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  1. Pragmatics and intensional logic.Richard Montague - 1970 - Synthese 22 (1-2):68--94.
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  • Pragmatics and intensional logic.Richard Montague - 1970 - Dialectica 24 (4):277-302.
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  • In memoriam: Leon Albert Henkin, 1921—2006.J. Donald Monk - 2009 - Bulletin of Symbolic Logic 15 (3):326-331.
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  • Kripke-style models for typed lambda calculus.John C. Mitchell & Eugenio Moggi - 1991 - Annals of Pure and Applied Logic 51 (1-2):99-124.
    Mitchell, J.C. and E. Moggi, Kripke-style models for typed lambda calculus, Annals of Pure and Applied Logic 51 99–124. The semantics of typed lambda calculus is usually described using Henkin models, consisting of functions over some collection of sets, or concrete cartesian closed categories, which are essentially equivalent. We describe a more general class of Kripke-style models. In categorical terms, our Kripke lambda models are cartesian closed subcategories of the presheaves over a poset. To those familiar with Kripke models of (...)
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  • Truth by default.Vann Mcgee - 2001 - Philosophia Mathematica 9 (1):5-20.
    There is no preferred reduction of number theory to set theory. Nonetheless, we confidently accept axioms obtained by substituting formulas from the language of set theory into the induction axiom schema. This is only possible, it is argued, because our acceptance of the induction axioms depends solely on the meanings of aritlunetical and logical terms, which is only possible if our 'intended models' of number theory are standard. Similarly, our acceptance of the second-order natural deduction rules depends solely on the (...)
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  • Structuralism and Isomorphism.C. McCarty - 2015 - Philosophia Mathematica 23 (1):1-10.
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  • Logic in the Tractatus.Max Weiss - 2017 - Review of Symbolic Logic 10 (1):1-50.
    I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. -/- There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably (...)
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  • A Higher-Order Theory of Presupposition.Scott Martin & Carl Pollard - 2012 - Studia Logica 100 (4):727-751.
    So-called 'dynamic' semantic theories such as Kamp's discourse representation theory and Heim's file change semantics account for such phenomena as cross-sentential anaphora, donkey anaphora, and the novelty condition on indefinites, but compare unfavorably with Montague semantics in some important respects (clarity and simplicity of mathematical foundations, compositionality, handling of quantification and coordination). Preliminary efforts have been made by Muskens and by de Groote to revise and extend Montague semantics to cover dynamic phenomena. We present a new higher-order theory of discourse (...)
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  • Identity, Equality, Nameability and Completeness.María Manzano & Manuel Crescencio Moreno - 2017 - Bulletin of the Section of Logic 46 (3/4).
    This article is an extended promenade strolling along the winding roads of identity, equality, nameability and completeness, looking for places where they converge. We have distinguished between identity and equality; the first is a binary relation between objects while the second is a symbolic relation between terms. Owing to the central role the notion of identity plays in logic, you can be interested either in how to define it using other logical concepts or in the opposite scheme. In the first (...)
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  • Identity, equality, nameability and completeness. Part II.María Manzano & Manuel Crescencio Moreno - 2018 - Bulletin of the Section of Logic 47 (3):141.
    This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view. In one case, identity is a notion which has to be defined and, in the (...)
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  • Hybrid Partial Type Theory.María Manzano, Antonia Huertas, Patrick Blackburn, Manuel Martins & Víctor Aranda - forthcoming - Journal of Symbolic Logic:1-43.
    In this article we define a logical system called Hybrid Partial Type Theory ( $\mathcal {HPTT}$ ). The system is obtained by combining William Farmer’s partial type theory with a strong form of hybrid logic. William Farmer’s system is a version of Church’s theory of types which allows terms to be non-denoting; hybrid logic is a version of modal logic in which it is possible to name worlds and evaluate expressions with respect to particular worlds. We motivate this combination of (...)
