•  945
    What is a Paraconsistent Logic?
    In Walter Carnielli & Jacek Malinowski (eds.), Contradictions, from Consistency to Inconsistency, Springer. 2018.
    Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a…Read more
  •  776
    Conjunction and Disjunction in Infectious Logics
    In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan), Springer. pp. 268-283. 2017.
    In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticin…Read more
  •  760
    An Epistemic Interpretation of Paraconsistent Weak Kleene Logic
    Logic and Logical Philosophy 1. forthcoming.
    This paper extends Fitting's epistemic interpretation of some Kleene logics, to also account for Paraconsistent Weak Kleene logic. To achieve this goal, a dualization of Fitting's "cut-down" operator is discussed, rendering a "track-down" operator later used to represent the idea that no consistent opinion can arise from a set including an inconsistent opinion. It is shown that, if some reasonable assumptions are made, the truth-functions of Paraconsistent Weak Kleene coincide with certain opera…Read more
  •  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
  •  681
    A recovery operator for nontransitive approaches
    Review of Symbolic Logic 13 (1): 80-104. 2020.
    In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut involving …Read more
  •  675
    A Hierarchy of Classical and Paraconsistent Logics
    Journal of Philosophical Logic 49 (1): 93-120. 2020.
    In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely cla…Read more
  •  652
    In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences—and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical…Read more
  •  586
    Metainferential duality
    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...
  •  578
    Substructural logics, pluralism and collapse
    Synthese 198 (Suppl 20): 4991-5007. 2018.
    When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in a cl…Read more
  •  575
    A New Hope for Philosophers' Appeal to Intuition
    Essays in Philosophy 13 (1): 336-353. 2012.
    Some recent researches in experimental philosophy have posed a problem for philosophers’ appeal to intuition (hereinafter referred to as PAI); the aim of this paper is to offer an answer to this challenge. The thesis against PAI implies that, given some experimental results, intuition does not seem to be a reliable epistemic source, and —more importantly— given the actual state of knowledge about its operation, we do not have sufficient resources to mitigate its errors and thus establish its rel…Read more
  •  570
    We provide a logical matrix semantics and a Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry’s logic of Analytic Implication. We achieve the former by introducing a logical matrix closely related to that inducing paracomplete weak Kleene logic, and the latter by presenting a calculus where the initial sequents and the left and right rules for negation are subject to linguistic constraints.
  •  521
    Meaningless Divisions
    Notre Dame Journal of Formal Logic 62 (3): 399-424. 2021.
    In this article we revisit a number of disputes regarding significance logics---i.e., inferential frameworks capable of handling meaningless, although grammatical, sentences---that took place in a series of articles most of which appeared in the Australasian Journal of Philosophy between 1966 and 1978. These debates concern (i) the way in which logical consequence ought to be approached in the context of a significance logic, and (ii) the way in which the logical vocabulary has to be modified (…Read more
  •  472
    This paper discusses a dualization of Fitting's notion of a "cut-down" operation on a bilattice, rendering a "track-down" operation, later used to represent the idea that a consistent opinion cannot arise from a set including an inconsistent opinion. The logic of track-down operations on bilattices is proved equivalent to the logic d_Sfde, dual to Deutsch's system S_fde. Furthermore, track-down operations are employed to provide an epistemic interpretation for paraconsistent weak Kleene logic. F…Read more
  •  449
    Relevant Logics Obeying Component Homogeneity
    with Roberto Ciuni and Thomas Macaulay Ferguson
    Australasian Journal of Logic 15 (2): 301-361. 2018.
    This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. …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
  •  370
    On Three-Valued Presentations of Classical Logic
    with Bruno da Ré, 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
  •  354
    A paraconsistent route to semantic closure
    Logic Journal of the IGPL 25 (4): 387-407. 2017.
    In this paper, we present a non-trivial and expressively complete paraconsistent naïve theory of truth, as a step in the route towards semantic closure. We achieve this goal by expressing self-reference with a weak procedure, that uses equivalences between expressions of the language, as opposed to a strong procedure, that uses identities. Finally, we make some remarks regarding the sense in which the theory of truth discussed has a property closely related to functional completeness, and we pre…Read more
  •  350
    Defining LFIs and LFUs in extensions of infectious logics
    Journal of Applied Non-Classical Logics 26 (4): 286-314. 2016.
    The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the -fragment of the logics of nonsense, such as the ones due to Bochvar and Halldén, among others. Here, we extend these logics with classical negations, and we furthermore show that some of these extended systems can be properly regarded as logics of formal inconsistency and logics of formal undeterminedness.
