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As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…
This dissertation explores the roles of polarities and focussing in various aspects of Computational Logic. These concepts play a key role in the the interpretation of proofs as programs, a.k.a. the Curry-Howard correspondence, in the…
Recent advances in Language Models (LMs) have failed to mask their shortcomings particularly in the domain of reasoning. This limitation impacts several tasks, most notably those involving ontology engineering. As part of a PhD research, we…
Legal reasoning requires both precise interpretation of statutory language and consistent application of complex rules, presenting significant challenges for AI systems. This paper introduces a modular multi-agent framework that decomposes…
Large language models (LLMs) are increasingly used to generate requirements specifications, design documents, code, and test cases. In contrast, much less attention has been given to a more difficult assurance problem: statically verifying…
Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…
Large language models perform well on many logical reasoning benchmarks, but it remains unclear which core logical skills they truly master. To address this, we introduce LogicSkills, a benchmark that isolates three fundamental logical…
Logical reasoning has been an ongoing pursuit in the field of AI. Despite significant advancements made by large language models (LLMs), they still struggle with complex logical reasoning problems. To enhance reasoning performance, one…
Large Language Models (LLMs) still struggle with complex logical reasoning. While previous works achieve remarkable improvements, their performance is highly dependent on the correctness of translating natural language (NL) problems into a…
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…
Deep Learning (DL) techniques are now widespread and being integrated into many important systems. Their classification and recognition abilities ensure their relevance for multiple application domains. As machine-learning that relies on…
This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…
We present the design, implementation, and foundation of a verifier for higher-order functional programs with generics and recursive data types. Our system supports proving safety and termination using preconditions, postconditions and…
Virtually all verification techniques using formal methods rely on the availability of a formal specification, which describes the design requirements precisely. However, formulating specifications remains a manual task that is notoriously…
The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…
Linear Temporal Logic (LTL) is a widely used task specification language for autonomous systems. To mitigate the significant manual effort and expertise required to define LTL-encoded tasks, several methods have been proposed for…
Coding conventions for naming, spacing, and other essentially stylistic properties are necessary for developers to effectively understand, review, and modify source code in large software projects. Consistent conventions in verification…
Recent advances in automated theorem proving use Large Language Models (LLMs) to translate informal mathematical statements into formal proofs. However, informal cues are often ambiguous or lack strict logical structure, making it hard for…
Fuzzy Description Logics (DLs) provide a means for representing vague knowledge about an application domain. In this paper, we study fuzzy extensions of conjunctive queries (CQs) over the DL $\mathcal{SROIQ}$ based on finite chains of…
Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this…