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  • Completeness in Equational Hybrid Propositional Type Theory.Maria Manzano, Manuel Martins & Antonia Huertas - 2019 - Studia Logica 107 (6):1159-1198.
    Equational hybrid propositional type theory ) is a combination of propositional type theory, equational logic and hybrid modal logic. The structures used to interpret the language contain a hierarchy of propositional types, an algebra and a Kripke frame. The main result in this paper is the proof of completeness of a calculus specifically defined for this logic. The completeness proof is based on the three proofs Henkin published last century: Completeness in type theory, The completeness of the first-order functional calculus (...)
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  • Completeness: from Gödel to Henkin.Maria Manzano & Enrique Alonso - 2014 - History and Philosophy of Logic 35 (1):1-26.
    This paper focuses on the evolution of the notion of completeness in contemporary logic. We discuss the differences between the notions of completeness of a theory, the completeness of a calculus, and the completeness of a logic in the light of Gödel's and Tarski's crucial contributions.We place special emphasis on understanding the differences in how these concepts were used then and now, as well as on the role they play in logic. Nevertheless, we can still observe a certain ambiguity in (...)
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  • Completeness in Equational Hybrid Propositional Type Theory.Maria Manzano, Manuel Martins & Antonia Huertas - 2019 - Studia Logica 107 (6):1159-1198.
    Equational hybrid propositional type theory ) is a combination of propositional type theory, equational logic and hybrid modal logic. The structures used to interpret the language contain a hierarchy of propositional types, an algebra and a Kripke frame. The main result in this paper is the proof of completeness of a calculus specifically defined for this logic. The completeness proof is based on the three proofs Henkin published last century: Completeness in type theory, The completeness of the first-order functional calculus (...)
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  • A generalisation of the concept of a relational model for modal logic.David Makinson - 1970 - Theoria 36 (3):331-335.
    Generalises the concept of a relational model for modal logic, due to Kripke, so as to obtain a closer correspondence between relational and algebraic models. The generalisation obtained is essentially equivalent to the notion of a "first-order" model that was defined independently by S.K.Thomason.
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  • Alonzo church:his life, his work and some of his miracles.Maía Manzano - 1997 - History and Philosophy of Logic 18 (4):211-232.
    This paper is dedicated to Alonzo Church, who died in August 1995 after a long life devoted to logic. To Church we owe lambda calculus, the thesis bearing his name and the solution to the Entscheidungsproblem.His well-known book Introduction to Mathematical LogicI, defined the subject matter of mathematical logic, the approach to be taken and the basic topics addressed. Church was the creator of the Journal of Symbolic Logicthe best-known journal of the area, which he edited for several decades This (...)
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  • On a Straw Man in the Philosophy of Science - A Defense of the Received View.Sebastian Lutz - 2012 - Hopos: The Journal of the International Society for the History of Philosophy of Science 2 (1):77–120.
    I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must include axioms for the mathematics used in the scientific theories. Next, I contend that models are important according to the Received View. Finally, I argue against the claim that the Received View is intended to (...)
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  • Introducing Kurt Gödel [review of Gödel, Collected Works, Vol. 1: Publications, 1929-1936 ].Billy Joe Lucas - 1989 - Russell: The Journal of Bertrand Russell Studies 9 (1).
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  • Circumscriptive theories: A logic-based framework for knowledge representation. [REVIEW]Vladimir Lifshitz - 1988 - Journal of Philosophical Logic 17 (4):391 - 441.
    The use of circumscription for formalizing commonsense knowledge and reasoning requires that a circumscription policy be selected for each particular application: we should specify which predicates are circumscribed, which predicates and functions are allowed to vary, and what priorities between the circumscribed predicates are established. The circumscription policy is usually described either informally or using suitable metamathematical notation. In this paper we propose a simple and general formalism which permits describing circumscription policies by axioms, included in the knowledge base along (...)
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  • Materialism and qualia: The explanatory gap.Joseph Levine - 1983 - Pacific Philosophical Quarterly 64 (October):354-61.
