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Forthcoming articles
  1. Nathanael Leedom Ackerman (forthcoming). On Transferring Model Theoretic Theorems of {Mathcal{L}_{{Infty},Omega}} in the Category of Sets to a Fixed Grothendieck Topos. Logica Universalis:1-47.
    Working in a fixed Grothendieck topos Sh(C, J C ) we generalize \({\mathcal{L}_{{\infty},\omega}}\) to allow our languages and formulas to make explicit reference to Sh(C, J C ). We likewise generalize the notion of model. We then show how to encode these generalized structures by models of a related sentence of \({\mathcal{L}_{{\infty},\omega}}\) in the category of sets and functions. Using this encoding we prove analogs of several results concerning \({\mathcal{L}_{{\infty},\omega}}\) , such as the downward Löwenheim–Skolem theorem, the completeness theorem and (...)
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  2. J. Y. Beziau & Logica Universalis (forthcoming). c© 2005 Birkhäuser Verlag Basel/Switzerland. Logica Universalis:19.
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  3. Jean-Yves Beziau (forthcoming). Preface: Scope of Logic Theorems In Memoriam Adolf Lindenbaum. Logica Universalis:1-2.
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  4. Marcelo E. Coniglio & Newton M. Peron (forthcoming). Dugundji's Theorem Revisited. Logica Universalis:1-16.
    In 1940 Dugundji proved that no system between S1 and S5 can be characterized by finite matrices. Dugundji’s result forced the development of alternative semantics, in particular Kripke’s relational semantics. The success of this semantics allowed the creation of a huge family of modal systems. With few adaptations, this semantics can characterize almost the totality of the modal systems developed in the last five decades. This semantics however has some limits. Two results of incompleteness (for the systems KH and VB) (...)
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  5. Roy T. Cook (forthcoming). There is No Paradox of Logical Validity. Logica Universalis:1-21.
    A number of authors (including Field in Saving Truth From Paradox. Oxford University Press, Oxford, 2008; Shapiro in Philos Q 61:320–342, 2010; Whittle in Analysis 64:318–326, 2004; Beall and Murzi in J Philos 110:143–165, 2013) have argued that Peano Arithmetic (PA) supplemented with a logical validity predicate is inconsistent in much the same manner as is PA supplemented with an unrestricted truth predicate. In this paper I show that, on the contrary, there is no genuine paradox of logical validity—a completely (...)
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  6. Răzvan Diaconescu, Till Mossakowski & Andrzej Tarlecki (forthcoming). The Institution-Theoretic Scope of Logic Theorems. Logica Universalis:1-14.
    In this essay we analyse and elucidate the method to establish and clarify the scope of logic theorems offered within the theory of institutions. The method presented pervades a lot of abstract model theoretic developments carried out within institution theory. The power of the proposed general method is illustrated with the examples of (Craig) interpolation and (Beth) definability, as they appear in the literature of institutional model theory. Both case studies illustrate a considerable extension of the original scopes of the (...)
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  7. Daniel Găină (forthcoming). Forcing, Downward Löwenheim-Skolem and Omitting Types Theorems, Institutionally. Logica Universalis:1-30.
    In the context of proliferation of many logical systems in the area of mathematical logic and computer science, we present a generalization of forcing in institution-independent model theory which is used to prove two abstract results: Downward Löwenheim-Skolem Theorem (DLST) and Omitting Types Theorem (OTT). We instantiate these general results to many first-order logics, which are, roughly speaking, logics whose sentences can be constructed from atomic formulas by means of Boolean connectives and classical first-order quantifiers. These include first-order logic (FOL), (...)
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  8. René Gazzari (forthcoming). Direct Proofs of Lindenbaum Conditionals. Logica Universalis:1-23.
    We discuss the problem raised by Miller (Log Univers 1:183–199, 2007) to re-prove the well-known equivalences of some Lindenbaum theorems for deductive systems (each equivalent to the Axiom of Choice) without an application of the Axiom of Choice. We present five special constructions of deductive systems, each of them providing some partial solutions to the mathematical problem. We conclude with a short discussion of the underlying philosophical problem of deciding, whether a given proof satisfies our demand that the Axiom of (...)
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  9. L. I. Perlovsky (forthcoming). Logic Versus Mind. Logica Universalis.
     
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  10. João Rasga, Cristina Sernadas & Amlcar Sernadas (forthcoming). Craig Interpolation in the Presence of Unreliable Connectives. Logica Universalis:1-24.
    Arrow and turnstile interpolations are investigated in UCL [introduced by Sernadas et al. (J Logic Comput, 2013)], a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos.
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