相关论文: Lemma Generation for Horn Clause Satisfiability: A…
Despite the recent advance of automated program verification, reasoning about recursive data structures remains as a challenge for verification tools and their backends such as SMT and CHC solvers. To address the challenge, we introduce the…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
Large Language Models (LLMs) trained on petabytes of data are highly compressed repositories of a significant proportion of the knowledge accumulated and distilled so far. In this paper we study techniques to elicit this knowledge in the…
Recent years have witnessed the rise of compositional semantics as a foundation for formal verification of complex systems. In particular, interaction trees have emerged as a popular denotational semantics. Interaction trees achieve…
An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of…
We introduce the framework FreeCHR which formalizes the embedding of Constraint Handling Rules (CHR) into a host language, using the concept of initial algebra semantics from category theory. We hereby establish a high-level implementation…
Representation intervention aims to locate and modify the representations that encode the underlying concepts in Large Language Models (LLMs) to elicit the aligned and expected behaviors. Despite the empirical success, it has never been…
Automated program verification is a difficult problem. It is undecidable even for transition systems over Linear Integer Arithmetic (LIA). Extending the transition system with theory of Arrays, further complicates the problem by requiring…
Automatic legal judgment prediction and its explanation suffer from the problem of long case documents exceeding tens of thousands of words, in general, and having a non-uniform structure. Predicting judgments from such documents and…
The need for rigorous process composition is encountered in many situations pertaining to the development and analysis of complex systems. We discuss the use of Classical Linear Logic (CLL) for correct-by-construction resource-based process…
Running LLMs with extended reasoning on every problem is expensive, but determining which inputs actually require additional compute remains challenging. We investigate whether their own likelihood of success is recoverable from their…
We address the satisfiability problem for string constraints that combine relational constraints represented by transducers, word equations, and string length constraints. This problem is undecidable in general. Therefore, we propose a new…
Hierarchical Text Classification (HTC) is a challenging task where a document can be assigned to multiple hierarchically structured categories within a taxonomy. The majority of prior studies consider HTC as a flat multi-label…
We present the derivation reduction problem for SLD-resolution, the undecidable problem of finding a finite subset of a set of clauses from which the whole set can be derived using SLD-resolution. We study the reducibility of various…
We show how to generate and validate logical proofs of unsatisfiability from delta-complete decision procedures that rely on error-prone numerical algorithms. Solving this problem is important for ensuring correctness of the decision…
Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving. Nevertheless, their full potential, particularly concerning the mitigation of hallucinations and refinement through prover…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
Heuristics are a central component of deterministic planning, particularly in domain-independent settings where general applicability is prioritized over task-specific tuning. This work revisits that paradigm in light of recent advances in…
Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its…
We establish proof-theoretic, constructive and coalgebraic foundations for proof search in coinductive Horn clause theories. Operational semantics of coinductive Horn clause resolution is cast in terms of coinductive uniform proofs; its…