Related papers: A Type-Based HFL Model Checking Algorithm

Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…

In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order…

We study a type checking algorithm that is able to type check a nontrivial subclass of functional programs that use features such as higher-rank, impredicative and second-order types. The only place the algorithm requires type annotation is…

Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…

In this article, we design and analyze a Hybrid High-Order (HHO) finite element approximation for a class of strongly nonlinear boundary value problems. We consider an HHO discretization for a suitable linearized problem and show its…

Due to its expressiveness and unambiguous nature, First-Order Logic (FOL) is a powerful formalism for representing concepts expressed in natural language (NL). This is useful, e.g., for specifying and verifying desired system properties.…

Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…

Model-checking HyperLTL, a temporal logic expressing properties of sets of traces with applications to information-flow based security and privacy, has a decidable, but TOWER-complete, model-checking problem. While the classical…

Reasoning in language models is difficult to evaluate: natural-language traces are unverifiable, symbolic datasets are too small, and most benchmarks conflate heuristics with inference. We present FOL-Traces, the first large-scale dataset…

Alternating-time temporal logic (ATL) allows to specify requirements on abilities that different agents should (or should not) possess in a multi-agent system. However, model checking ATL specifications in realistic systems is…

This work discusses the reachability analysis (RA) of Max-Plus Linear (MPL) systems, a class of continuous-space, discrete-event models defined over the max-plus algebra. Given the initial and target sets, we develop algorithms to verify…

Fine-tuning large language models (LLMs) using standard first-order (FO) optimization often drives training toward sharp, poorly generalizing minima. Conversely, zeroth-order (ZO) methods offer stronger exploratory behavior without relying…

We introduce a hybrid spatiotemporal logic for automotive safety applications (HSTL), focused on highway driving. Spatiotemporal logic features specifications about vehicles throughout space and time, while hybrid logic enables precise…

Many types of attacks on confidentiality stem from the nondeterministic nature of the environment that computer programs operate in (e.g., schedulers and asynchronous communication channels). In this paper, we focus on verification of…

In runtime verification, pattern matching, which searches for occurrences of a specific pattern within a word, provides more information than a simple violation detection of the monitored property, by locating concrete evidence of the…

Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…

In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to…

Ensuring that safety-critical applications behave as intended is an important yet challenging task. Modeling languages like differential dynamic logic (dL) have proof calculi capable of proving guarantees for such applications. However, dL…

We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP). Unlike most learning based approaches, we focus on generalising from very little training data and…

The historic background of algorithmic processing with regard to etymology and methodology is translated into terms of mathematical logic and Computer Science. A formal logic structure is introduced by exemplaryquestions posed to…