  •  319
    We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics …Read more
  •  292
    Modeling the interaction of computer errors by four-valued contaminating logics
    with Roberto Ciuni and Thomas Macaulay Ferguson
    In Rosalie Iemhoff, Michael Moortgat & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation. pp. 119-139. 2019.
    Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of…Read more
  •  261
    On Pathological Truths
    Review of Symbolic Logic 7 (4): 601-617. 2014.
    In Kripke’s classic paper on truth it is argued that by adding a new semantic category different from truth and falsity it is possible to have a language with its own truth predicate. A substantial problem with this approach is that it lacks the expressive resources to characterize those sentences which fall under the new category. The main goal of this paper is to offer a refinement of Kripke’s approach in which this difficulty does not arise. We tackle this characterization problem by letting …Read more
  •  251
    The aim of this article is to show that, just like in recent years Cobreros, Égré, Ripley and van Rooij provided a non-transitive counterpart of classical logic (meaning by this that all classically acceptable inferences are valid, but Cut and other metainferences are not) the same can be done for every Tarskian logic, with full generality. In order to establish this fact, we take a semantic approach, by showing that appropriate structures can be devised to characterize a non-transitive counterp…Read more
  •  206
    Remarks on the Epistemic Interpretation of Paraconsistent Logic
    Principia: An International Journal of Epistemology 22 (1): 153-170. 2018.
    In a recent work, Walter Carnielli and Abilio Rodrigues present an epistemically motivated interpretation of paraconsistent logic. In their view, when there is conflicting evidence with regard to a proposition A (i.e. when there is both evidence in favor of A and evidence in favor of ¬A) both A and ¬A should be accepted without thereby accepting any proposition B whatsoever. Hence, reasoning within their system intends to mirror, and thus, should be constrained by, the way in which we reason abo…Read more
  •  186
    Non-reflexive Nonsense: Proof-Theory for Paracomplete Weak Kleene Logic
    with Bruno Da Ré 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
  •  158
    Liberating classical negation from falsity conditions
    Proceedings of the 52nd International Symposium on Multiple-Valued Logic (ISMVL 2022). 2022.
    In one of their papers, Michael De and Hitoshi Omori observed that the notion of classical negation is not uniquely determined in the context of so-called Belnap-Dunn logic, and in fact there are 16 unary operations that qualify to be called classical negation. These varieties are due to different falsity conditions one may assume for classical negation. The aim of this paper is to observe that there is an interesting way to make sense of classical negation independent of falsity conditions. We …Read more
  •  152
    Logics Based on Linear Orders of Contaminating Values
    with Roberto Ciuni and Thomas Macaulay Ferguson
    Journal of Logic and Computation 29 (5). 2019.
    A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ⁠, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with mu…Read more
  •  37
    A Note on Goddard and Routley's Significance Logic
    Australasian Journal of Logic 15 (2): 431-448. 2018.
    The present note revisits the joint work of Leonard Goddard and Richard Routley on significance logics with the aim of shedding new light on their understanding by studying them under the lens of recent semantic developments, such as the plurivalent semantics developed by Graham Priest. These semantics allow sentences to receive one, more than one, or no truth-value at all from a given carrier set. Since nonsignificant sentences are taken to be neither true nor false, i.e. truth-value gaps, in t…Read more
  •  33
    Pure Variable Inclusion Logics
    with Francesco Paoli and Michele Pra Baldi
    Logic and Logical Philosophy 1-22. forthcoming.
    The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Cl…Read more
  •  24
    Pure Refined Variable Inclusion Logics
    Australasian Journal of Logic 19 (5). 2022.
    In this article, we explore the semantic characterization of the (right) pure refined variable inclusion companion of all logics, which is a further refinement of the nowadays well-studied pure right variable inclusion logics. In particular, we will focus on giving a characterization of these fragments via a single logical matrix, when possible, and via a class of finite matrices, otherwise. In order to achieve this, we will rely on extending the semantics of the logics whose companions we will …Read more
  •  19
    Two-valued weak Kleene logics
    with Bruno da Ré
    Manuscrito 42 (1): 1-43. 2019.
    In the literature, Weak Kleene logics are usually taken as three-valued logics. However, Suszko has challenged the main idea of many-valued logic claiming that every logic can be presented in a two-valued fashion. In this paper, we provide two-valued semantics for the Weak Kleene logics and for a number of four-valued subsystems of them. We do the same for the so-called Logics of Nonsense, which are extensions of the Weak Kleene logics with unary operators that allow looking at them as Logics of…Read more