•  689
    Theories of truth based on four-valued infectious logics
    Logic Journal of the IGPL 28 (5): 712-746. 2020.
    Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least some of thes…Read more
  •  586
    Metainferential duality
    with Federico Pailos, Damian Szmuc, and Paula Teijeiro
    Journal of Applied Non-Classical Logics 30 (4): 312-334. 2020.
    The aim of this article is to discuss the extent to which certain substructural logics are related through the phenomenon of duality. Roughly speaking, metainferences are inferences between collect...
  •  446
    Contraction, Infinitary Quantifiers, and Omega Paradoxes
    Journal of Philosophical Logic 47 (4): 611-629. 2018.
    Our main goal is to investigate whether the infinitary rules for the quantifiers endorsed by Elia Zardini in a recent paper are plausible. First, we will argue that they are problematic in several ways, especially due to their infinitary features. Secondly, we will show that even if these worries are somehow dealt with, there is another serious issue with them. They produce a truth-theoretic paradox that does not involve the structural rules of contraction.
  •  445
    Truth without standard models: some conceptual problems reloaded
    Journal of Applied Non-Classical Logics 28 (1): 122-139. 2018.
    A theory of truth is usually demanded to be consistent, but -consistency is less frequently requested. Recently, Yatabe has argued in favour of -inconsistent first-order theories of truth, minimising their odd consequences. In view of this fact, in this paper, we present five arguments against -inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known -inconsistent theories of truth: the classical theory of symmetric truth FS and the non-classical the…Read more
  •  424
    Derivability and Metainferential Validity
    Journal of Philosophical Logic 51 (6): 1521-1547. 2021.
    The aim of this article is to study the notion of derivability and its semantic counterpart in the context of non-transitive and non-reflexive substructural logics. For this purpose we focus on the study cases of the logics _S__T_ and _T__S_. In this respect, we show that this notion doesn’t coincide, in general, with a nowadays broadly used semantic approach towards metainferential validity: the notion of local validity. Following this, and building on some previous work by Humberstone, we prov…Read more
  •  368
    On Three-Valued Presentations of Classical Logic
    with Damian Szmuc, Emmanuel Chemla, and Paul Égré
    Review of Symbolic Logic 1-23. forthcoming.
    Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations $st$, $ss$, $tt$, $ss\cap tt$, and $ts$, when the connectives are negation, conjunction, and disjunction. For $ts$ and $ss\cap tt$ the answer is trivial (no scheme works), and for $ss$ and $tt$ it is straightforward (they are the collaps…Read more
  •  186
    Non-reflexive Nonsense: Proof-Theory for Paracomplete Weak Kleene Logic
    with Damian Szmuc and María Inés Corbalán
    Studia Logica 1-17. forthcoming.
    Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion condition…Read more
  •  79
    Paraconsistency and its Philosophical Interpretations
    Australasian Journal of Logic 15 (2): 151-170. 2018.
    Many authors have considered that the notions of paraconsistency and dialetheism are intrinsically connected, in many cases, to the extent of confusing both phenomena. However, paraconsistency is a formal feature of some logics that consists in invalidating the rule of explosion, whereas dialetheism is a semantical/ontological position consisting in accepting true contradictions. In this paper, we argue against this connection and show that it is perfectly possible to adopt a paraconsistent logi…Read more
  •  32
    Sequent-Calculi for Metainferential Logics
    Studia Logica 110 (2): 319-353. 2021.
    In recent years, some theorists have argued that the clogics are not only defined by their inferences, but also by their metainferences. In this sense, logics that coincide in their inferences, but not in their metainferences were considered to be different. In this vein, some metainferential logics have been developed, as logics with metainferences of any level, built as hierarchies over known logics, such as \, and \. What is distinctive of these metainferential logics is that they are mixed, …Read more
  •  26
    Sorites, Curry and Suitable Models
    Logic and Logical Philosophy 1. forthcoming.
    In this paper we present two new approaches for dealing with semantic paradoxes and soritical predicates based on fuzzy logic. We show that both of them have conceptual advantages over the more traditional Łukasiewicz approach, and that the second one even avoids standard proofs of ω-nconsistency.
  •  25
    Metainferential Paraconsistency
    Logic and Logical Philosophy 1-26. forthcoming.
    In this article, our aim is to take a step towards a full understanding of the notion of paraconsistency in the context of metainferential logics. Following the work initiated by Barrio et al. [2018], we will consider a metainferential logic to be paraconsistent whenever the metainferential version of Explosion is invalid. However, our contribution consists in modifying the definition of meta-Explosion by extending the standard framework and introducing a negation for inferences and metainferenc…Read more
  •  20
    Structural Weakening and Paradoxes
    Notre Dame Journal of Formal Logic 62 (2): 369-398. 2021.
