Related papers: System Description: H-PILoT (Version 1.9)
This paper introduces a framework for the bottom-up simulation of SLD-resolution based on partial evaluation. The main idea is to use database facts to represent a set of SLD goals. For deductive databases it is natural to assume that the…
We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…
We apply a compositional formal modeling and verification method to an autonomous aircraft taxi system. We provide insights into the modeling approach and we identify several research areas where further development is needed. Specifically,…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
HPC environments have traditionally been designed to meet the compute demand of scientific applications and data has only been a second order concern. With science moving toward data-driven discoveries relying more on correlations in data…
This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…
Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…
Dedukti is a type-checker for the $\lambda$$\Pi$-calculus modulo rewriting, an extension of Edinburgh's logicalframework LF where functions and type symbols can be defined by rewrite rules. It thereforecontains an engine for rewriting LF…
We present CoqPilot, a VS Code extension designed to help automate writing of Coq proofs. The plugin collects the parts of proofs marked with the admit tactic in a Coq file, i.e., proof holes, and combines LLMs along with…
Model checking approaches can be divided into two broad categories: global approaches that determine the set of all states in a model M that satisfy a temporal logic formula f, and local approaches in which, given a state s in M, the…
In this article, the decidability and computability issues of dynamic probability logic (DPL) are addressed. Firstly, a proof system $\mathcal{H}_{DPL}$ is introduced for DPL and shown that it is weakly complete. Furthermore, this logic has…
To mitigate hallucinations in large language models (LLMs), we propose a framework that focuses on errors induced by prompts. Our method extends a chain-style knowledge distillation approach by incorporating a programmable module that…
Security properties of real-time systems often involve reasoning about hyper-properties, as opposed to properties of single executions or trees of executions. These hyper-properties need to additionally be expressive enough to reason about…
We introduce Refinement Reflection, a new framework for building SMT-based deductive verifiers. The key idea is to reflect the code implementing a user-defined function into the function's (output) refinement type. As a consequence, at uses…
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…
Prompt learning has become a prevalent strategy for adapting vision-language foundation models to downstream tasks. As large language models (LLMs) have emerged, recent studies have explored the use of category-related descriptions as input…
The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic…
We develop the first two heap logics that have implicit heaplets and that admit FO-complete program verification. The notion of FO-completeness is a theoretical guarantee that all theorems that are valid when recursive definitions are…
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization…
Tabular reasoning involves interpreting natural language queries about tabular data, which presents a unique challenge of combining language understanding with structured data analysis. Existing methods employ either textual reasoning,…