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We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of…
I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a…
In this paper, we introduce Linear Logic with a nondeterministic facility, which has a self-dual additive connective. In the system the proof net technology is available in a natural way. The important point is that nondeterminism in the…
Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the…
The paper presents a software tool for analysis and interactive engagement in various logical reasoning tasks. A first feature of the program consists in providing an interface for working with logic-specific repositories of formal…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
We advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The…
We present Isabellm, an LLM-powered theorem prover for Isabelle/HOL that performs fully automatic proof synthesis. Isabellm works with any local LLM on Ollama and APIs such as Gemini CLI, and it is designed to run on consumer grade…
We report on several scenarios of using automated theorem proving software in university education. In particular, we focus on using the Theorema system in a software-enhanced logic-course for students in computer science or artificial…
We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…
Quantum Hoare Logic (QHL) was introduced in Ying's work to specify and reason about quantum programs. In this paper, we implement a theorem prover for QHL based on Isabelle/HOL. By applying the theorem prover, verifying a quantum program…
One of the main issues in proof certification is that different theorem provers, even when designed for the same logic, tend to use different proof formalisms and produce outputs in different formats. The project ProofCert promotes the…
MerLean-Prover is an end-to-end Lean4 theorem prover that replaces sorry declarations with kernel-checkable proofs. It is built from three agent types (Planning, Check, and Lean) composed by a recursive outer loop whose unit of revision is…
LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely…
The combination of verifiable languages and LLMs has significantly influenced both the mathematical and computer science communities because it provides a rigorous foundation for theorem proving. Recent advancements in the field provide…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Chain-of-thought (CoT) reasoning improves large language models (LLMs) on difficult tasks, but it also makes inference expensive because every intermediate step must be generated as a discrete token. Latent reasoning reduces visible token…
Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…
Recent advances in large language models (LLMs) have enabled more semantic-aware recommendations through natural language generation. Existing LLM for recommendation (LLM4Rec) methods mostly operate in a System 1-like manner, relying on…
The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules…