Results for ' Finiteness'

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  1. A New Modal Lindstrom Theorem.Finite Depth Property - 2006 - In Henrik Lagerlund, Sten Lindström & Rysiek Sliwinski (eds.), Modality Matters: Twenty-Five Essays in Honour of Krister Segerberg. Uppsala Philosophical Studies 53. pp. 55.
     
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  2. An algorithm for axiomatizing and theorem proving in finite many-valued propositional logics* Walter A. Carnielli.Proving in Finite Many-Valued Propositional - forthcoming - Logique Et Analyse.
     
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  3. Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...)
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  4.  5
    Finite Freedom and its split from the Absolute in Schelling’s Bruno.Juan José Rodríguez - 2024 - Neue Zeitschrift für Systematicsche Theologie Und Religionsphilosophie 66 (2):93-115.
    The dialogue Bruno of 1802 is arguably the natural starting point for any investigation on the concepts of finitude, evil and human freedom in Schelling’s middle metaphysics. In this dialogue the author elaborates for the first time in his system a concept of freedom and independence of the finite, which extends via his reformulation in Philosophy and Religion of 1804 to the Freedom Essay of 1809 and beyond to the works of 1810 and 1811 – Stuttgart Private Lectures and The (...)
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  5. Finite and Infinite Goods: A Framework for Ethics.Robert Merrihew Adams - 1999 - New York: Oxford University Press.
    Renowned scholar Robert Adams explores the relation between religion and ethics through a comprehensive philosophical account of a theistically-based framework for ethics. Adams' framework begins with the good rather than the right, and with excellence rather than usefulness. He argues that loving the excellent, of which adoring God is a clear example, is the most fundamental aspect of a life well lived. Developing his original and detailed theory, Adams contends that devotion, the sacred, grace, martyrdom, worship, vocation, faith, and other (...)
  6.  49
    A finite thinking.Jean-Luc Nancy - 2003 - Stanford, Calif.: Stanford University Press. Edited by Simon Sparks.
    This book is a rich collection of philosophical essays radically interrogating key notions and preoccupations of the phenomenological tradition. While using Heidegger’s Being and Time as its permanent point of reference and dispute, this collection also confronts other important philosophers, such as Kant, Nietzsche, and Derrida. The projects of these pivotal thinkers of finitude are relentlessly pushed to their extreme, with respect both to their unexpected horizons and to their as yet unexplored analytical potential. A Finite Thinking shows that, paradoxically, (...)
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  7. Finite additivity, another lottery paradox and conditionalisation.Colin Howson - 2014 - Synthese 191 (5):1-24.
    In this paper I argue that de Finetti provided compelling reasons for rejecting countable additivity. It is ironical therefore that the main argument advanced by Bayesians against following his recommendation is based on the consistency criterion, coherence, he himself developed. I will show that this argument is mistaken. Nevertheless, there remain some counter-intuitive consequences of rejecting countable additivity, and one in particular has all the appearances of a full-blown paradox. I will end by arguing that in fact it is no (...)
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  8.  30
    The finite model property for semilinear substructural logics.San-Min Wang - 2013 - Mathematical Logic Quarterly 59 (4-5):268-273.
    In this paper, we show that the finite model property fails for certain non‐integral semilinear substructural logics including Metcalfe and Montagna's uninorm logic and involutive uninorm logic, and a suitable extension of Metcalfe, Olivetti and Gabbay's pseudo‐uninorm logic. Algebraically, the results show that certain classes of bounded residuated lattices that are generated as varieties by their linearly ordered members are not generated as varieties by their finite members.
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  9.  44
    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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  10.  18
    Finite and Infinite Goods: A Framework for Ethics.Robert Merrihew Adams - 1999 - New York, US: Oxford University Press USA.
    Adams offers a theistically-based framework for ethics, based upon the idea of a transcendent, infinite good, which is God, and its relation to the many finite examples of good in our experience. His account shows how philosophically unfashionable religious concepts can enrich ethical thought. "...one of the two most important books in moral philosophy of the last quarter century, the other being After Virtue."--Theology Today.
  11.  11
    All Finitely Axiomatizable Normal Extensions of K4.3 are Decidable.Michael Zakharyaschevm & Alexander Alekseev - 1995 - Mathematical Logic Quarterly 41 (1):15-23.
