Related papers: The Higher-Order Prover Leo-III (Extended Version)
We introduce a new framework to evaluate and improve first-order (FO) ontologies using automated theorem provers (ATPs) on the basis of competency questions (CQs). Our framework includes both the adaptation of a methodology for evaluating…
A classical result in descriptive complexity theory states that Datalog expresses exactly the class of polynomially computable queries on ordered databases. In this paper we extend this result to the case of higher-order Datalog. In…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
Modern saturation-based Automated Theorem Provers typically implement the superposition calculus for reasoning about first-order logic with or without equality. Practical implementations of this calculus use a variety of literal selections…
Sequences of numbers (either natural integers, or integers or rational) of level $k \in \mathbb{N}$ have been defined in \cite{Fra05,Fra-Sen06} as the sequences which can be computed by deterministic pushdown automata of level $k$. This…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…
Deontic logic is a very well researched branch of mathematical logic and philosophy. Various kinds of deontic logics are discussed for different application domains like argumentation theory, legal reasoning, and acts in multi-agent…
Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning.…
Temporal logics are a powerful tool to specify properties of computational systems. For concurrent programs, Higher Dimensional Automata (HDA) are a very expressive model of non-interleaving concurrency. HDA recognize languages of partially…
Large Language Models (LLMs) still struggle with complex logical reasoning. While previous works achieve remarkable improvements, their performance is highly dependent on the correctness of translating natural language (NL) problems into a…
Logical reasoning is a key task for artificial intelligence due to it's role in major downstream tasks such as Question Answering, Summarization. Recent methods in improving the reasoning ability of LLMs fall short in correctly converting a…
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…
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
We present a neurosymbolic approach, i.e., combining symbolic and subsymbolic artificial intelligence, to validating offer documents in regulated public institutions. We employ a language model to extract information and then aggregate with…
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for…
We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We first observe that logical predicates are…
This thesis delves into a fortiori arguments in deductive reasoning, underscoring their relevance in various domains such as law, philosophy, and artificial intelligence. The research is centred on employing GPT-3.5-turbo to automate the…
This workshop brings together practioners and researchers who are involved in the everyday aspects of logical systems based on higher-order logic. We hope to create a friendly and highly interactive setting for discussions around the…
In this article, we develop a new and somewhat unexpected connection between higher-order model-checking and linear logic. Our starting point is the observation that once embedded in the relational semantics of linear logic, the Church…