Reasoning in Logic and in Language Models

Description: This is an interdisciplinary and exploratory workshop on the topic of reasoning in logic and in language models, exploring some aspects of common interest to logicians, cognitive psychologists, computational linguists, and AI engineers, on topics that include negation, compositionality, and meaning. 

Zoom Link for the workshop: 

https://cnrs.zoom.us/j/97776192717?pwd=Qn9Boa7RYREK2h5zNEQIHneQMMxmm6.1

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Program 

December 4, 2025

• 9:30: Welcome and Introduction

• 10:00-11:00 Yulia Otmakhova & Thinh Truong (University of Melbourne): Language Models are still not Naysayers

• 11:15-12:15 Paul Égré (IRL Crossing): Reasoning from Contradictions

• 14:00-15:00 Andy Perfors (University of Melbourne): The Nature of Meaning: What LLMs miss

• 15:15-16:15: Hannah Clark-Younger (Iostack.ai, Auckland): LLMs as Reliable Pedagogical Tools

• 16:30-17:30: Ellie Ripley: What does Frege's argument show (about cognition)?

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December 5, 2025

• 10h-11:00: Jen Davoren (University of Melbourne): Temporal logic for reasoning about discrete, continuous and hybrid dynamical systems 

•  11h15-12:15: Lloyd Humberstone (Monash): Protection by Embedding, Protection by Non-embedding

• 14:00-15:00: Tansu Alpcan (University of Melbourne): On Memory, Systems, and Logic in a Counting Game

• 15:15-16:15: Zach Weber (Otago): Logical Paradoxes, Methodology, and Metalogic

Abstracts
 

Yulia Otmakhova & Thinh Truong: Language Models are still not Naysayers  

Abstract: Negation is central to human language, lying at the core of inference and reasoning. However, in natural language processing, most prior work has treated negation superficially, that is detecting whether a negation marker is present in text, and disregarding both more intricate types of negation and the ways it affects meaning. In this talk, we examine how different types of negation affect the behaviour of modern large language models. We find that models can recognize negative statements, but fail to reason with them on downstream tasks, and still struggle with scope and compositionality. Thus, despite recent advances in many other areas, negation remains problematic for language models, which highlights its complexity as a cognitive and linguistic phenomenon.

Paul Égré: Reasoning from Contradictions

Abstract: Contradictory sentences like "Mary is in Melbourne and Mary is not in Melbourne" classically entail any proposition, they are said to "explode". As pointed out by relevantist logicians, in natural language inferences and in mathematical inferences we seem reluctant to infer arbitrary conclusions from a contradiction. In this talk I will present a different account in which most contradictions "implode", namely entail nothing. The approach is based on the application of a conversational and cognitive non-vacuity constraint on inference, and on a Strawsonian account of ordinary negation as cancelling content. I will present a logic based on Cooper's logic OL, in which simple contradictions entail nothing, but conditional contradictions still permit reductio reasoning. In an exploratory way, I will also consider whether LLMs can give us relevant evidence about reasoning from contradictions. 

Andy Perfors: The Nature of Meaning: What LLMs miss  

Abstract: This is going to be a general talk — part cognitive science, part computer science, and part philosophy — where I discuss where meaning comes from for people. I'll argue that the deepest forms of meaning inherently require other minds, and is a process of collaboration whose results become deeply embedded in, and inextricable from, our environment and culture. This has implications for our understanding of LLMs, the interaction between people and LLMs, and the consequences for ourselves and our society.

Hannah Clark-Younger: LLMs as Reliable Pedagogical Tools

Abstract: I present a practical approach to combining the rigor of symbolic procedures with the generative strengths of large language models. Drawing on a background in imperative logic and nearly a decade of production AI work, I introduce iostack, a system that encodes procedural knowledge into stagewise structures an LLM can safely navigate. I show how tightly scoped process control prevents common failure modes of both classic chatbots and unconstrained, unwieldy LLM prompts. Through short, hands-on demos I show how iostack can be used to enable step-by-step automated assessment with granular, personalised feedback; teach a specific set of concepts in a specific order while remaining flexible to the needs of individual students; and turn syllabi and readings into a Socratic tutor that understands the specifics of your course. I argue that the right abstraction for useful conversation AI systems is not bigger models but better process boundaries: move through atomic stages of a process and give the model only the information, instructions, and decisions relevant to the current stage.