    We use the apparatus of the canonical formulas introduced by Zakharyaschev [10] to prove that all finitely axiomatizable normal modal logics containing K4.3 are decidable, though possibly not characterized by classes of finite frames. Our method is purely frame-theoretic. Roughly, given a normal logic L above K4.3, we enumerate effectively a class of frames with respect to which L is complete, show how to check effectively whether a frame in the class validates a given formula, and then apply a Harropstyle (...)
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  12. Définitions et fins du droit.Michel Villey - 1975 - Paris: Dalloz.
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  13.  4
    Finite perfection: reflections on virtue.Michael A. Weinstein - 1985 - Amherst: University of Massachusetts Press.
  14.  33
    On Finite Model Property for Admissible Rules.Vladimir V. Rybakov, Vladimir R. Kiyatkin & Tahsin Oner - 1999 - Mathematical Logic Quarterly 45 (4):505-520.
    Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, (...)
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  15.  15
    Finite Axiomatizability of Transitive Modal Logics of Finite Depth and Width with Respect to Proper-Successor-Equivalence.Yan Zhang & X. U. Ming - forthcoming - Review of Symbolic Logic:1-14.
    This paper proves the finite axiomatizability of transitive modal logics of finite depth and finite width w.r.t. proper-successor-equivalence. The frame condition of the latter requires, in a rooted transitive frame, a finite upper bound of cardinality for antichains of points with different sets of proper successors. The result generalizes Rybakov’s result of the finite axiomatizability of extensions of$\mathbf {S4}$of finite depth and finite width.
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  16.  61
    Finite state automata and simple recurrent networks.Axel Cleeremans & David Servan-Schreiber - unknown
    We explore a network architecture introduced by Elman (1988) for predicting successive elements of a sequence. The network uses the pattern of activation over a set of hidden units from time-step 25-1, together with element t, to predict element t + 1. When the network is trained with strings from a particular finite-state grammar, it can learn to be a perfect finite-state recognizer for the grammar. When the network has a minimal number of hidden units, patterns on the hidden units (...)
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  17.  31
    Finite Models of Some Substructural Logics.Wojciech Buszkowski - 2002 - Mathematical Logic Quarterly 48 (1):63-72.
    We give a proof of the finite model property of some fragments of commutative and noncommutative linear logic: the Lambek calculus, BCI, BCK and their enrichments, MALL and Cyclic MALL. We essentially simplify the method used in [4] for proving fmp of BCI and the Lambek ca culus and in [5] for proving fmp of MALL. Our construction of finite models also differs from that used in Lafont [8] in his proof of fmp of MALL.
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  18.  68
    Finite conformal hypergraph covers and Gaifman cliques in finite structures.Ian Hodkinson & Martin Otto - 2003 - Bulletin of Symbolic Logic 9 (3):387-405.
    We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques-thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms, we show that every finite hypergraph admits a bisimilar cover by a finite conformal hypergraph. In terms (...)
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  19. Finite and Infinite Goods: A Framework for Ethics.Thomas Pink - 2004 - Mind 113 (449):142-147.
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  20. Finite and Infinite Goods: A Framework for Ethics.[author unknown] - 2001 - Philosophical Quarterly 51 (203):280-282.
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  21.  23
    Finite replacement and finite hilbert‐style axiomatizability.B. Herrmann & W. Rautenberg - 1992 - Mathematical Logic Quarterly 38 (1):327-344.
    We define a property for varieties V, the f.r.p. . If it applies to a finitely based V then V is strongly finitely based in the sense of [14], see Theorem 2. Moreover, we obtain finite axiomatizability results for certain propositional logics associated with V, in its generality comparable to well-known finite base results from equational logic. Theorem 3 states that each variety generated by a 2-element algebra has the f.r.p. Essentially this implies finite axiomatizability of a 2-valued logic in (...)
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  22. 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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  23.  93
    Finite forms of de finetti's theorem on exchangeability.Persi Diaconis - 1977 - Synthese 36 (2):271 - 281.
    A geometrical interpretation of independence and exchangeability leads to understanding the failure of de Finetti's theorem for a finite exchangeable sequence. In particular an exchangeable sequence of length r which can be extended to an exchangeable sequence of length k is almost a mixture of independent experiments, the error going to zero like 1/k.
