a central issue which (...)
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  31.  3
    The Coincidence of the Finite and the Infinite in Spinoza and Hegel.José María Sánchez de León Serrano & Noa Shein - 2019 - Idealistic Studies 49 (1):23-44.
    This paper proposes a reassessment of Hegel’s critical reading of Spinoza and of the charge of acosmism, for which this reading is known. We argue that this charge is actually the consequence of a more fundamental criticism, namely Spinoza’s presumable inability to conceive the unity of the finite and the infinite. According to Hegel, the infinite and the finite remain two poles apart in Spinoza’s metaphysics, which thus fails to be a true monism, insofar as it contains an irreducible duality. (...)
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  32. 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, vertices (...)
     
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  33. The Finite and the Infinite in Frege's Grundgesetze der Arithmetik.Richard G. Heck - 1998 - In Matthias Schirn (ed.), Philosophy of Mathematics Today. Oxford University Press.
    Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice.
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  34.  53
    The Finite Model Property for Various Fragments of Intuitionistic Linear Logic.Mitsuhiro Okada & Kazushige Terui - 1999 - Journal of Symbolic Logic 64 (2):790-802.
    Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic (MALL) and for affine logic (LLW), i.e., linear logic with weakening. In this paper, we shall prove the finite model property for intuitionistic versions of those, i.e. intuitionistic MALL (which we call IMALL), and intuitionistic LLW (which we call ILLW). In addition, we shall show the finite model property for contractive linear logic (LLC), i.e., linear logic with contraction, and for its intuitionistic version (ILLC). (...)
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  35.  16
    The Large Structures of Grothendieck Founded on Finite Order Arithmetic.Colin Mclarty - forthcoming - Review of Symbolic Logic:1-30.
    The large-structure tools of cohomology including toposes and derived categories stay close to arithmetic in practice, yet published foundations for them go beyond ZFC in logical strength. We reduce the gap by founding all the theorems of Grothendieck’s SGA, plus derived categories, at the level of Finite-Order Arithmetic, far below ZFC. This is the weakest possible foundation for the large-structure tools because one elementary topos of sets with infinity is already this strong.
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  36.  10
    The Finite Model Property for Logics with the Tangle Modality.Robert Goldblatt & Ian Hodkinson - 2018 - Studia Logica 106 (1):131-166.
    The tangle modality is a propositional connective that extends basic modal logic to a language that is expressively equivalent over certain classes of finite frames to the bisimulation-invariant fragments of both first-order and monadic second-order logic. This paper axiomatises several logics with tangle, including some that have the universal modality, and shows that they have the finite model property for Kripke frame semantics. The logics are specified by a variety of conditions on their validating frames, including local and global connectedness (...)
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  37.  20
    The Bayes Blind Spot of a Finite Bayesian Agent is a Large Set.Zalán Gyenis & Miklós Rédei - unknown
    The Bayes Blind Spot of a Bayesian Agent is the set of probability measures on a Boolean algebra that are absolutely continuous with respect to the background probability measure of a Bayesian Agent on the algebra and which the Bayesian Agent cannot learn by conditionalizing no matter what evidence he has about the elements in the Boolean algebra. It is shown that if the Boolean algebra is finite, then the Bayes Blind Spot is a very large set: it has the (...)
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  38.  34
    Automata Presenting Structures: A Survey of the Finite String Case.Sasha Rubin - 2008 - Bulletin of Symbolic Logic 14 (2):169-209.
    A structure has a (finite-string) automatic presentation if the elements of its domain can be named by finite strings in such a way that the coded domain and the coded atomic operations are recognised by synchronous multitape automata. Consequently, every structure with an automatic presentation has a decidable first-order theory. The problems surveyed here include the classification of classes of structures with automatic presentations, the complexity of the isomorphism problem, and the relationship between definability and recognisability.
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  39. Splittings and the Finite Model Property.Marcus Kracht - 1993 - Journal of Symbolic Logic 58 (1):139-157.
    An old conjecture of modal logics states that every splitting of the major systems K4, S4, G and Grz has the finite model property. In this paper we will prove that all iterated splittings of G have fmp, whereas in the other cases we will give explicit counterexamples. We also introduce a proof technique which will give a positive answer for large classes of splitting frames. The proof works by establishing a rather strong property of these splitting frames namely that (...)
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  40.  35
    Embedding Finite Lattices Into the Σ20 Enumeration Degrees.Steffen Lempp & Andrea Sorbi - 2002 - Journal of Symbolic Logic 67 (1):69-90.
    We show that every finite lattice is embeddable into the Σ 0 2 enumeration degrees via a lattice-theoretic embedding which preserves 0 and 1.
