Related papers: Natural Deduction and the Isabelle Proof Assistant
A protocol-independent secrecy theorem is established and applied to several non-trivial protocols. In particular, it is applied to protocols proposed for protecting the computation results of free-roaming mobile agents doing comparison…
Inspired by the recent evolution of deep neural networks (DNNs) in machine learning, we explore their application to PL-related topics. This paper is the first step towards this goal; we propose a proof-synthesis method for the…
Introductory Software Engineering (SE) courses face rapidly increasing student enrollment numbers, participants with diverse backgrounds and the influence of Generative AI (GenAI) solutions. High teacher-to-student ratios often challenge…
Induction lies at the heart of mathematics and computer science. However, automated theorem proving of inductive problems is still limited in its power. In this abstract, we first summarize our progress in automating inductive theorem…
While recent works have been considerably improving the quality of the natural language explanations (NLEs) generated by a model to justify its predictions, there is very limited research in detecting and alleviating inconsistencies among…
Mathematical text is written using a combination of words and mathematical expressions. This combination, along with a specific way of structuring sentences makes it challenging for state-of-art NLP tools to understand and reason on top of…
This paper describes NAIVE, a low-level knowledge representation language and inferencing process. NAIVE has been designed for reasoning about nondeterministic dynamic systems like those found in medicine. Knowledge is represented in a…
Demonstration learning aims to guide the prompt prediction via providing answered demonstrations in the few shot settings. Despite achieving promising results, existing work only concatenates the answered examples as demonstrations to the…
Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in…
We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors. To express such models, we…
As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…
We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded…
Generative AI is expected to have a vast, positive impact on education; however, at present, this potential has not yet been demonstrated at scale at university level. In this study, we present first evidence that generative AI can increase…
Mathematical proofs are a cornerstone of control theory, and it is important to get them right. Deduction systems can help with this by mechanically checking the proofs. However, the structure and level of detail at which a proof is…
There are two kinds of systems that programming language researchers use for their work. Semantics engineering tools let them interactively explore their definitions, while proof assistants can be used to check the proofs of their…
An efficient intuitionistic first-order prover integrated into Coq is useful to replay proofs found by external automated theorem provers. We propose a two-phase approach: An intuitionistic prover generates a certificate based on the matrix…
This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each individual learning…
The Isabelle/HOL proof assistant has a powerful library for continuous analysis, which provides the foundation for verification of hybrid systems. However, Isabelle lacks automated proof support for continuous artifacts, which means that…
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…
Early identification of Adverse Drug Events (ADE) is critical for taking prompt actions while introducing new drugs into the market. These ADEs information are available through various unstructured data sources like clinical study reports,…