XIV Workshop on Philosophical Logic

August 6–8, 2025

IIF - SADAF - CONICET

Buenos Aires, Argentina

Pedro del Valle-Inclán (Scuola Normale Superiore di Pisa, Italy)

Alejandro Díaz-Caro (Institut National de Recherche en Sciences et Technologies du Numérique, France)

Thomas Macaulay Ferguson (Rensselaer Polytechnic Institute, USA)

Roberto Giuntini (Università degli studi di Cagliari, Italy)

Bas Kortenbach (Scuola Normale Superiore di Pisa, Italy)

Ryan Simonelli (Wuhan University, China)

Martina Zirattu (Università degli studi di Torino, Italy) 

Wednesday 06/08 (GMT-3)

14:00 – 15:00 Mariela Rubin (IIF-SADAF-CONICET)

15:10 – 16:10 Joaquín Toranzo Calderón (UTN/UBA/IIF-SADAF-CONICET) 

16:10 – 16:50 coffee break

16:50 – 17:50 Alejandro Díaz-Caro (Institut National de Recherche en Sciences et Technologies du Numérique) 

18:00 – 19:00 Roberto Giuntini (Università degli studi di Cagliari)

Thursday 07/08 (GMT-3)

14:00 – 15:00 Pedro del Valle-Inclán (Scuola Normale Superiore di Pisa)

15:10 – 16:10 Agustina Borzi (IIF-SADAF-CONICET)

16:10 – 16:50  coffee break

16:50 – 17:50 Edson Bezerra (IIF-SADAF-CONICET)

18:00 – 19:00 Bas Kortenbach (Scuola Normale Superiore di Pisa)

19:00 and on Workshop Dinner

Friday 08/08 (GMT-3)

14:00 – 15:00 Ryan Simonelli (Wuhan University)

15:10 – 16:10  Aylén Bavosa Castro (IIF-SADAF-CONICET)

16:10 – 16:50  coffee break

16:50 – 17:50 Martina Zirattu (Università degli studi di Torino)

18:00 – 19:00  Thomas Macaulay Ferguson (Rensselaer Polytechnic Institute)

Aylén Bavosa Castro: “Metainferential Normativity”

Facing Harman’s challenge (1984) against logic as a normative theory applied to reasoning, the most common approach to bridge this gap has been what MacFarlane (2004) conceived as bridge principles. These principles focus mainly on inferential practices: for example, if A and B imply C, then you ought not to believe A and B and disbelieve C. However, many authors have not explored a directive presentation for metainferences, such as Harman's skeptical challenge demands. Metainferences, for many, are explained as “inferences between inferences”, and given that inferential practices are normative for reasoning, it seems natural to accept that metainferences must be normative, too. Nevertheless, the present work aims to discuss and explore how exactly normativity could be spelled out for metainferences. We explore several ways in which this could be carried out. The main drawback we reveal is that no known notion of normativity performs well for metainferences: if we consider logic to be essential to reasoning, then metainferences play an unknown role in that enterprise. More so, as we deviate from inferences, our usual concept of normativity becomes more and more unsustainable. 

This is a joint work with Diego Tajer.

Edson Bezerra: “ST, Deductive Closure and Entailment”

In this talk, we analyse the complex interplay between consequence relations and conditionals within logical systems. The main goal is to show how the non-transitive property of the consequence relation can be represented within a Tarskian framework. We will take the non-Tarskian logic ST as our case study. A distinction will be drawn between what this logic validates internally—essentially all the inferences valid in CL—and what it invalidates externally, namely the set of metainferences it rejects (essentially those rejected by LP). The central aim is to explore how ST’s external, non-transitive consequence relation may be faithfully internalized within a logical theory whose external logic remains Tarskian. So, we seek to reconcile the following two ideas: (a) that any external notion of consequence must be Tarskian, and (b) that there can be legitimate non-transitive logics—understood as systems whose internal entailments, expressed via a conditional, fail to validate Hypothetical Syllogism. These non-transitive logics do not incur the defects noted above, provided we separate the external consequence operator from the internal logic of implication. In sum, the approach is to introduce a second conditional into the language and obtain a conservative extension of ST, called ST+, which internalizes its own implication by means of an adequate entailment. However, given the result introduced by  Barrio et al. (2015), in the case of ST, one might attempt to internalize its inferential structure using the conditional of LP. But, a conditional without Modus ponens does not seem to be appropriate for such a purpose. Then, for this reason, using a modal semantics equipped with ternary relations, we introduce another conservative extension of ST, called ST++, which features an internal conditional that validates Modus ponens but does not validate Hypothetical Syllogism. We believe this provides a balanced way to capture failures of transitivity within a logic that does not suffer from failures of Modus ponens.

