Related papers: From Program Logics to Language Logics

Large language models (LLMs) have recently demonstrated an impressive ability to perform arithmetic and symbolic reasoning tasks, when provided with a few examples at test time ("few-shot prompting"). Much of this success can be attributed…

Causal reasoning, the ability to identify cause-and-effect relationship, is crucial in human thinking. Although large language models (LLMs) succeed in many NLP tasks, it is still challenging for them to conduct complex causal reasoning…

Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be…

We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…

This dissertation is concerned with the study of program equivalence and algebraic effects as they arise in the theory of programming languages. Algebraic effects represent impure behaviour in a functional programming language, such as…

Logical reasoning is a pivotal component in the field of artificial intelligence. Proof planning, particularly in contexts requiring the validation of explanation accuracy, continues to present challenges. The recent advancement of large…

Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…

Weighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path…

Completeness of a logic program means that the program produces all the answers required by its specification. The cut is an important construct of programming language Prolog. It prunes part of the search space, this may result in a loss…

Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…

Visual reasoning is central to human cognition, enabling individuals to interpret and abstractly understand their environment. Although recent Multimodal Large Language Models (MLLMs) have demonstrated impressive performance across language…

While LLM-based agents are able to tackle a wide variety of code reasoning questions, the answers are not always correct. This prevents the agent from being useful in situations where high precision is desired: (1) helping a software…

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…

Document forgery poses a growing threat to legal, economic, and governmental processes, requiring increasingly sophisticated verification mechanisms. One approach involves the use of plausibility checks, rule-based procedures that assess…

In recent years, large language models (LLMs) have demonstrated significant success in performing varied natural language tasks such as language translation, question-answering, summarizing, fact-checking, etc. Despite LLMs' impressive…

There have been a huge number of benchmarks proposed to evaluate how large language models (LLMs) behave for logic inference tasks. However, it remains an open question how to properly evaluate this ability. In this paper, we provide a…

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…

We present realizability and realization logic, two program logics that jointly address the problem of finding solutions in semantics-guided synthesis. What is new is that we proceed eagerly and not only analyze a single candidate program…

Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…

Relying on the formulae-as-types paradigm for classical logic, we define a program logic for an imperative language with higher-order procedural variables and non-local jumps. Then, we show how to derive a sound program logic for this…