Related papers: Step-Indexed Relational Reasoning for Countable No…
Language models have demonstrated remarkable performance on complex multi-step reasoning tasks. However, their evaluation has been predominantly confined to high-resource languages such as English. In this paper, we introduce a manually…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Understanding the abilities of LLMs to reason about natural language plans, such as instructional text and recipes, is critical to reliably using them in decision-making systems. A fundamental aspect of plans is the temporal order in which…
In this paper, general logic-systems and a necessary and sufficient algorithm are used to substantiate significant consequence operator properties. It is shown, among other results, that, in certain cases, (1) if the number of steps in a…
Entity matching is a fundamental task in data cleaning and data integration. With the rapid adoption of large language models (LLMs), recent studies have explored zero-shot and few-shot prompting to improve entity matching accuracy.…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
Chain-of-Thought (CoT) reasoning, which breaks down complex tasks into intermediate reasoning steps, has significantly enhanced the performance of large language models (LLMs) on challenging tasks. However, the detailed reasoning process in…
In a paper presented at SOS 2010, we developed a framework for big-step semantics for interactive input-output in combination with divergence, based on coinductive and mixed inductive-coinductive notions of resumptions, evaluation and…
The use of non-deterministic functions is a distinctive feature of modern functional logic languages. The semantics commonly adopted is call-time choice, a notion that at the operational level is related to the sharing mechanism of lazy…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Language models are increasingly being used in important decision pipelines, so ensuring the correctness of their outputs is crucial. Recent work has proposed evaluating the "factuality" of claims decomposed from a language model generation…
Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates…
In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…
While Pre-trained Language Models (PLMs) internalize a great amount of world knowledge, they have been shown incapable of recalling these knowledge to solve tasks requiring complex & multi-step reasoning. Similar to how humans develop a…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
Nondeterministic choice is a useful program construct that provides a way to describe the behaviour of a program without specifying the details of possible implementations. It supports the stepwise refinement of programs, a method that has…
A modal logic is \emph{non-iterative} if it can be defined by axioms that do not nest modal operators, and \emph{rank-1} if additionally all propositional variables in axioms are in scope of a modal operator. It is known that every…
Sequential modelling entails making sense of sequential data, which naturally occurs in a wide array of domains. One example is systems that interact with users, log user actions and behaviour, and make recommendations of items of potential…
Reconfigurable interaction induces another dimension of nondeterminism in concurrent systems which makes it hard to reason about the different choices of the system from a global perspective. Namely, (1) choices that correspond to…