Related papers: Lemma Generation for Horn Clause Satisfiability: A…

This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…

Constraint Handling Rules (CHR) are a committed-choice declarative language which has been designed for writing constraint solvers. A CHR program consists of multi-headed guarded rules which allow one to rewrite constraints into simpler…

We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…

Heap-manipulating programs are known to be challenging to reason about. We present a novel verifier for heap-manipulating programs called S2TD, which encodes programs systematically in the form of Constrained Horn Clauses (CHC) using a…

This paper investigates the problem of testing clause sets for membership in classes known from literature. In particular, we are interested in classes defined via renaming: Is it possible to rename the predicates in a way such that…

We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…

Horn-satisfiability or Horn-SAT is the problem of deciding whether a satisfying assignment exists for a Horn formula, a conjunction of clauses each with at most one positive literal (also known as Horn clauses). It is a well-known…

This paper presents a study of operational and type-theoretic properties of different resolution strategies in Horn clause logic. We distinguish four different kinds of resolution: resolution by unification (SLD-resolution), resolution by…

Machine learning systems regularly deal with structured data in real-world applications. Unfortunately, such data has been difficult to faithfully represent in a way that most machine learning techniques would expect, i.e. as a real-valued…

One of the main challenges in software verification is efficient and precise compositional analysis of programs with procedures and loops. Interpolation methods remain one of the most promising techniques for such verification, and are…

LLMs have been extensively used for the task of automated code generation. In this work, we examine the applicability of LLMs for the related but relatively unexplored task of code-equivalence checking, i.e., given two programs, whether…

We propose a new type-theoretic approach to SLD-resolution and Horn-clause logic programming. It views Horn formulas as types, and derivations for a given query as a construction of the inhabitant (a proof-term) for the type given by the…

We investigate representations of imperative programs as constrained Horn clauses. Starting from operational semantics transition rules, we proceed by writing interpreters as constrained Horn clause programs directly encoding the rules. We…

Verification of higher-order probabilistic programs is a challenging problem. We present a verification method that supports several quantitative properties of higher-order probabilistic programs. Usually, extending verification methods to…

We study how to subvert large language models (LLMs) from following prompt-specified rules. We first formalize rule-following as inference in propositional Horn logic, a mathematical system in which rules have the form "if $P$ and $Q$, then…

Temporal logic is a framework for representing and reasoning about propositions that evolve over time. It is commonly used for specifying requirements in various domains, including hardware and software systems, as well as robotics.…

In recent years, transformer-based large language models (LLMs) have revolutionised natural language processing (NLP), with generative models opening new possibilities for tasks that require context-aware text generation. Requirements…

Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated…

A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of…

Large language models (LLMs) are increasingly used for high-stakes decision-making, yet existing approaches struggle to reconcile scalability, interpretability, and reproducibility. Black-box models obscure their reasoning, while recent…