Related papers: Nominal LCF: A Language for Generic Proof
Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…
Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Rational verification refers to the problem of checking which temporal logic properties hold of a concurrent multiagent system, under the assumption that agents in the system choose strategies that form a game-theoretic equilibrium.…
Effectively translating between natural language (NL) and formal logics like Linear Temporal Logic (LTL) requires expertise that limits formal verification's reach in safety-critical development. Template-based approaches sacrifice…
Recent advancements in large language models (LLMs) have extended their capabilities from basic text processing to complex reasoning tasks, including legal interpretation, argumentation, and strategic interaction. However, empirical…
Neurosymbolic approaches can add robustness to opaque neural systems by incorporating explainable symbolic representations. However, previous approaches have not used formal logic to contextualize queries to and validate outputs of large…
Computation Tree Logic (CTL) and its extensions CTL* and CTL+ are widely used in automated verification as a basis for common model checking tools. But while they can express many properties of interest like reachability, even simple…
Formal patterns are formally specified solutions to frequently occurring distributed system problems that are generic, executable, and come with strong qualitative and/or quantitative formal guarantees. A formal pattern is a generic system…
Large Language Models (LLMs) are increasingly being used to automate programming tasks. Yet, LLMs' capabilities in reasoning about program semantics are still inadequately studied, leaving significant potential for further exploration. This…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
Linear Temporal Logic over finite traces ($\text{LTL}_f$) is a widely used formalism with applications in AI, process mining, model checking, and more. The primary reasoning task for $\text{LTL}_f$ is satisfiability checking; yet, the…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
In the last years, there has been an increasing demand of a variety of logical systems, prompted mostly by applications of logic in AI and other related areas. Labeled Deductive Systems (LDS) were developed as a flexible methodology to…
The DL-Lite description logics allow for modeling domain knowledge on top of databases and for efficient reasoning. We focus on metric temporal extensions of DL-Lite_bool and its fragments, and study the complexity of satisfiability. In…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…
The Web of Linked Data is composed of tons of RDF documents interlinked to each other forming a huge repository of distributed semantic data. Effectively querying this distributed data source is an important open problem in the Semantic Web…
Artificial intelligence systems have achieved remarkable capability in natural language processing, perception and decision-making tasks. However, their behaviour often remains opaque and difficult to verify, limiting their applicability in…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…