Paraconsistent logic

About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.

Proof-Nets, Hybrid Logics and Minimalist Representations

Abstract: In this paper, we aim at giving a logical account of the representationalist view of minimalist grammars by referring to the notion of Proof-Net in Linear Logic. We propose, at the same time, a hybrid logic which mixes one logic (Lambek calculus) for building up elementary proofs and another one for combining the proofs so obtained. Because the first logic is non-commutative and the second one is commutative, this brings us a way to combine commutativity and non-commutativity in the same framework. The dynamic of cut-elimination in proof-nets is used to formalise the move-operation. Otherwise, we advocate a proof-net formalism which allows us to consider formulae as nodes to which it is possible to assign weights which determine the final phonological interpretation.

Paraconsistency of Interactive Computation

Abstract: The goal of computational logic is to allow us to model computation as well as to reason about it. We argue that a computational logic must be able to model interactive computation. We show that first-order logic cannot model interactive computation due to the incompleteness of interaction. We show that interactive computation is necessarily paraconsistent, able to model both a fact and its negation, due to the role of the world (environment) in determining the course of the computation. We conclude that paraconsistency is a necessary property for a logic that can model interactive computation.

Recovering Consistency by Forgetting Inconsistency

Abstract: In this paper, we introduce and study a new paraconsistent inference relation i¾? c in the setting of 3-valued paraconsistent logics Using inconsistency forgetting as a key mechanism for recovering consistency, it guarantees that the deductive closure $Cn_{\models_c}(\Sigma)$ of any belief base Σis classically consistent and classically closed This strong feature, not shared by previous inference relations in the same setting, allows to interpret an inconsistent belief base as a set of classical worlds (hence to reason classically from them)

Logical Autobiography 50

Abstract: After describing my family background and interest in mathematics and philosophy at school, I explain how I became interested in logic when studying at university in Paris. I describe how I discovered the work of Newton da Costa on paraconsistent logic, how I met him in Paris, and then go to do research in Brazil, Poland and USA before defending my PhD on universal logic at the Department of Mathematics of the University of Paris 7 and a PhD on logical truth at the Department of Philosophy at the University of Sao Paulo. I recount my postdoctoral years in Rio de Janeiro and Stanford and how I settled down for a couple of years in Neuchâtel, Switzerland, organizing the First World Congress on Universal Logic in Montreux and launching a journal and book series on this topic. I tell how I came back to the land of the future, starting more editorial projects, organizing logic events around the world (Paris, Beirut, Vatican, Lisbon, etc.) and continuing to develop research related to all aspects of logic (mathematical, philosophical, semiotical, historical). I finish with a short overview of my future projects, supported by a list of potential papers and books following a complete list of my writings to date.

Synonymy and Intra-Theoretical Pluralism

Abstract: The starting point of this paper is a version of intra-theoretical (logical) pluralism that was recently proposed by Hjortland [2013]. In a first move, I use synonymy-relations to formulate an intuitively compelling objection against Hjortland's claim that, if one uses a single calculus to characterise the consequence relations of the paraconsistent logic LP and the paracomplete logic K3, one immediately obtains multiple consequence relations for a single language and hence a reply to the Quinean charge of meaning variance. In a second move, I explain how a natural generalisation of the notion of synonymy (adapted to the 3-sided sequent-calculus used by Hjortland) can be used to counter this objection, but I also show how the solution can be turned into an equally devastating ‘one logic after all’ type of objection. Finally, I propose the general diagnosis that these problems could only arise in the presence of conceptual distinctions that are too coarse to accommodate coherent pluralist theses. T...