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Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
The integration of extensive, dynamic knowledge into Large Language Models (LLMs) remains a significant challenge due to the inherent entanglement of factual data and reasoning patterns. Existing solutions, ranging from non-parametric…
This reproducibility study analyzes and extends the paper "Axiomatic Causal Interventions for Reverse Engineering Relevance Computation in Neural Retrieval Models," which investigates how neural retrieval models encode task-relevant…
Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for…
In-context learning (ICL) has garnered significant attention for its ability to grasp functions/tasks from demonstrations. Recent studies suggest the presence of a latent task/function vector in LLMs during ICL. Merullo et al. (2024) showed…
We present an abstract machine and a reduction semantics for the lambda-calculus extended with control operators that give access to delimited continuations in the CPS hierarchy. The abstract machine is derived from an evaluator in…
Recent advancements in long-context language models (LCLMs) promise to transform Retrieval-Augmented Generation (RAG) by simplifying pipelines. With their expanded context windows, LCLMs can process entire knowledge bases and perform…
Scientists often infer abstract procedures from specific instances of problems and use the abstractions to generate new, related instances. For example, programs encoding the formal rules and properties of a system have been useful in…
This article is devoted to the study of methods to change defeasible logic programs (de.l.p.s) which are the knowledge bases used by the Defeasible Logic Programming (DeLP) interpreter. DeLP is an argumentation formalism that allows to…
Linear Logic and Defeasible Logic have been adopted to formalise different features of knowledge representation: consumption of resources, and non monotonic reasoning in particular to represent exceptions. Recently, a framework to combine…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
This note points out a lemma on closures of monotonic increasing functions and shows how it is applicable to decomposition and modularity for semantics defined as the least fixedpoint of some monotonic function. In particular it applies to…
In-context learning (ICL) has proven to be a significant capability with the advancement of Large Language models (LLMs). By instructing LLMs using few-shot demonstrative examples, ICL enables them to perform a wide range of tasks without…
Existing debiasing techniques are typically training-based or require access to the model's internals and output distributions, so they are inaccessible to end-users looking to adapt LLM outputs for their particular needs. In this study, we…
Terminological knowledge representation systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose…
Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and…
Constrained Horn Clauses (CHCs) are often used in automated program verification. Thus, techniques for (dis-)proving satisfiability of CHCs are a very active field of research. On the other hand, acceleration techniques for computing…
The lambda-calculus is a peculiar computational model whose definition does not come with a notion of machine. Unsurprisingly, implementations of the lambda-calculus have been studied for decades. Abstract machines are implementations…
Excellent progress has been made recently in solving ARC Challenge problems. However, it seems that new techniques may be required to push beyond 60% accuracy. Even commercial Large Language Models (LLMs) struggle to 'understand' many of…
We design various logics for proving hyper properties of iterative programs by application of abstract interpretation principles. In part I, we design a generic, structural, fixpoint abstract interpreter parameterized by an algebraic…