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Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for…
Compiler correctness proofs for higher-order concurrent languages are difficult: they involve establishing a termination-preserving refinement between a concurrent high-level source language and an implementation that uses low-level shared…
Non-interference is a program property that ensures the absence of information leaks. In the context of programming languages, there exist two common approaches for establishing non-interference: type systems and program logics. Type…
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
Contextual refinement and separation logics are successful verification techniques that are very different in nature. First, the former guarantees behavioral refinement between a concrete program and an abstract program while the latter…
Logical reasoning is a core capability for large language models (LLMs), yet existing benchmarks that rely solely on final-answer accuracy fail to capture the quality of the reasoning process. To address this, we introduce FineLogic, a…
The paper presents our research on quantifier elimination (QE) for compositional reasoning and verification. For compositional reasoning, QE provides the foundation of our approach, serving as the calculus for composition to derive the…
While reasoning models (e.g., DeepSeek R1) trained with reinforcement learning (RL), excel in textual reasoning, they struggle in scenarios requiring structured problem-solving, such as geometric reasoning, concise computation, or complex…
Large Language Models (LLMs) often fail to utilize their latent reasoning capabilities due to a distributional mismatch between ambiguous human inquiries and the structured logic required for machine activation. Existing alignment methods…
This paper presents a theory for the refinement of shared-memory concurrent algorithms from specifications. We augment pre and post condition specifications with Jones' rely and guarantee conditions, all of which are encoded as commands…
Lighthouse projects such as CompCert, seL4, IronFleet, and DeepSpec have demonstrated that full verification of entire systems is feasible by establishing a refinement relation between an abstract system specification and an executable…
With the rise of LLMs, there is an increasing need for intelligent recommendation assistants that can handle complex queries and provide personalized, reasoning-driven recommendations. LLM-based recommenders show potential but face…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
Looped computation shows promise in improving the reasoning-oriented performance of LLMs by scaling test-time compute. However, existing approaches typically require either training recurrent models from scratch or applying disruptive…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
Contemporary progress in large language models (LLMs) has revealed notable inferential capacities via reinforcement learning (RL) employing verifiable reward, facilitating the development of O1 and R1-like reasoning models. Directly…
Recommender systems are critical for delivering personalized content across digital platforms, and recent advances in Large Language Models (LLMs) offer new opportunities to enhance them with richer world knowledge and explicit reasoning…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…