Agustina Borzi: “Negative and positive characterization of a Tarskian logic”

Some authors (e.g. Cobreros et al. (2020), Scambler (2020), Pailos and Barrio (2022)) discussed and developed a two-sided conception of what a logic is, distinguishing between its positive and its negative sides, the former being the set of its valid inferences, the latter being the set of its valid anti-inferences. As usual, an inference Γ ⊨ ∆ is valid if it is satisfied by all valuations, while an anti-inference from Γ to ∆ is said to be valid if there’s no valuation satisfying Γ ⊨ ∆. Building on this idea, in this work we dualize the general construction developed by Szmuc (2023), who showed that for any Tarskian logic L, one can define a non-transitive counterpart of it, namely a logic sharing exactly the same positive part, though differing from L as it locally invalidates transitivity. Here, we provide a dual result: for every Tarskian logic L, we can construct a logic which shares with L its negative part, but differs from it as reflexivity fails. Our construction makes use of the so-called infectious extension of an algebra and of Malinowski’s q-matrices (Malinowski (1990)), namely a generalization of the usual notion of logical matrices where premises and conclusions are given (possibly) different sets of designated values, the latter being a subset of the former. Finally, we offer some commentaries about the duality of both constructions.

Pedro del Valle-Inclán: “Structural Rules and the Meaning of Logical Connectives”

According to a well-known thesis of Quine’s (1986) logics that validate different arguments use different logical vocabulary. In a certain sense, then, partisans of different logics are partisans of different languages, who don’t so much disagree as talk past each other. A common response, going back to Putnam (1957) and Morton (1973), is to claim that sides who agree on enough logical principles use the same logical vocabulary. The obvious difficulty with this approach is spelling out what counts as ‘enough’ agreement. Recently, some inferentialists have tried to do just that (Restall 2002, 2014; Paoli 2003, 2014; Dicher 2016). They are often called minimalists, following Hjortland’s (2014) terminology. Minimalists draw a boundary along the line between the operational and structural rules of sequent calculi: operational rules confer meaning, structural rules don’t. Disagreements about validity that can be recast disagreements about structural rules, therefore, need not involve a change of language. In this talk I will argue that current minimalist proposals lead to untenable views about which connectives are identical, and try to sketch an alternative picture of the role of structural rules and the meaning-variance debate.

Alejandro Díaz-Caro: “Towards a Computational Quantum Logic”

(Based on DOI) This talk will be an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations for quantum programming languages. The first framework, the Lambda-S calculus, extends the lambda calculus by incorporating quantum superposition, enforcing linearity, and ensuring unitarity, to model quantum control. Its categorical semantics establishes a structured connection between classical and quantum computation through an adjunction between Cartesian closed categories and additive symmetric monoidal closed categories. The second framework, the L^C calculus, introduces a proof language for intuitionistic linear logic augmented with sum and scalar operations. This enables the formal encoding of quantum superpositions and measurements, leading to a computational model grounded in categorical structures with biproducts. These approaches suggest a fundamental duality between quantum computation and linear logic, highlighting structural correspondences between logical proofs and quantum programs.  We discuss ongoing developments, including extensions to polymorphism, categorical and realizability models, as well as the integration of the modality !, which further solidify the connection between logic and quantum programming languages.

Thomas Macaulay Ferguson: “A Family of Epistemic Logics of Zero Knowledge Proof"

In this talk, we will discuss some work in progress concerning giving a formal analysis of the cryptographic concept of a zero knowledge proof as an epistemic logic. We will introduce a family of multimodal, non-normal modal logics induced by adding to EK4 a "zero knowledge axiom" indicating the non-transferability of zero knowledge proofs between agents and show how to characterize the logics with neighborhood models with regular frames. We will then consider a hierarchy of non-normal extensions to EK4 characterized by their "contranormality" i.e. that they have no normal extensions. We will conclude by investigating how to provide explicit justification logic versions of these logics. (Joint work with Eke Gertler and Jitka Kadlecikova)

Roberto Giuntini: “{0, 1} and [0, 1]: From Classical Logic to Fuzzy Quantum Logic”

This talk explores a generalization of the standard formalism of quantum mechanics, replacing sharp quantum events (projections) with unsharp events (effects), represented by bounded linear operators satisfying the Born rule. The set of effects, unlike projections, forms a genuinely fuzzy structure that violates classical logical principles, such as non-contradiction. Giuntini examines how this structure can be organized into a Brouwer–Zadeh poset and, using an alternative spectral order, into a complete lattice. He introduces BZ*-lattices as abstract counterparts to the effect structure, unifying different notions of unsharpness. The presentation concludes with insights into the structure theory of PBZ*-lattices and the classification of their varieties.