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  • Partial monotonic protothetics.François Lepage - 2000 - Studia Logica 66 (1):147-163.
    This paper has four parts. In the first part, I present Leniewski's protothetics and the complete system provided for that logic by Henkin. The second part presents a generalized notion of partial functions in propositional type theory. In the third part, these partial functions are used to define partial interpretations for protothetics. Finally, I present in the fourth part a complete system for partial protothetics. Completeness is proved by Henkin's method [4] using saturated sets instead of maximally saturated sets. This (...)
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  • That principia mathematica, first edition, has a predicative interpretation after all.Hugues Leblanc - 1975 - Journal of Philosophical Logic 4 (1):67 - 70.
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  • Matters of relevance.Hugues Leblanc - 1972 - Journal of Philosophical Logic 1 (3/4):269 - 286.
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  • Intuitionist type theory and foundations.J. Lambek & P. J. Scott - 1981 - Journal of Philosophical Logic 10 (1):101 - 115.
    A version of intuitionistic type theory is presented here in which all logical symbols are defined in terms of equality. This language is used to construct the so-called free topos with natural number object. It is argued that the free topos may be regarded as the universe of mathematics from an intuitionist's point of view.
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  • Dunn’s relevant predication, real properties and identity.Philip Kremer - 1997 - Erkenntnis 47 (1):37-65.
    We critically investigate and refine Dunn's relevant predication, his formalisation of the notion of a real property. We argue that Dunn's original dialectical moves presuppose some interpretation of relevant identity, though none is given. We then re-motivate the proposal in a broader context, considering the prospects for a classical formalisation of real properties, particularly of Geach's implicit distinction between real and ''Cambridge'' properties. After arguing against these prospects, we turn to relevance logic, re-motivating relevant predication with Geach's distinction in mind. (...)
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  • Strong logics of first and second order.Peter Koellner - 2010 - Bulletin of Symbolic Logic 16 (1):1-36.
    In this paper we investigate strong logics of first and second order that have certain absoluteness properties. We begin with an investigation of first order logic and the strong logics ω-logic and β-logic, isolating two facets of absoluteness, namely, generic invariance and faithfulness. It turns out that absoluteness is relative in the sense that stronger background assumptions secure greater degrees of absoluteness. Our aim is to investigate the hierarchies of strong logics of first and second order that are generically invariant (...)
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  • Standard Formalization.Jeffrey Ketland - 2022 - Axiomathes 32 (3):711-748.
    A standard formalization of a scientific theory is a system of axioms for that theory in a first-order language (possibly many-sorted; possibly with the membership primitive $$\in$$ ). Suppes (in: Carvallo M (ed) Nature, cognition and system II. Kluwer, Dordrecht, 1992) expressed skepticism about whether there is a “simple or elegant method” for presenting mathematicized scientific theories in such a standard formalization, because they “assume a great deal of mathematics as part of their substructure”. The major difficulties amount to these. (...)
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  • Characterizing all models in infinite cardinalities.Lauri Keskinen - 2013 - Annals of Pure and Applied Logic 164 (3):230-250.
    Fix a cardinal κ. We can ask the question: what kind of a logic L is needed to characterize all models of cardinality κ up to isomorphism by their L-theories? In other words: for which logics L it is true that if any models A and B of cardinality κ satisfy the same L-theory then they are isomorphic?It is always possible to characterize models of cardinality κ by their Lκ+,κ+-theories, but we are interested in finding a “small” logic L, i.e., (...)
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  • Analyticity versus fuzziness.John G. Kemeny - 1963 - Synthese 15 (1):57 - 80.
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  • Domains of Sciences, Universes of Discourse and Omega Arguments.Jose M. Saguillo - 1999 - History and Philosophy of Logic 20 (3-4):267-290.