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  41.  15
    A Finite Lattice Without Critical Triple That Cannot Be Embedded Into the Enumerable Turing Degrees.Steffen Lempp & Manuel Lerman - 1997 - Annals of Pure and Applied Logic 87 (2):167-185.
    We exhibit a finite lattice without critical triple that cannot be embedded into the enumerable Turing degrees. Our method promises to lead to a full characterization of the finite lattices embeddable into the enumerable Turing degrees.
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  42.  50
    The Evolution of Cooperation in the Centipede Game with Finite Populations.Rory Smead - 2008 - Philosophy of Science 75 (2):157-177.
    The partial cooperation displayed by subjects in the Centipede Game deviates radically from the predictions of traditional game theory. Even standard, infinite population, evolutionary settings have failed to provide an explanation for this behavior. However, recent work in finite population evolutionary models has shown that such settings can produce radically different results from the standard models. This paper examines the evolution of partial cooperation in finite populations. The results reveal a new possible explanation that is not open to the standard (...)
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  43.  10
    The Evolution of Cooperation in Finite Populations with Synergistic Payoffs.Rafael Ventura - 2019 - Biology and Philosophy 34 (4):43.
    In a series of papers, Forber and Smead :151–166, 2014, Biol Philos 30:405–421, 2015) and Smead and Forber :698–707, 2013) make a valuable contribution to the study of cooperation in finite populations by analyzing an understudied model: the prisoner’s delight. It always pays to cooperate in the one-shot prisoner’s delight, so this model presents a best-case scenario for the evolution of cooperation. Yet, what Forber and Smead find is highly counterintuitive. In finite populations playing the prisoner’s delight, increasing the benefit (...)
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  44.  68
    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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  45.  12
    On the Modal Definability of Simulability by Finite Transitive Models.David Fernández Duque - 2011 - Studia Logica 98 (3):347-373.
    We show that given a finite, transitive and reflexive Kripke model 〈 W , ≼, ⟦ ⋅ ⟧ 〉 and $${w \in W}$$ , the property of being simulated by w (i.e., lying on the image of a literalpreserving relation satisfying the ‘forth’ condition of bisimulation) is modally undefinable within the class of S4 Kripke models. Note the contrast to the fact that lying in the image of w under a bi simulation is definable in the standard modal language even (...)
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  46.  61
    The Logic of Finite Order.Simon Hewitt - 2012 - Notre Dame Journal of Formal Logic 53 (3):297-318.
    This paper develops a formal system, consisting of a language and semantics, called serial logic ( SL ). In rough outline, SL permits quantification over, and reference to, some finite number of things in an order , in an ordinary everyday sense of the word “order,” and superplural quantification over things thus ordered. Before we discuss SL itself, some mention should be made of an issue in philosophical logic which provides the background to the development of SL , and with (...)
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  47.  6
    On the Minimal Cover Property and Certain Notions of Finite.Eleftherios Tachtsis - 2018 - Archive for Mathematical Logic 57 (5-6):665-686.
    In set theory without the axiom of choice, we investigate the deductive strength of the principle “every topological space with the minimal cover property is compact”, and its relationship with certain notions of finite as well as with properties of linearly ordered sets and partially ordered sets.
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  48.  58
    Maps Between Some Different Kinds of Contraction Function: The Finite Case.Carlos E. Alchourrón & David Makinson - 1986 - Studia Logica 45 (2):187 - 198.
    In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet contraction over that theory. The purpose (...)
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  49.  7
    The Finite Submodel Property and Ω-Categorical Expansions of Pregeometries.Marko Djordjević - 2006 - Annals of Pure and Applied Logic 139 (1):201-229.
    We prove, by a probabilistic argument, that a class of ω-categorical structures, on which algebraic closure defines a pregeometry, has the finite submodel property. This class includes any expansion of a pure set or of a vector space, projective space or affine space over a finite field such that the new relations are sufficiently independent of each other and over the original structure. In particular, the random graph belongs to this class, since it is a sufficiently independent expansion of an (...)
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  50.  57
    The Geometry of Forking and Groups of Finite Morley Rank.Anand Pillay - 1995 - Journal of Symbolic Logic 60 (4):1251-1259.
    The notion of CM-triviality was introduced by Hrushovski, who showed that his new strongly minimal sets have this property. Recently Baudisch has shown that his new ω 1 -categorical group has this property. Here we show that any group of finite Morley rank definable in a CM-trivial theory is nilpotent-by-finite, or equivalently no simple group of finite Morley rank can be definable in a CM-trivial theory.
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