Link to abstract.

Bas Kortenbach: “A New Framework for Metainferential Validity”

In the now standard way of framing the debate about metainferential validity, it is assumed that there is a single type of metainferential object. The question thus becomes when objects of this type are valid according to a given logic, or whether we should be pluralists about this. Yet in natural language, we can easily distinguish claims about inferences preserving satisfaction from those about inferences preserving validity. This observation motivates not only a form of pluralism about metavalidity, but a multiplicity of metainferential objects. Thus this talk proposes a new framework for thinking about metainferential validity, in which there are different metainferential objects, expressing different types of preservation claims. We develop it formally, explore its relations to the old framework, and consider some philosophical applications.

Mariela Rubin: “Your Modus Ponens is my Modus Tollens: Theories of Conditionals and Model Pluralism”

Model Pluralism in philosophy of science interprets theories as models, and claims that some phenomena can be understood using different (even sometimes incompatible) models. In philosophy of logic, many authors have endorsed the idea of ‘Logic as a model’, which sees logical theories as idealized models of logical concepts. Under this perspective, logical theories are idealized, incomplete abstractions aspiring to explain, predict or elucidate some aspect of the target phenomenon. In what follows we will take a look at the literature on conditionals, and argue that there is no one correct theory of conditionals. Rather, one should understand these theories as a variety of models intending to represent conditionals with different theoretical purposes or focusing on different aspects. We will analyze some of these theories and determine which kind of idealizations, distorsions, or fictionalizations they make regarding the target phenomenon. This analysis will motivate a version of logical pluralism regarding conditionals, where questions about validity of inferences only make sense in relation to a specific epistemic purpose.
This is a joint work with Diego Tajer.

Ryan Simonelli: “Asserting, Denying, and Challenging: A Framework and a Puzzle”

Logical bilateralists treat assertion and denial as equally fundamental in formulating systems of logic. This talk introduces a new framework for bilateral systems that, in addition to distinguishing between the opposite discursive moves of assertion and denial, explicitly represents the distinction between making a discursive move and challenging a move. Building on my recent work on subclassical bilateral logics that forgo the usual “coordination principles” linking assertion and denial, I show how this framework enables us to formally clarify the positions of proponents of different subclassical and substructural approaches to paradox.  Finally, I use the framework to crystallize and strengthen a familiar kind of revenge paradox that confronts all such approaches.

Joaquín Toranzo Calderón: “Three Ways of Producing Reasoning Minimal Pairs for Language Models Evaluation”

We propose an extension of the minimal pairs methodology from linguistics for assessing language model skills on reasoning by testing pairs of forms of reasoning. Evaluation on reasoning minimal pairs provides a way of testing different reasoning schema so different capabilities can be grouped, isolated and related according to their dependencies. The opposition between each element of the pair is such that we could oppose a valid form of reasoning against an invalid one (e.g. a Modus Ponens vs. the affirming the consequent fallacy), but also between valid arguments that require different assumptions (as in presence of existential quantification). Thus, the opposition can be understood in different ways. Which one should we choose? In this talk we present some syntactical, logical and psychological ways of guiding the generation of testing cases in order to build a benchmark for reasoning.

Martina Zirattu: “Bipolar Logics”

This work offers a philosophical and technical investigation of a new subfamily within the broader class of logics of analytic implication---a family of logical systems that capture notions of entailment understood as relations in which the content of the conclusion is contained within that of the premises. Embracing Yablo's (Yablo 2014) view of such relation as joint truth and subject matter preservation, the consequence relations characterizing these logics may be seen as the result of two components at play: on the one hand the alethic assumptions leading to different ways of defining preservation of truth, on the other hand the modeling of topics and of topic preservation. This naturally leads to two-component semantic frameworks which capture the interplay between two independent structures, namely an algebra of truth values and an algebra of topics (as in Ferguson 2017, Berto 2022, Bonzio et al. 2022, Song et al. 2024, Randriamahazaka 2024 etc.). Our aim is to explore a novel way to characterize and interpret the algebra of topics as well as to study the resulting notion of truth and topic preservation, hence of content inclusion, arising from this characterization. In particular, we consider a framework in which negation can be seen both as a topic-transformative and as a topic-cancellative operator. Namely, not only negation changes the topical status of statements, but it is also such that if a statement and its negation are combined then their topics cancel out resulting in a statement void of content.

Eduardo Barrio (UBA/IIF-SADAF-CONICET)

Agustina Borzi (IIF-SADAF-CONICET)

Camillo Fiore (UBA/IIF-SADAF-CONICET)

Damián Szmuc (IIF-SADAF-CONICET)

We are thankful for the support provided by CONICET