Paris PLEXUS workshop in Philosophical Logic

Paris PLEXUS workshop in Philosophical Logic

Organized by Paul Égré (Crossing CNRS / ENS-PSL) and Francesca Poggiolesi (IHPST CNRS / Panthéon-Sorbonne)

Location: Salle de réunion du DEC, 29 rue d’Ulm, 75005 PARIS (Ground floor after entrance)

Organized with the support of the PLEXUS project (Grant Agreement no 101086295) a Marie Sklodowska-Curie action funded by the EU under the Horizon Europe Research and Innovation Programme)

Hybrid format - To attend in person, registration is mandatory due to the room's limited capacity (please email: [email protected])

Zoom link:

https://cnrs.zoom.us/j/98581949980?pwd=9qbp6gbffaJ5xbKgLZ8a2CqbkfUzaX.1

ID: 985 8194 9980

Code: rej9kX

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9:15: Introduction, Paul ÉGRÉ and Francesca POGGIOLESI

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9h30-10h30

Clara LEROUVILLOIS (IHPST / Université de Toulouse)

Representing dynamics in logic: from models to proof (joint work with Francesca Poggiolesi)

Dynamic Epistemic Logic (DEL) extends modal logic to model both knowledge and its change. Epistemic modalities capture what agents know, while dynamic operators describe how knowledge is revised through communication. A central example is Public Announcement Logic (PAL), where knowledge states are modeled by sets of possible worlds and announcements update these models by eliminating worlds. Thus, DEL’s semantics is inherently dynamic. By contrast, its proof theory does not immediately reflect this dynamic character.  In this talk, I develop a method to proof-theoretically represent the dynamic character of DEL, and  I use it to construct a proof calculus for PAL. This calculus serves as a syntactic counterpart to epistemic models and their updates, and it enjoys strong structural properties such as admissibility of structural rules and cut-elimination.

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10h40-11h40

Jakob SÜSKIND (IJN, ENS-PSL)

Logical Properties of Comparative Verisimilitude (Joint work with Hans Rott)

What can we infer when we know that some statement is close to truth (‘verisimilar’, ‘truthlike’); or that it is closer to truth than some other statement? A claim can be very close to truth and yet have logical consequences that are very far from truth. This has made the prospects for a ‘logic of truthlikeness’ rather bleak. And yet, there are some valid inferences which can obviously be drawn based on, for instance, the transitivity of comparative verisimilitude: If we know that A is at least as truthlike as B (notation: ‘A ≥ B’), and that B ≥ C, then we can infer A ≥ C. Are there other more interesting inferences that can be drawn with regard to comparative verisimilitude? In this joint work with Hans Rott, we investigate the logical properties of a question-relative definition of comparative verisimilitude described in (Süskind, 2023), and we explore the combinative preferences to which it gives rise when interpreted as a preference relation. It turns out that comparative verisimilitude has logical properties that are very different from those of other preference relations, such as relations of comparative plausibility. Interestingly, however, verisimilitude also seems to share some logical properties with other well-known preference relations: In particular, it seems to exhibit a property which (Touazi/Cayrol/Dubois, 2015) call ‘stability for union’, viz. that if A ≥ B, then (A ∨ C) ≥ (B ∨ C) for any C. This property entails the validity of a number of other interesting inference schemata, which point towards a surprisingly rich logic of verisimilitude as a preference relation.

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11h50-12h50

Camille FLEURET (IHPST, Panthéon-Sorbonne)

Solving the NYC/Georgia Problem with Causal Models

Causal models, as introduced by Pearl (2000), offer a powerful framework for understanding causation (Hitchcock, 2001; Halpern, 2016), non-causal dependencies (Schaffer, 2016; Woodward, 2018), and scientific explanation (Woodward, 2003). More recently, it has been proposed that they could also ground a theory of counterfactual conditionals (Briggs, 2012; Ciardelli et al., 2018). To assess this proposal, one must ask whether causal models can handle the challenging cases that motivate possible-world approaches (Lewis, 1973; Kratzer, 2012). A classic example, due to Goodman (1947), consists of the pair: if New York City were in Georgia, New York City would be in the South / if Georgia included New York City, Georgia would not be entirely in the South. Both claims seem true, yet apparently conflict. I argue that causal models can resolve this puzzle, thereby passing an important test for their adequacy in analyzing counterfactuals.

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14h30-15h30

Yassine ELMOUHI (Université de Nantes)

Ternary Logic Architectures for Uncertainty-Aware AI (joint work with Jean-Philippe Diguet and Paul Egré)

Modern AI systems often operate under imperfect conditions where noise, quantization, and hardware faults degrade performance. Classical approaches such as ensemble learning or variational inference address uncertainty at the model-output level but remain resource-intensive and limited in scope. In this work, we explore an alternative paradigm: incorporating three-valued (ternary) logics into arithmetic and neural computations. Unlike classical binary logic, which only distinguishes between true and false, ternary logics add a third value that explicitly represents unknown or uncertain. This additional state allows uncertainty to be represented and propagated during computation rather than being forced into premature binary decisions. To the best of our knowledge, ternary logics have never been applied to arithmetic units, despite their proven usefulness in other areas such as databases, circuit design, and reasoning systems. We design ternary adders based on different logics and study how uncertainty propagates through arithmetic operations, establishing formal properties and proofs that clarify uncertainty dynamics. At the perception level, we extend convolutional neural networks with uncertainty-aware operators, enabling models to retain and process uncertainty throughout the pipeline instead of discarding it early. By combining low-level ternary arithmetic with high-level perception models, we aim to better represent, understand, and control uncertainty, ultimately improving robustness in edge and embedded AI systems.

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15h40-16h40

Jonathan Erenfryd (UBA / IIF - SADAF - CONICET)

Struggling with Coherence (joint work with Lucas Rosenblatt)

In this talk, I will analyze the debate within bilateralist inferentialism concerning the relative priority of incoherence over coherence. Building on Rosenblatt’s suggestion that coherence and incoherence should be treated as equally primitive, I will challenge Golan’s recent arguments for privileging incoherence. I argue, first, that Golan’s objections rely on assumptions that are questionable from an inferentialist perspective. Second, I introduce a new hybrid calculus that axiomatizes both coherence and incoherence while avoiding the limitations of previous systems. I conclude, contra Golan, that coherence is no less fundamental than incoherence, and that bilateralist approaches should treat them on a par.

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16h50-17h50

Quentin Blomet (IJN, ENS-PSL)

Mixed Consequence Fuzzy Logics

We investigate the class of many-valued logics based on linearly ordered bounded De Morgan algebras—that is, bounded algebras where conjunction is interpreted as min, disjunction as max, and negation as 1-x. We show that all such logics reduce to one of three paradigmatic systems—the strong Kleene logic K3, the Logic of Paradox LP, or classical logic CL—by validating the same sequents. We then introduce the notions of mixed consequence and bi-matrix, which allow us to define mixed versions of these many-valued logics, in the same spirit as the strict-tolerant logic ST. We prove a reduction theorem showing that they likewise reduce to the mixed versions of K3, LP, and CL. Building on these results, we define a family of fuzzy logics grounded in MV-algebras equipped with mixed consequence relations. We show that each of these systems conservatively extends one of the three mixed consequence logics mentioned above, maintaining key structural properties while incorporating new features introduced by the t-norm and its residual.