[Pop-up Workshop] The NTU-LMU Workshop on Synonymy in AI and Logic (4/11)

The NTU-LMU Workshop on Synonymy in AI and

Logic

April 11 , 2025, Room 302

Presentation

13:00—14:15  Levin Hornischer

Learning How to Vote With Principles: Axiomatic Insights Into the Collective Decisions of Neural Networks

14:30—15:45  Andrew Tedder

Relevance Via Topicality in First-Order Logics

16:00—17:15  Wai-Chun Chris Pang

On the Categoricity of Some Non-classical Logics

17:15—18:30  Shawn Standefer

Equivalence Concepts in Some Non-Classical Logics

Abstract

Levin Hornischer 

Title: Learning How to Vote With Principles: Axiomatic Insights Into the Collective Decisions of Neural Networks

Abstract: Can neural networks be applied in voting theory, while satisfying the need for transparency in collective decisions? We propose axiomatic deep voting: a framework to build and evaluate neural networks that aggregate preferences, using the well-established axiomatic method of voting theory. Our findings are: (1) Neural networks, despite being highly accurate, often fail to align with the core axioms of voting rules, revealing a disconnect between mimicking outcomes and reasoning. (2) Training with axiom-specific data does not enhance alignment with those axioms. (3) By solely optimizing axiom satisfaction, neural networks can synthesize new voting rules that often surpass and substantially differ from existing ones. This offers insights for both fields: For AI, important concepts like bias and value-alignment are studied in a mathematically rigorous way; for voting theory, new areas of the space of voting rules are explored.

This is joint work with Zoi Terzopoulou (GATE Lyon-Saint-Etienne). The full paper is available at: https://arxiv.org/abs/2410.16170

Wai-Chun Chris Pang 

Title:On the Categoricity of Some Non-classical Logics

Abstract:This paper concerns the categoricity problems, or Carnap’s problems, of some non-classical logics. I first review the categoricity theorems of LP and K3 proved by Tabakci(2024). I then point out a loophole in the proof of a proposition in the paper. I then turn to the categoricity of FDE, showing that FDE is categorical for the star models. I also prove that LP and K3 are not categorical for their star models.

Shawn Standefer

Title: Equivalence Concepts in Some Non-Classical Logics

Abstract: In this talk, we present different definitions of extensionality and hyperintensionality for some non-classical logics. The goal is identify some limits on different equivalence concepts in logics and to highlight divergences from synonymy relations.  

Andrew Tedder 

Title: Relevance Via Topicality in First-Order Logics

Abstract: We investigate the problem of providing relevance properties for first order logics by expanding on recent work concerning relevance as topical in propositional relevant logics. We propose a theory of topic for first order languages, relying on the use of focus markers in an extension of the usual first order language, and suggest how such an enrichment of the language and conceptual apparatus of the logic can provide avenues into the first order relevance problem. (Joint work with Nicholas Ferenz (Lisbon))