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Logic, Epistemology, and the Unity of Science aims to reconsider the question of the unity of science in light of recent developments in logic. At present, no single logical, semantical or methodological framework dominates the philosophy of science. However, the editors of this series believe that formal techniques like, for example, independence friendly logic, dialogical logics, multimodal logics, game theoretic semantics and linear logics, have the potential to cast new light on basic issues in the discussion of the unity of science.This series provides a venue where philosophers and logicians can apply specific technical insights to fundamental philosophical problems. While the series is open to a wide variety of perspectives, including the study and analysis of argumentation and the critical discussion of the relationship between logic and the philosophy of science, the aim is to provide an integrated picture of the scientific enterprise in all its diversity.More information about this series at

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This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning.

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The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. Contradictions are, instead, epistemically understood as conflicting evidence, where evidence for a proposition A is understood as reasons for believing that A is true. The paper defines a paraconsistent and paracomplete natural deduction system, called the Basic Logic of Evidence (BLE ), and extends it to the Logic of Evidence and Truth (LETJ ). The latter is a logic of formal inconsistency and undeterminedness that is able to express not only preservation of evidence but also preservation of truth. LETJ is anti-dialetheist in the sense that, according to the intuitive interpretation proposed here, its consequence relation is trivial in the presence of any true contradiction. Adequate semantics and a decision method are presented for both BLE and LETJ , as well as some technical results that fit the intended interpretation.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Association for Symbolic Logic is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Symbolic Logic.Abstract. This paper presents a unified treatment of the propositional and first-order manyvalued logics through the method of tableaux. It is shown that several important results on the proof theory and model theory of those logics can be obtained in a general way.We obtain, in this direction, abstract versions of the completeness theorem, model existence theorem (using a generalization of the classical analytic consistency properties), compactness theorem and Ldwenheim-Skolem theorem.The paper is completely self-contained and includes examples of application to particular many-valued formal systems.?1. Introduction. The main purpose of this work is to show how the formalization of finite many-valued logics, usually presented in the most diverse ways, can be unified under the point of view of analytic tableaux.Many-valued logics can be considered as natural generalizations of classical logic, due to the fact that, as in the classical case, the truth values of propositional complex formulas depend functionally on the truth value of elementary subformulas. To maintain a similar relationship for quantified formulas, we introduce the notion of distribution quantifiers: these are quantifiers which have associated with them an interpretation function which maintains a connection with the quantifier analogous to that between tables and logical connectives.In this paper we show that it is possible to present a tableau-type proof theory for every many-valued logic with distribution quantifiers, provided that among the quantifiers there are at least two which could be viewed as having the minimal properties of the universal and existential quantifiers. Indeed, our method allows the construction of the proof theory of any of those logics as soon as we know the tables and the interpretation functions.This proof theory is sound and complete with respect to the semantics of the calculus, and basic results in model theory for many-valued first-order logics can be obtained in general, as for example the compactness theorem, the Ldwenheim-Skolem theorem, and the model-existence theorem. This suggests that such a 473 This content downloaded from 151.227.68.60 on Fri, 11 Jul 2014 13:48:46 PM All use subject to JSTOR Terms and Conditions 474 WALTER A. CARNIELLI uniform treatment could be used in a systematic study of the model theory of manyvalued logics, since some model-theoretical problems are closely related to the combinatorial relationships among the connectives and quantifiers of the language considered (as examples of this point of view, we recall the prenex th...