Related papers: The computability path ordering
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We present a construction of a certain infinite complete partial order (CPO) that differs from the standard construction used in Scott's denotational semantics. In addition, we construct several other infinite CPO's. For some of those, we…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
The recent development of chain-of-thought (CoT) decoding has enabled large language models (LLMs) to generate explicit logical reasoning paths for complex problem-solving. However, research indicates that these paths are not always…
Computational paths treat propositional equality as explicit paths built from labelled deduction steps and rewrite rules. This view originates in work by de Queiroz and collaborators [1] and yields a weak groupoid structure for equality,…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
We introduce a reduction order called the weighted path order (WPO) that subsumes many existing reduction orders. WPO compares weights of terms as in the Knuth-Bendix order (KBO), while WPO allows weights to be computed by a wide class of…
Termination is a major question in both logic and computer science. In logic, termination is at the heart of proof theory where it is usually called strong normalization (of cut elimination). In computer science, termination has always been…
Direct Preference Optimization (DPO) has emerged as a popular alternative to Reinforcement Learning from Human Feedback (RLHF), offering theoretical equivalence with simpler implementation. We prove this equivalence is conditional rather…
This paper introduces Completion Pruning Policy Optimization (CPPO) to accelerate the training of reasoning models based on Group Relative Policy Optimization (GRPO). GRPO, while effective, incurs high training costs due to the need to…
Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all…
This work proposes tractable bisimulations for the higher-order pi-calculus with session primitives (HOpi) and offers a complete study of the expressivity of its most significant subcalculi. First we develop three typed bisimulations, which…
The main objective of this work is to study mathematical properties of computational paths. Originally proposed by de Queiroz \& Gabbay (1994) as `sequences of rewrites', computational paths can be seen as the grounds on which the…
Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit…
We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise…
Advanced models such as OpenAI o1 exhibit impressive problem-solving capabilities through step-by-step reasoning. However, they may still falter on more complex problems, making errors that disrupt their reasoning paths. We attribute this…
We show a method of describing processes with indefinite causal order (ICO) by a definite causal order. We do so by relabeling the processes that take place in the circuit in accordance with the basis of measurement of control qubit. Causal…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…