Ellie Ripley: What does Frege's argument show (about cognition)?

Abstract: Negations are cognitively hard to deal with. (Compare "I don't want to go where X isn't" to "I want to go where X is" or "I used to want to go where X was"; I don't know about you, but the first one feels more difficult to understand to me.) So-called "Spinozan" theories of belief have attempted to explain this difficulty by proposing: first, that rejecting a claim is a more effortful process than accepting it; and second, that understanding negation somehow recruits this effortful rejection process.

There is an argument going back to Frege, though, that can appear to show that this kind of explanation can't work. The idea is that negation's difficulty persists in sentences like "If I don't want to go where X isn't, then I should pay attention to where X is"---and here there seems to be nothing rejected at all. In this talk, I try to evalute the prospects of the Spinozan explanation for negation's difficulty in light of such an argument.

Jen Davoren: Temporal logics for reasoning about discrete, continuous and hybrid dynamical systems

Hybrid systems with interacting discrete and continuous dynamics arise in both engineered and natural environments; in particular, they include so-called Cyber-Physical Systems consisting of digital hardware and software interacting with physical processes.  The use of temporal or modal logics for the formal specification and verification of hybrid systems has to date largely fallen into one of two approaches. One approach is to abstract away real time and effectively reduce to discrete time transition system (Kripke frame) models. The other approach is to project off discrete time and treat hybrid trajectories as discontinuous functions of real time. In this talk, I will develop signals and systems over hybrid and higher-dimensional time domains sufficient to provide a semantics for temporal logics and to give truth-preservation via an enriched notion of bisimulation.  

Lloyd Humberstone: Protection by Embedding, Protection by Non-embedding

Abstract: A proposed account of some phenomenon, such as the possession of a given concept, may meet with any of a cluster of what go collectively under the heading of circularity objections. Arguably, in some cases, what on syntactical grounds counts as circularity in an account of the application conditions of some concept may be unobjectionable (‘non-vicious’), because the account does not aspire to being an analysis of the concept in question. A natural response to the worries here gestured at may involve making sure that crucial parts of the account are suitably embedded within the scope of certain, e.g., intensional – indeed, typically, intentional – operators. Such moves bear also on attempts to isolate one kind of discourse from another, for example: normatively neutral description of the world from normatively committal language. In other cases, the response may consist in ensuring – or in emphasizing – that the material in question is not thus embedded.  ‘Protection’ in the title refers to protection against potential objections to projects of the kind just alluded to. Particular interest is taken in some of the logical issues arising in this area.

Tansu Alpcan: On Memory, Systems, and Logic in a Counting Game

Abstract: This paper introduces a systems engineering framework for understanding the fundamental principles of counting and the nature of natural numbers, arguing that traditional axiomatic approaches overlook the essential functional and computational components. We define counting as a Wittgensteinian ``counting game'' in which an agent, the Counter, must employ robust perception and classification capabilities within a given environment. Central to this approach is the claim that counting is a stateful computational activity that requires memory, leading to the definition of a natural number as the unique state of a counting system stored in that memory. We examine the role of symbolic representation, identifying numerals as efficient encoding schemes for these numerical states, and argue that this analysis contributes to improving symbolic features in Artificial Intelligence (AI) systems. Furthermore, our model contributes to a long-standing philosophical debate, suggesting that ordinals come first rather than cardinals due to practical memory storage limitations.

Zach Weber: Logical Paradoxes, Methodology, and Metalogic  

Abstract: Logical paradoxes are arguments where reasoning seems to go wrong. After briefly recalling some famous paradoxes, this talk has two aims. First, we will survey a few proposals for dealing with the paradoxes, and compare their relative merits. These include proposals about (1) negation, where there may be truth-value `gluts'; (2) structural rules, where contraction or transitivity may fail; and (3) truth, where some have gone so far as to claim that, to avert the paradoxes, we should accept that there are no truths at all. Second, we will look at the methodology for weighing up and deciding between such options. I will argue from an `anti-exceptionalist' view about logic, that whatever criteria we apply when deciding which logics to adopt, applies equally to deciding how we reason *about* logics themselves---that is, to metalogic.  

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The workshop is funded by the University of Monash, it is hosted by the University of Melbourne, and it is linked to network PLEXUS.