Related papers: On Incorrectness Logic and Kleene Algebra with Top…
While there is a long tradition of reasoning about (non)termination in program analysis, specialized logics are typically needed to give different termination criteria. This includes partial correctness, where termination is not guaranteed,…
We give a decision procedure and proof of correctness for the equational theory of probabilistic Kleene algebra with angelic nondeterminism introduced in Ong, Ma, and Kozen (2025).
Large Language Models (LLMs) excel at linear reasoning tasks but remain underexplored on non-linear structures such as those found in natural debates, which are best expressed as argument graphs. We evaluate whether LLMs can approximate…
Chain of Thought (CoT) reasoning has demonstrated remarkable deep reasoning capabilities in both large language models (LLMs) and multimodal large language models (MLLMs). However, its reliability is often undermined by the accumulation of…
Hoare logic provides a syntax-oriented method to reason about program correctness and has been proven effective in the verification of classical and probabilistic programs. Existing proposals for quantum Hoare logic either lack completeness…
High-rate quantum error correcting (QEC) codes encode many logical qubits in a given number of physical qubits, making them promising candidates for quantum computation. Implementing high-rate codes at a scale that both frustrates classical…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
A propositional logic program $P$ may be identified with a $P_fP_f$-coalgebra on the set of atomic propositions in the program. The corresponding $C(P_fP_f)$-coalgebra, where $C(P_fP_f)$ is the cofree comonad on $P_fP_f$, describes…
Large Language Models (LLMs) have shown impressive performance on complex tasks through Chain-of-Thought (CoT) reasoning. However, conventional CoT relies on explicitly verbalized intermediate steps, which constrains its broader…
Chain-of-thought (CoT) rationale enables language models to use additional task-related text for problem-solving, benefiting not only from detailed reasoning steps but also from the expanded computational space of longer inputs. Prior work…
Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…
Automated legal reasoning and its application in smart contracts and automated decisions are increasingly attracting interest. In this context, ethical and legal concerns make it necessary for automated reasoners to justify in…
Automated verification of all members of a (potentially infinite) set of programs has the potential to be useful in program synthesis, as well as in verification of dynamically loaded code, concurrent code, and language properties. Existing…
Large Language Models (LLMs) can achieve strong performance on many tasks by producing step-by-step reasoning before giving a final output, often referred to as chain-of-thought reasoning (CoT). It is tempting to interpret these CoT…
The likelihood of an automated reasoning program being of substantial assistance for a wide spectrum of applications rests with the nature of the options and parameters it offers on which to base needed strategies and methodologies. This…
Reasoning capability is pivotal for Large Language Models (LLMs) to solve complex tasks, yet achieving reliable and scalable reasoning remains challenging. While Chain-of-Thought (CoT) prompting has become a mainstream approach, existing…
Classical results in computability theory, notably Rice's theorem, focus on the extensional content of programs, namely, on the partial recursive functions that programs compute. Later and more recent work investigated intensional…
High-assurance reasoning, particularly in critical domains such as law and medicine, requires conclusions that are accurate, verifiable, and explicitly grounded in evidence. This reasoning relies on premises codified from rules, statutes,…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
While Chain-of-Thought (CoT) prompting enhances the reasoning capabilities of large language models, the faithfulness of the generated rationales remains an open problem for model interpretability. We propose a novel theoretical lens for…