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  24.  35
    Finite Tree Property for First-Order Logic with Identity and Functions.Merrie Bergmann - 2005 - Notre Dame Journal of Formal Logic 46 (2):173-180.
    The typical rules for truth-trees for first-order logic without functions can fail to generate finite branches for formulas that have finite models–the rule set fails to have the finite tree property. In 1984 Boolos showed that a new rule set proposed by Burgess does have this property. In this paper we address a similar problem with the typical rule set for first-order logic with identity and functions, proposing a new rule set that does have the finite tree property.
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  25.  71
    Locally finite theories.Jan Mycielski - 1986 - Journal of Symbolic Logic 51 (1):59-62.
    We say that a first order theoryTislocally finiteif every finite part ofThas a finite model. It is the purpose of this paper to construct in a uniform way for any consistent theoryTa locally finite theory FIN which is syntactically isomorphic toT.Our construction draws upon the main idea of Paris and Harrington [6] and generalizes the syntactic aspect of their result from arithmetic to arbitrary theories. The first mathematically strong locally finite theory, called FIN, was defined in [1]. Now we get (...)
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  26.  38
    The finite model property in tense logic.Frank Wolter - 1995 - Journal of Symbolic Logic 60 (3):757-774.
    Tense logics in the bimodal propositional language are investigated with respect to the Finite Model Property. In order to prove positive results techniques from investigations of modal logics above K4 are extended to tense logic. General negative results show the limits of the transfer.
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  27.  38
    A finite model theorem for the propositional μ-calculus.Dexter Kozen - 1988 - Studia Logica 47 (3):233 - 241.
    We prove a finite model theorem and infinitary completeness result for the propositional -calculus. The construction establishes a link between finite model theorems for propositional program logics and the theory of well-quasi-orders.
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  28.  60
    Finite partially-ordered quantification.Wilbur John Walkoe Jr - 1970 - Journal of Symbolic Logic 35 (4):535-555.
  29.  39
    Finitely generated free Heyting algebras: the well-founded initial segment.R. Elageili & J. K. Truss - 2012 - Journal of Symbolic Logic 77 (4):1291-1307.
    In this paper we describe the well-founded initial segment of the free Heyting algebra ������α on finitely many, α, generators. We give a complete classification of initial sublattices of ������₂ isomorphic to ������₁ (called 'low ladders'), and prove that for 2 < α < ω, the height of the well-founded initial segment of ������α.
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  30.  19
    Finitely generated submodels of an uncountably categorical homogeneous structure.Tapani Hyttinen - 2004 - Mathematical Logic Quarterly 50 (1):77.
    We generalize the result of non-finite axiomatizability of totally categorical first-order theories from elementary model theory to homogeneous model theory. In particular, we lift the theory of envelopes to homogeneous model theory and develope theory of imaginaries in the case of ω-stable homogeneous classes of finite U-rank.
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  31.  12
    Multiplicative finite embeddability vs divisibility of ultrafilters.Boris Šobot - 2022 - Archive for Mathematical Logic 61 (3):535-553.
    We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations \ and \. The set of its minimal elements proves to be very rich, and the \-hierarchy is used to get a better intuition of this richness. We find the place of the set of \-maximal ultrafilters among some known families of ultrafilters. Finally, we introduce new notions of largeness of subsets (...)
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  32.  30
    Finite and infinite support in nominal algebra and logic: nominal completeness theorems for free.Murdoch J. Gabbay - 2012 - Journal of Symbolic Logic 77 (3):828-852.
    By operations on models we show how to relate completeness with respect to permissivenominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal models, so the construction hinges on generating from an instance of the latter, some instance of the former in which sufficiently many inequalities are preserved between elements. We do this using an infinite generalisation of nominal atoms-abstraction. The results are of interest in their own right, (...)
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  33. Finite-state temporal projection.Tim Fernando - manuscript
    Finite-state methods are applied to determine the consequences of events, represented as strings of sets of fluents. Developed to flesh out events used in natural language semantics, the approach supports reasoning about action in AI, including the frame problem and inertia. Representational and inferential aspects of the approach are explored, centering on conciseness of language, context update and constraint application with bias.
     
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  34.  27
    Finite and Physical Modalities.Mauro Gattari - 2005 - Notre Dame Journal of Formal Logic 46 (4):425-437.