    Recently, several authors have pointed out that substructural logics are adequate for developing naive theories that represent semantic concepts such as truth. Among them, three proposals have been explored: dropping cut, dropping contraction and dropping reflexivity. However, nowhere in the substructural literature has anyone proposed rejecting the structural rule of weakening, while accepting the other rules. Some theorists have even argued that this task was not possible, since weakening play…Read more
  •  16
    Immune Logics
    Australasian Journal of Logic 18 (1): 29-52. 2021.
    This article is concerned with an exploration of a family of systems—called immune logics—that arise from certain dualizations of the well-known family of infectious logics. The distinctive feature of the semantic of infectious logics is the presence of a certain “infectious” semantic value, by which two different though equivalent things are meant. On the one hand, it is meant that these values are zero elements for all the operations in the underlying algebraic structure. On the other hand, it…Read more
  •  15
    Inconsistency, Paraconsistency and ω-Inconsistency
    Principia: An International Journal of Epistemology 22 (1): 171-188. 2018.
    In this paper I’ll explore the relation between ω-inconsistency and plain inconsistency, in the context of theories that intend to capture semantic concepts. In particular, I’ll focus on two very well known inconsistent but non-trivial theories of truth: LP and STTT. Both have the interesting feature of being able to handle semantic and arithmetic concepts, maintaining the standard model. However, it can be easily shown that both theories are ω- inconsistent. Although usually a theory of truth i…Read more
  •  13
    Metainferential Logics
    Springer Verlag. 2023.
    This book is the first to present a comprehensive investigation of the technical features of the metainferential logics developed in the last years, with their most relevant results and applications. It provides some new paths to define and investigate metainferential logics and offers a thorough study of the semantics and the proof-theories of this new and exciting variety of families of logics. This volume examines the hierarchies of metainferential logics and gives a general and systematic th…Read more
  •  12
    Book Review: Dubucs, J., & Bourdeau, M.. Constructivity and Computability in Historical and Philosophical Perspective. Springer Netherlands, XI. 214, pp. ISBN: 978-94-017-9216-5 978-94-017-9217-2, €83.29.
  •  11
    Paraconsistencia pura
    Revista de Humanidades de Valparaíso 13 90-101. 2019.
    Dentro del conjunto de las lógicas no clásicas, las lógicas paraconsistentes han suscitado de manera particular el interés de diversos filósofos. Además de las definiciones tradicionales, en los últimos años, se han propuesto nuevas maneras de caracterizar a la paraconsistencia. Lo que tienen en común todas estas definiciones es que alguna forma de la regla o de la metarregla de explosión debe ser rechazada. En este artículo, presentaré dichas definiciones y evaluaré el rol que juegan la negació…Read more
  •  10
    En los últimos años se han desarrollado diversas soluciones subestructurales a las paradojas semánticas. En particular, se han postulado teorías no transitivas, no contractivas, no reflexivas y, recientemente, no monotónicas. Sin embargo, cuando dichas soluciones son presentadas mediante cálculos de secuentes surge el problema de la dependencia. En pocas palabras, este problema consiste en que no es posible separar las reglas estructurales de la formulación de las otras reglas del cálculo. En es…Read more
  •  10
    Total Paraconsistency
    Humanities Journal of Valparaiso 13 90-101. 2019.
    In the context of non-classical logics, many philosophers have been particularly interested in the paraconsistent logics. In addition to traditional definitions, in recent years, new ways of characterizing the notion of paraconsistency have been proposed. In all of these definitions the rule or the meta-rule of explosion is abandoned. In this article, I present those definitions and evaluate the role that the negation and the transitivity play in each of them. Finally, I propose a new definition…Read more
  •  7
    Book Review: Dubucs, J., & Bourdeau, M.. Constructivity and Computability in Historical and Philosophical Perspective. Springer Netherlands, XI. 214, pp. ISBN: 978-94-017-9216-5 978-94-017-9217-2, €83.29.
  •  2
    Total Paraconsistency
    Revista de Humanidades de Valparaíso 13 90-101. 2019.
    In the context of non-classical logics, many philosophers have been particularly interested in the paraconsistent logics. In addition to traditional definitions, in recent years, new ways of characterizing the notion of paraconsistency have been proposed. In all of these definitions the rule or the meta-rule of explosion is abandoned. In this article, I present those definitions and evaluate the role that the negation and the transitivity play in each of them. Finally, I propose a new definition…Read more