    Each science has its own domain of investigation, but one and the same science can be formalized in different languages with different universes of discourse. The concept of the domain of a science and the concept of the universe of discourse of a formalization of a science are distinct, although they often coincide in extension. In order to analyse the presuppositions and implications of choices of domain and universe, this article discusses the treatment of omega arguments in three very different (...)
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  • The compactness of first-order logic:from gödel to lindström.John W. Dawson - 1993 - History and Philosophy of Logic 14 (1):15-37.
    Though regarded today as one of the most important results in logic, the compactness theorem was largely ignored until nearly two decades after its discovery. This paper describes the vicissitudes of its evolution and transformation during the period 1930-1970, with special attention to the roles of Kurt Gödel, A. I. Maltsev, Leon Henkin, Abraham Robinson, and Alfred Tarski.
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  • Reduction and Tarski's Definition of Logical Consequence.Jim Edwards - 2003 - Notre Dame Journal of Formal Logic 44 (1):49-62.
    In his classic 1936 paper Tarski sought to motivate his definition of logical consequence by appeal to the inference form: P(0), P(1), . . ., P(n), . . . therefore ∀nP(n). This is prima facie puzzling because these inferences are seemingly first-order and Tarski knew that Gödel had shown first-order proof methods to be complete, and because ∀nP(n) is not a logical consequence of P(0), P(1), . . ., P(n), . . . by Taski's proposed definition. An attempt to resolve (...)
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  • Boolean-Valued Second-Order Logic.Daisuke Ikegami & Jouko Väänänen - 2015 - Notre Dame Journal of Formal Logic 56 (1):167-190.
    In so-called full second-order logic, the second-order variables range over all subsets and relations of the domain in question. In so-called Henkin second-order logic, every model is endowed with a set of subsets and relations which will serve as the range of the second-order variables. In our Boolean-valued second-order logic, the second-order variables range over all Boolean-valued subsets and relations on the domain. We show that under large cardinal assumptions Boolean-valued second-order logic is more robust than full second-order logic. Its (...)
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  • On second-order characterizability.T. Hyttinen, K. Kangas & J. Vaananen - 2013 - Logic Journal of the IGPL 21 (5):767-787.
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  • Probabilities on Sentences in an Expressive Logic.Marcus Hutter, John W. Lloyd, Kee Siong Ng & William T. B. Uther - 2013 - Journal of Applied Logic 11 (4):386-420.
    Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being (...)
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  • The semantic view of theories and higher-order languages.Laurenz Hudetz - 2019 - Synthese 196 (3):1131-1149.
    Several philosophers of science construe models of scientific theories as set-theoretic structures. Some of them moreover claim that models should not be construed as structures in the sense of model theory because the latter are language-dependent. I argue that if we are ready to construe models as set-theoretic structures (strict semantic view), we could equally well construe them as model-theoretic structures of higher-order logic (liberal semantic view). I show that every family of set-theoretic structures has an associated language of higher-order (...)
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  • Truth definitions, Skolem functions and axiomatic set theory.Jaakko Hintikka - 1998 - Bulletin of Symbolic Logic 4 (3):303-337.
    §1. The mission of axiomatic set theory. What is set theory needed for in the foundations of mathematics? Why cannot we transact whatever foundational business we have to transact in terms of our ordinary logic without resorting to set theory? There are many possible answers, but most of them are likely to be variations of the same theme. The core area of ordinary logic is by a fairly common consent the received first-order logic. Why cannot it take care of itself? (...)
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  • Quantifiers vs. Quantification Theory.Jaakko Hintikka - 1973 - Dialectica 27 (3‐4):329-358.
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  • On göde's philosophical assumptions.Jaakko Hintikka - 1998 - Synthese 114 (1):13-23.
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  • Independence-friendly logic and axiomatic set theory.Jaakko Hintikka - 2004 - Annals of Pure and Applied Logic 126 (1-3):313-333.
