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  1. FDE Circumscription.Skurt Daniel - 2017 - Australasian Journal of Logic 14 (2).
    In his article "Reassurance via Translation" Marcel Crabbe proposed a formalism to obtain reassurance and classical recapture in the setting of minimal FDE. His formalism proved to be general enough to be extended in order to formalize other forms of non-monotonic systems based on preference relations. It is the aim of this article to show how his result can be extended in a natural way by combining two different reasoning systems, namely minimal FDE and circumscription, in order to get a (...)
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  2. A Remark on Maksimova's Variable Separation Property in Super-Bi-Intuitionistic Logics.Guillermo Badia - 2017 - Australasian Journal of Logic 14 (1).
    We provide a sucient frame-theoretic condition for a super bi-intuitionistic logic to have Maksimova's variable separation property. We conclude that bi-intuitionistic logic enjoys the property. Furthermore, we offer an algebraic characterization of the super-bi-intuitionistic logics with Maksimova's property.
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  3.  8
    There is No Logical Negation: True, False, Both, and Neither.Jc Beall - 2017 - Australasian Journal of Logic 14 (1).
    In this paper I advance and defend a very simple position according to which logic is subclassical but is weaker than the leading subclassical-logic views have it.
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  4.  17
    Resolving Quine's Confict: A Neo-Quinean View of the Rational Revisability of Logic.Amanda Bryant - 2017 - Australasian Journal of Logic 14 (1).
    There is an apparent conflict in Quine’s work between, on the one hand, his clear commitment to the rational revisability of logic and, on the other, his principle of charitable translation and ‘change of logic, change of subject’ argument. I argue that the apparent conflict is mostly resolved under close exegesis, but that the translation argument normatively rules out collaborative revision and allows only revision by individuals. However, I articulate a Neo-Quinean view that preserves the rational acceptability of collaborative revision. (...)
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  5.  4
    Hybridized Paracomplete and Paraconsistent Logics.Colin R. Caret - 2017 - Australasian Journal of Logic 14 (1):281-325.
    This paper contributes to the study of paracompleteness and paraconsistency. We present two logics that address the following questions in novel ways. How can the paracomplete theorist characterize the formulas that defy excluded middle while maintaining that not all formulas are of this kind? How can the paraconsistent theorist characterize the formulas that obey explosion while still maintaining that there are some formulas not of this kind?
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  6.  2
    Metametaphysics and Dialetheism.Suki Finn - 2017 - Australasian Journal of Logic 14 (1).
    This paper reflects on metametaphysics and as such develops a metametameta-physical view: that quietist metametaphysics requires dialetheism, and in turn a paraconsistent logic. I demonstrate this using Carnap’s metametaphysical position in his 'Empiricism, Semantics and Ontology' as an example, with regard to how it exhibits self-reference and results in inconsistency. I show how applying Carnap’s position to itself produces a dilemma, both horns of which lead to a contradiction. Such inconsistency commonly arises from meta-theories with global scope, as the 'meta' (...)
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  7.  1
    Neighborhood Semantics for Logics of Unknown Truths and False Beliefs.Gilbert David & Venturi Giorgio - 2017 - Australasian Journal of Logic 14 (1).
    This article outlines a semantic approach to the logics of unknown truths, and the logic of false beliefs, using neighborhood structures, giving results on soundness, completeness, and expressivity. Relational semantics for the logics of unknown truths are also addressed, specically the conditions under which sound axiomatizations of these logics might be obtained from their normal counterparts, and the relationship between refexive insensitive logics and logics containing the provability operator as the primary modal operator.
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  8.  7
    What If? The Exploration of an Idea.Graham Priest - 2017 - Australasian Journal of Logic 14 (1).
    A crucial question here is what, exactly, the conditional in the naive truth/set comprehension principles is. In 'Logic of Paradox', I outlined two options. One is to take it to be the material conditional of the extensional paraconsistent logic LP. Call this "Strategy 1". LP is a relatively weak logic, however. In particular, the material conditional does not detach. The other strategy is to take it to be some detachable conditional. Call this "Strategy 2". The aim of the present essay (...)
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  9.  2
    Fixed-Point Models for Theories of Properties and Classes.Greg Restall - 2017 - Australasian Journal of Logic 14 (1).
    There is a vibrant community among philosophical logicians seeking to resolve the paradoxes of classes, properties and truth by way of adopting some non-classical logic in which trivialising paradoxical arguments are not valid. There is also a long tradition in theoretical computer science|going back to Dana Scott's fixed point model construction for the untyped lambda-calculus of models allowing for fixed points. In this paper, I will bring these traditions closer together, to show how these model constructions can shed light on (...)
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  10.  1
    Non-Classical Circular Definitions.Shawn Standefer - 2017 - Australasian Journal of Logic 14 (1).
    Circular denitions have primarily been studied in revision theory in the classical scheme. I present systems of circular denitions in the Strong Kleene and supervaluation schemes and provide complete proof systems for them. One class of denitions, the intrinsic denitions, naturally arises in both schemes. I survey some of the features of this class of denitions.
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  11.  1
    Paraconsistent Measurement of the Circle.Zach Weber & Maarten McKubre-Jordens - 2017 - Australasian Journal of Logic 14 (1).
    A theorem from Archimedes on the area of a circle is proved in a setting where some inconsistency is permissible, by using paraconsistent reasoning. The new proof emphasizes that the famous method of exhaustion gives approximations of areas closer than any consistent quantity. This is equivalent to the classical theorem in a classical context, but not in a context where it is possible that there are inconsistent innitesimals. The area of the circle is taken 'up to inconsistency'. The fact that (...)
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  12.  1
    Front Matter.Zach Weber, Maarten McKubre-Jordens & Patrick Girard - 2017 - Australasian Journal of Logic 14 (1).
    Editors' Introduction and List of Contributors.
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  13.  1
    Skolem Functions in Non-Classical Logics.Tore Fjetland Øgaard - 2017 - Australasian Journal of Logic 14 (1).
    This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A determines the extension of a function and f is a Skolem function for A.
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