Related papers: Transporting Theorems about Typeability in LF Acro…

Long-context reasoning is essential for complex real-world applications, yet remains a significant challenge for Large Language Models (LLMs). Despite the rapid evolution in long-context reasoning, current research often overlooks the…

Large Language Models (LLM) have emerged as a tool for robots to generate task plans using common sense reasoning. For the LLM to generate actionable plans, scene context must be provided, often through a map. Recent works have shifted from…

A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…

Grounding the common-sense reasoning of Large Language Models (LLMs) in physical domains remains a pivotal yet unsolved problem for embodied AI. Whereas prior works have focused on leveraging LLMs directly for planning in symbolic spaces,…

Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid…

This paper synthesizes a series of formal proofs to construct a unified theory on the logical limits of the Symbol Grounding Problem. We distinguish between internal meaning (sense), which formal systems can possess via axioms, and external…

LLMs show remarkable emergent abilities, such as inferring concepts from presumably out-of-distribution prompts, known as in-context learning. Though this success is often attributed to the Transformer architecture, our systematic…

Rule-based explanations provide simple reasons explaining the behavior of machine learning classifiers at given points in the feature space. Several recent methods (Anchors, LORE, etc.) purport to generate rule-based explanations for…

Defeasible reasoning is a kind of reasoning where some generalisations may not be valid in all circumstances, that is general conclusions may fail in some cases. Various formalisms have been developed to model this kind of reasoning, which…

We report on the mechanization of (preference-based) conditional normative reasoning. Our focus is on Aqvist's system E for conditional obligation, and its extensions. Our mechanization is achieved via a shallow semantical embedding in…

We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity…

We reformulate recent advances in directed type theory--a type theory where the types have the structure of synthetic (higher) categories--as a logical calculus with multiple context 'zones', following the example of Pfenning and Davies.…

Large Language Models (LLMs) based on Transformers excel at text processing, but their reliance on prompts for specialized behavior introduces computational overhead. We propose a modification to a Transformer architecture that eliminates…

We introduce a new nameless representation of lambda terms inspired by ordered logic. At a lambda abstraction, number and relative position of all occurrences of the bound variable are stored, and application carries the additional…

We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of…

In a previous work Baillot and Terui introduced Dual light affine logic (DLAL) as a variant of Light linear logic suitable for guaranteeing complexity properties on lambda calculus terms: all typable terms can be evaluated in polynomial…

We develop team semantics for Linear Temporal Logic (LTL) to express hyperproperties, which have recently been identified as a key concept in the verification of information flow properties. Conceptually, we consider an asynchronous and a…

This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…

Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account…

Influence diagrams (IDs) are well-known formalisms extending Bayesian networks to model decision situations under uncertainty. Although they are convenient as a decision theoretic tool, their knowledge representation ability is limited in…