Sonja Smets: "Comparing knowledge"
I will present a novel type of epistemic logic, employing comparative knowledge assertions, to analyze the relative epistemic powers of individuals or groups of agents. Such assertions can express that a group of agents collectively knows at least as much as another individual or group of agents. I will provide examples of epistemic comparison statements and analyze them in the context of different epistemic conditions. Formally, I introduce the logic obtained by adding a ‘group epistemic comparison’ operator to the standard multi-agent epistemic logic with distributed and common knowledge. I will report on the joint work with A. Baltag in [1].
[1] Alexandru Baltag and Sonja Smets, "Comparing Knowledge: An Analysis of the Relative Epistemic Powers of Groups". Philosophies 10 (6):136 (2025)
Pablo Cobreros: "CL and ST Valid Metainferences"
Abstract: The seminal articles about ST and semantic paradoxes begin with the controversial claim that its authors defend a way to add a transparent truth predicate to classical logic. Many philosophers reacted against this claim by arguing that the logic ST is not quite classical logic. Specifically, some argue that ST is classical in its inferences but not in its metainferences. Following three lustra since the publication of those articles, we have now a much clearer understanding of the varieties of metainference validity and their interrelationships. Making use of this knowledge, we would like to clarify in exactly what sense, from a strict semantic perspective, ST's metainferences are or are not classical. A consequence of this clarification is that it can be claimed that ST's metainferences are classical in a deeper sense than is commonly thought.
Eduardo Barrio: "Fixed-point constructions and classicality"
Abstract: In his Outline of a Theory of Truth, Kripke maintained that his fixed-point construction needs involve no departure from classical logic. Undefinedness, on his classical gloss, does not constitute a further truth-value borne by propositions, but reflects the partiality of the truth predicate and, in the paradoxical cases, the failure of a sentence to express a proposition. Field has challenged this diagnosis by arguing that the model-relative values delivered by fixed-point constructions cannot straightforwardly determine proposition-expression simpliciter. We argue that this relativity objection establishes an important limitation, but does not settle the issue of classicality. First, it blocks a direct definitional identification between receiving the intermediate value in a model and failing to express a proposition, while leaving open a modest use of the construction. Second, even if the intermediate status is treated as a genuine semantic value borne by propositions, a non-classical consequence relation does not follow automatically. Finally, we argue that the classical reading enjoys a prima facie advantage of continuity and uniformity with familiar mathematical treatments of partiality, while acknowledging the expressive costs it incurs. The fixed-point construction underdetermines its philosophical and logical interpretation, while leaving the classical reading as a natural option.
Lucas Rosenblatt: "K3, LP, FDE and Their Generalised Classical Collapse"
Abstract: Roughly, classical recapture results for non-classical logics say that, under certain conditions, all the principles of classical logic can be used. Arguably, such results are quite important for friends of non-classical logics: among other things, they enable a possible answer to the well-known objection that these logics are too weak. Jc Beall has devised well-known classical recapture results for the logics LP, K3, and FDE. Each of these results says that an inference is valid in classical logic just in case there is a corresponding inference (with some additional premises and/or conclusions) that is valid in the target non-classical system. However, the applicability of Beall’s results has been recently put into question. The main criticism is that they presuppose that a non-logical theory is just a set of statements closed under consequence. But many actual theories cannot be plausibly so understood; besides statements they comprise inferences, and perhaps even metainferences. In this paper, we provide a series of generalisations of Beall’s results that eschew this criticism. Our generalisations can be described as extending Beall’s recapture procedure to the so-called metainferential levels. They are compatible with understanding non-logical theories as including not only statements, but also inferences and/or metainferences of arbitrary levels.
Matteo Plebani: "Trivalent Conditionals and Truthmaker Semantics"
Abstract: This paper connects truthmaker semantics with a trivalent interpretation of the indicative conditional. This merger substantially extends the scope of both approaches and has attractive philosophical implications. First, it need not postulate a third, non-classical truth value with contentious interpretation. Second, it unifies a realist and an epistemic interpretation of when a state verifies or accepts a sentence. Third, the framework recaptures central features of various analyses of conditionals: the material conditional analysis, Leitgeb’s HYPE conditional, the Chrysippus test, and the Ramsey test.
(joint work with Jan Sprenger)
José Martínez Fernández: "A revenge paradox for alethic nihilisme"
Abstract: In Truth Without Truths (Oxford U.P., 2024), David Liggins defends alethic nihilism, characterized as the doctrine that no proposition is true and no proposition is false. Liggins argues that the main advantage of this position is its capacity to resolve all paradoxes involving the truth predicate. Furthermore, because this approach requires no new semantic concepts, the nihilist strategy avoids generating revenge paradoxes. In the talk we will discuss the revenge paradoxes proposed by Armour-Garb and Woodbridge, evaluate Liggins’ response, and introduce a new revenge paradox that challenges alethic nihilism.
Xuefeng Wen: "The Barbershop Paradox Revisited"
Abstract: We argue that Lewis Carroll’s Barbershop Paradox remains a significant challenge for existing theories of conditionals. A critical examination reveals that current approaches, including material, strict, variably strict, dynamic strict, and connexive implication, cannot solve the paradox without sacrificing intuitively valid principles. To address this, we propose contextual implication, a novel semantic framework that evaluates formulas relative to a dynamic context and distinguishes between belief-validity and assertion-validity. By abandoning the transitivity of logical consequence, this theory accommodates Boethius’ thesis and resolves the paradox in a new way. This synthesis aims to offer new insights into the fundamental concepts of conditionals, modality, inconsistency, and validity in logic.
