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This paper presents an in-depth analysis of Large Language Models (LLMs), focusing on LLaMA, a prominent open-source foundational model in natural language processing. Instead of assessing LLaMA through its generative output, we design…
We study the complexity of the model checking problem, for fixed model A, over certain fragments L of first-order logic. These are sometimes known as the expression complexities of L. We obtain various complexity classification theorems for…
The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…
Large Language Models (LLMs) have demonstrated strong generalization across a wide range of tasks. Reasoning with LLMs is central to solving multi-step problems and complex decision-making. To support efficient reasoning, recent studies…
We have only limited understanding of how and why large language models (LLMs) respond in the ways that they do. Their neural networks have proven challenging to interpret, and we are only beginning to tease out the function of individual…
When large language models (LLMs) use in-context learning (ICL) to solve a new task, they must infer latent concepts from demonstration examples. This raises the question of whether and how transformers represent latent structures as part…
We consider the problem of automatically inferring specifications in the branching-time logic, Computation Tree Logic (CTL), from a given system. Designing functional and usable specifications has always been one of the biggest challenges…
HyLL (Hybrid Linear Logic) and SELL (Subexponential Linear Logic) are logical frameworks that have been extensively used for specifying systems that exhibit modalities such as temporal or spatial ones. Both frameworks have linear logic (LL)…
While Large Language Models (LLMs) have achieved strong performance across many NLP tasks, their opaque internal mechanisms hinder trustworthiness and safe deployment. Existing surveys in explainable AI largely focus on post-hoc explanation…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
We bring an abstract model theory perspective to interpolation. We ask, what is the role of interpolation in the study of extensions of first order logic, such as infinitary logics, generalized quantifiers and higher order logics? The…
Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded into a differential net, which is its Taylor expansion. We prove that two different MELL proof-nets have two different Taylor expansions. As a corollary, we prove…
Description logics (DLs) are standard knowledge representation languages for modelling ontologies, i.e. knowledge about concepts and the relations between them. Unfortunately, DL ontologies are difficult to learn from data and…
Large Language Models (LLMs) have been shown to achieve breakthrough performance on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs to derive reliable reasoning paths,…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations, there are non-causal relationships among variables. For example, we may want variables…
Large language models (LLMs) are increasingly used in domains where causal reasoning matters, yet it remains unclear whether their judgments reflect normative causal computation, human-like shortcuts, or brittle pattern matching. We…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
Hyperproperties, which generalize trace properties by relating multiple traces, are widely studied in information-flow security. Recently, a number of logics for hyperproperties have been proposed, and there is a need to understand their…
This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…