    The logic Kf of the modalities of finite, devised to capture the notion of 'there exists a finite number of accessible worlds such that . . . is true', was introduced and axiomatized by Fattorosi. In this paper we enrich the logical framework of Kf: we give consistency properties and a tableau system (which yields the decidability) explicitly designed for Kf, and we introduce a shorter and more natural axiomatization. Moreover, we show the strong and suggestive relationship between Kf and (...)
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  35.  55
    A Finite Basis Theorem For Residually Finite, Congruence Meet-semidistributive Varieties.Ross Willard - 2000 - Journal of Symbolic Logic 65 (1):187-200.
    We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. $\mathbf{Theorem A:}$ if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then it is finitely based. $\mathbf{Theorem B:}$ there is an algorithm which, given $m < \omega$ and a finite algebra in a finite language, determines whether the variety generated by the algebra is congruence meet-semidistributive and residually less than m.
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  36. Finite-Time Destruction of Entanglement and Non-Locality by Environmental Influences.Kevin Ann & Gregg Jaeger - 2009 - Foundations of Physics 39 (7):790-828.
    Entanglement and non-locality are non-classical global characteristics of quantum states important to the foundations of quantum mechanics. Recent investigations have shown that environmental noise, even when it is entirely local in influence, can destroy both of these properties in finite time despite giving rise to full quantum state decoherence only in the infinite time limit. These investigations, which have been carried out in a range of theoretical and experimental situations, are reviewed here.
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  37.  70
    Finite Cardinals in Quasi-set Theory.Jonas R. Becker Arenhart - 2012 - Studia Logica 100 (3):437-452.
    Quasi-set theory is a ZFU-like axiomatic set theory, which deals with two kinds of ur-elements: M-atoms, objects like the atoms of ZFU, and m-atoms, items for which the usual identity relation is not defined. One of the motivations to advance such a theory is to deal properly with collections of items like particles in non-relativistic quantum mechanics when these are understood as being non-individuals in the sense that they may be indistinguishable although identity does not apply to them. According to (...)
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  38.  39
    Locally Finite Reducts of Heyting Algebras and Canonical Formulas.Guram Bezhanishvili & Nick Bezhanishvili - 2017 - Notre Dame Journal of Formal Logic 58 (1):21-45.
    The variety of Heyting algebras has two well-behaved locally finite reducts, the variety of bounded distributive lattices and the variety of implicative semilattices. The variety of bounded distributive lattices is generated by the →-free reducts of Heyting algebras, while the variety of implicative semilattices is generated by the ∨-free reducts. Each of these reducts gives rise to canonical formulas that generalize Jankov formulas and provide an axiomatization of all superintuitionistic logics. The ∨-free reducts of Heyting algebras give rise to the (...)
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  39. Finite and Absolute Idealism.Robert Pippin - 2015 - In Sebastian Gardner & Matthew Grist (eds.), The Transcendental Turn. Oxford, GB: Oxford University Press UK.
    Any interpretation of Hegel which stresses both his deep dependence on and radical revision of Kant must account for the nature of the difference between what Hegel calls a merely finite idealism and a so-called ’Absolute Idealism’. Such a clarification in turn depends on understanding Hegel’s claim to have preserved the distinguishability of intuition and concept, but to have insisted on their inseparability, or, to have defended their ’organic’ rather than ’mechanical’ relation. This is the main issue in this chapter, (...)
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  40.  28
    Finite partially-ordered quantification.Wilbur John Walkoe - 1970 - Journal of Symbolic Logic 35 (4):535-555.
  41.  91
    On finite hume.Fraser Macbride - 2000 - Philosophia Mathematica 8 (2):150-159.
    Neo-Fregeanism contends that knowledge of arithmetic may be acquired by second-order logical reflection upon Hume's principle. Heck argues that Hume's principle doesn't inform ordinary arithmetical reasoning and so knowledge derived from it cannot be genuinely arithmetical. To suppose otherwise, Heck claims, is to fail to comprehend the magnitude of Cantor's conceptual contribution to mathematics. Heck recommends that finite Hume's principle be employed instead to generate arithmetical knowledge. But a better understanding of Cantor's contribution is achieved if it is supposed that (...)