    In order to be able to express all possible patterns of dependence and independence between variables, we have to replace the traditional first-order logic by independence-friendly (IF) logic. Our natural concept of truth for a quantificational sentence S says that all the Skolem functions for S exist. This conception of truth for a sufficiently rich IF first-order language can be expressed in the same language. In a first-order axiomatic set theory, one can apparently express this same concept in set-theoretical terms, (...)
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  • Carnap's work in the foundations of logic and mathematics in a historical perspective.Jaakko Hintikka - 1992 - Synthese 93 (1-2):167 - 189.
    Carnap's philosophy is examined from new viewpoints, including three important distinctions: (i) language as calculus vs language as universal medium; (ii) different senses of completeness: (iii) standard vs nonstandard interpretations of (higher-order) logic. (i) Carnap favored in 1930-34 the "formal mode of speech," a corollary to the universality assumption. He later gave it up partially but retained some of its ingredients, e.g., the one-domain assumption. (ii) Carnap's project of creating a universal self-referential language is encouraged by (ii) and by the (...)
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  • A revolution in the foundations of mathematics?Jaakko Hintikka - 1997 - Synthese 111 (2):155-170.
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  • The discovery of my completeness proofs.Leon Henkin - 1996 - Bulletin of Symbolic Logic 2 (2):127-158.
    §1. Introduction. This paper deals with aspects of my doctoral dissertation which contributed to the early development of model theory. What was of use to later workers was less the results of my thesis, than the method by which I proved the completeness of first-order logic—a result established by Kurt Gödel in his doctoral thesis 18 years before.The ideas that fed my discovery of this proof were mostly those I found in the teachings and writings of Alonzo Church. This may (...)
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  • Russell's 1925 logic.A. P. Hazen & J. M. Davoren - 2000 - Australasian Journal of Philosophy 78 (4):534 – 556.
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  • Second-Order Logic of Paradox.Allen P. Hazen & Francis Jeffry Pelletier - 2018 - Notre Dame Journal of Formal Logic 59 (4):547-558.
    The logic of paradox, LP, is a first-order, three-valued logic that has been advocated by Graham Priest as an appropriate way to represent the possibility of acceptable contradictory statements. Second-order LP is that logic augmented with quantification over predicates. As with classical second-order logic, there are different ways to give the semantic interpretation of sentences of the logic. The different ways give rise to different logical advantages and disadvantages, and we canvass several of these, concluding that it will be extremely (...)
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  • Pecularities of Some Three- and Four-Valued Second Order Logics.Allen P. Hazen & Francis Jeffry Pelletier - 2018 - Logica Universalis 12 (3-4):493-509.
    Logics that have many truth values—more than just True and False—have been argued to be useful in the analysis of very many philosophical and linguistic puzzles. In this paper, which is a followup to, we will start with a particularly well-motivated four-valued logic that has been studied mainly in its propositional and first-order versions. And we will then investigate its second-order version. This four-valued logic has two natural three-valued extensions: what is called a “gap logic”, and what is called a (...)
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  • Zur Axiomatisierung der k‐zahlig allgemeingültigen Ausdrücke des Stufenkalküls.Gisbert Hasenjaeger - 1958 - Mathematical Logic Quarterly 4 (12‐16):175-177.
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  • Zur Axiomatisierung derk-zahlig allgemeingültigen Ausdrücke des Stufenkalküls.Gisbert Hasenjaeger - 1958 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 4 (12-16):175-177.
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  • The three arrows of Zeno.Craig Harrison - 1996 - Synthese 107 (2):271 - 292.
    We explore the better known paradoxes of Zeno including modern variants based on infinite processes, from the point of view of standard, classical analysis, from which there is still much to learn (especially concerning the paradox of division), and then from the viewpoints of non-standard and non-classical analysis (the logic of the latter being intuitionist).The standard, classical or Cantorian notion of the continuum, modeled on the real number line, is well known, as is the definition of motion as the time (...)
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  • Mathematical modal logic: A view of its evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.
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