Jan Sprenger: "Presuppositions, Conditionals and Substructural Logic"
Abstract: Trivalent theories of indicative conditionals are thought to be at odds with trivalent theories of presupposition, and in particular, with an adequate analysis of the presuppositions of conditionals. We addressvthis challenge with a principle for felicitous assertion that we callvAvoid Void: do not assert a sentence that takes the value voidveverywhere in the context. This account highlights the semanticvdifferences between conditionals and other presupposition carriers, andvyields the intuitively correct presuppositions of conditionals.vMoreover, we argue that Avoid Void constrains not only assertion, butvalso logical inference: bringing the conditional logic C (defendedvelsewhere by the authors) in line with Avoid Void yields a properlyvsubstructural logic C# that resembles Strawson-entailment and explains the oddness of inferring “if A, B” from “not A”.
(joint work with Paul Égré & Lorenzo Rossi)
Federico Pailos: “Modal Metainferential Theories”
Abstract: The strict-tolerant logic ST has proven to be a powerful tool for handling semantic paradoxes: it retains every classically valid inference while admitting conservative extensions with a transparent truth predicate. Bezerra (2025) extended this approach to a modal setting, showing that ST(S5), a S5-based version of ST, is compatible with self-referential procedures and provides a uniform solution to modal paradoxes such as the Knower. However, ST(S5) faces a major shortcoming, as it fails to validate several classically valid metainferences of S5, including modal versions of modus ponens for the box operator.
In this paper we argue that this problem can be solved by constructing a hierarchy of modal metainferential logics. Building on the ST-hierarchy of Barrio, Pailos and Szmuc, we define a sequence ST(S5)₀, ST(S5)₁, ST(S5)₂, … of logics, where each ST(S5)ₙ recovers every S5-valid metainference up to level n while retaining the characteristic substructural features of ST. We then define the limit logic ST(S5)ω as the union of this hierarchy and prove the Absolute General Modal Collapse Result: for every finite metainference of level n, that metainference is valid in ST(S5)ω if and only if it is valid in S5. Finally, we show that the diagonal extension ST(S5)*ω, obtained by adding Smoryński-style fixed-point constants, is satisfiable, yielding a non-trivial modal theory that simultaneously recovers all S5-valid metainferences at every finite level and handles modal paradoxical sentences without triviality. We close by presenting a tableaux proof system for ST(S5)ω and discussing an open question regarding the relationship between model-validity and world-validity for metainferences in this setting.
(joint work with Edson Bezerra and Jonathan Erenfryd)
Xavi Viñeta: "Alternative Metainferential Validities"
Abstract: In the past ten years, there has been growing interest in metainferences and a prolific development of metainferential logics. One of the most important points of discussion has been to determine the appropriate notion of validity for metainferences. In this vein, the main proposals in the literature have favored either explicitly or implicitly one of two notions: the local and the global versions of metainferential validity. The aim of this article is two-fold. First, we will systematize and critically discuss the main arguments in favor of each of these notions. Second, we will present a third notion not so much studied in the literature, and evaluate how it compares with the other two notions already mentioned.
Robert van Rooij: "Teams and truth makers: Free Choice and more"
Abstract: Look at the following inferences:
Free Choice
1. Paul might be in Paris or Pamplona —> Paul might be in Paris and he might be in Pamplona
2. You may take an apple or a pear —> You may take an apple and a pear
Ignorance inferences
3. Paul ate an apple or a pear —> It is possible that Paul ate an apple and it is possible that Paul ate a pear.
4. Paul ate an apple or a pear —> it is possible that Paul didn’t ate an apple and it is possible that Paul didn’t eat a pear.
Epistemic contradiction (also in embeddings)
5. #It is raining and it is possible that it is not raining.
6. #If it is raining and it is possible that it is not raining, then ….
Epistemic must is weaker than plain assertion (7c is weaker than 7b(
7a. Where are the keys?
7b. They are in the kitchen drawer
7c. They must be in the kitchen drawer.
I this talk I am going to propose an analysis of disjunction and modals that can account for all these phenomena.
For this I am using a team semantics, where a team is a set of Van Fraassian truth makers.
(joint work with Soeren Knudstorp)
Heinrich Wansing: "A bimodal connexive logic of logical and metaphysical necessity"
Abstract: The notion of metaphysical necessity is controversial, and even if it is conceded that there is a distinct concept of metaphysical necessity along-side logical necessity, its exact relationship to logical necessity remains a matter of debate. In this paper, I propose to capture the distinction between metaphysical and logical necessity from the perspective of logical bilateralism. Whilst statements of logical and metaphysical necessity share the same (support of) truth conditions, they differ in their (support of) falsity conditions. The distinction is made precise by introducing a bimodal connexive propositional logic called ‘S5-ML’ (S5 with metaphysical and logical necessity). The system has a bilateralist semantics that enables a differentiation between ascriptions of metaphysical and logical necessity, and at the same time allows upholding modal monism, insofar as no distinction is drawn between metaphysically and logically possible worlds or states. Another bimodal system aimed at capturing a distinction between logical and metaphysical necessity has recently been presented by Marcin Łyczak. Łyczak’s logic of logical necessity is a proper extension of the modal propositional logic S5 and is not closed under uniform substitution. In contrast to this, the bimodal logic S5-ML is closed under uniform substitution, whereas the class of necessities is not.