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  42.  7
    Adaptive Finite-Time Fault-Tolerant Control for Half-Vehicle Active Suspension Systems with Output Constraints and Random Actuator Failures.Jie Lan & Tongyu Xu - 2021 - Complexity 2021:1-16.
    The problem of adaptive finite-time fault-tolerant control and output constraints for a class of uncertain nonlinear half-vehicle active suspension systems are investigated in this work. Markovian variables are used to denote in terms of different random actuators failures. In adaptive backstepping design procedure, barrier Lyapunov functions are adopted to constrain vertical motion and pitch motion to suppress the vibrations. Unknown functions and coefficients are approximated by the neural network. Assisted by the stochastic practical finite-time theory and FTC theory, the proposed (...)
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  43.  20
    Dp-finite fields I(A): The infinitesimals.Will Johnson - 2021 - Annals of Pure and Applied Logic 172 (6):102947.
    We prove that NIP valued fields of positive characteristic are henselian, and we begin to generalize the known results on dp-minimal fields to dp-finite fields. On any unstable dp-finite field K, we define a type-definable group of “infinitesimals,” corresponding to a canonical group topology on (K, +). We reduce the classification of positive characteristic dp-finite fields to the construction of non-trivial Aut(K/A)-invariant valuation rings.
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  44. Effective finite-valued approximations of general propositional logics.Matthias Baaz & Richard Zach - 2008 - In Arnon Avron & Nachum Dershowitz (eds.), Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday. Springer Verlag. pp. 107–129.
    Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented in various ways can (...)
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  45.  44
    Finite models constructed from canonical formulas.Lawrence S. Moss - 2007 - Journal of Philosophical Logic 36 (6):605 - 640.
    This paper obtains the weak completeness and decidability results for standard systems of modal logic using models built from formulas themselves. This line of work began with Fine (Notre Dame J. Form. Log. 16:229-237, 1975). There are two ways in which our work advances on that paper: First, the definition of our models is mainly based on the relation Kozen and Parikh used in their proof of the completeness of PDL, see (Theor. Comp. Sci. 113-118, 1981). The point is to (...)
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  46. Non-finite-axiomatizability results in algebraic logic.Balázs Biró - 1992 - Journal of Symbolic Logic 57 (3):832 - 843.
  47.  28
    On Finite-Valued Propositional Logical Calculi.O. Anshakov & S. Rychkov - 1995 - Notre Dame Journal of Formal Logic 36 (4):606-629.
    In this paper we describe, in a purely algebraic language, truth-complete finite-valued propositional logical calculi extending the classical Boolean calculus. We also give a new proof of the Completeness Theorem for such calculi. We investigate the quasi-varieties of algebras playing an analogous role in the theory of these finite-valued logics to the role played by the variety of Boolean algebras in classical logic.
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  48. Finite Exchangeable Sequences.P. Diaconis & D. Freedman - 1980 - The Annals of Probability 8:745--64.
     
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  49.  21
    Finite Beings, Finite Goods: The Semantics, Metaphysics and Ethics of Naturalist Consequentialism, Part I 1.Richard Boyd - 2003 - Philosophy and Phenomenological Research 66 (3):505-553.
    0.0. Theistic Ethics as a Challenge and a Diagnostic Tool. Naturalistic conceptions in metaethics come in many varieties. Many philosophers who have sought to situate moral reasoning in a naturalistic metaphysical conception have thought it necessary to adopt non-cognitivist, prescriptivist, projectivist, relativist, or otherwise deflationary conceptions. Recently there has been a revival of interest in non-deflationary moral realist approaches to ethical naturalism. Many non-deflationary approaches have exploited the resources of non-empiricist “causal” or “naturalistic” conceptions of reference and of kind definitions (...)
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  50.  33
    Finite Methods in Mathematical Practice.Peter Schuster & Laura Crosilla - 2014 - In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. Boston: De Gruyter. pp. 351-410.
    In the present contribution we look at the legacy of Hilbert's programme in some recent developments in mathematics. Hilbert's ideas have seen new life in generalised and relativised forms by the hands of proof theorists and have been a source of motivation for the so--called reverse mathematics programme initiated by H. Friedman and S. Simpson. More recently Hilbert's programme has inspired T. Coquand and H. Lombardi to undertake a new approach to constructive algebra in which strong emphasis is laid on (...)
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