Related papers: Representing Isabelle in LF
Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis,…
In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics).…
Large language models (LLM), such as Google's Minerva and OpenAI's GPT families, are becoming increasingly capable of solving mathematical quantitative reasoning problems. However, they still make unjustified logical and computational…
A focused proof system provides a normal form to cut-free proofs that structures the application of invertible and non-invertible inference rules. The focused proof system of Andreoli for linear logic has been applied to both the proof…
Over the past three decades, there have been several attempts to characterize modules over affine Lie superalgebras. One of the main issues in this regard is dealing with zero-level modules. In this paper, we study these modules and…
An important application of Synthetic Biology is the engineering of the host cell system to yield useful products. However, an increase in the scale of the host system leads to huge design space and requires a large number of validation…
We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental…
We propose a formalism for representation of finite languages, referred to as the class of IDL-expressions, which combines concepts that were only considered in isolation in existing formalisms. The suggested applications are in natural…
The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…
This paper introduces a novel perspective about error in machine learning and proposes inverse feature learning (IFL) as a representation learning approach that learns a set of high-level features based on the representation of error for…
Modular reasoning about class invariants is challenging in the presence of dependencies among collaborating objects that need to maintain global consistency. This paper presents semantic collaboration: a novel methodology to specify and…
Large Language Models (LLMs) demonstrate an impressive capacity to recall a vast range of factual knowledge. However, understanding their underlying reasoning and internal mechanisms in exploiting this knowledge remains a key research area.…
Isabelle2Cpp is a code generation framework that supports automatic generation of C++ code from Isabelle/HOL specifications. However, if some type information of Isabelle/HOL specification is missing, Isabelle2Cpp may not complete the code…
We present in this paper the preliminary design of a module system based on a notion of components such as they are found in COM. This module system is inspired from that of Standard ML, and features first-class instances of components,…
A new area of application of methods of algebra of logic and to valued logic, which has emerged recently, is the problem of recognizing a variety of objects and phenomena, medical or technical diagnostics, constructing modern machines,…
Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…
The integration of lexical semantics and pragmatics in the analysis of the meaning of natural lan- guage has prompted changes to the global framework derived from Montague. In those works, the original lexicon, in which words were assigned…
While large language models (LLMs) have shown great potential across various domains, their applications in robotics remain largely limited to static prompt-based behaviors and still face challenges in complex tasks under zero-shot or…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…