Related papers: Generating Theorems by Generating Proof Structures
We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…
The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…
To obtain high-quality sentence embeddings from pretrained language models (PLMs), they must either be augmented with additional pretraining objectives or finetuned on a large set of labeled text pairs. While the latter approach typically…
Machine-generated citation sentences can aid automated scientific literature review and assist article writing. Current methods in generating citation text were limited to single citation generation using the citing document and a cited…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…
Goal-directed proof search in first-order logic uses meta-variables to delay the choice of witnesses; substitutions for such variables are produced when closing proof-tree branches, using first-order unification or a theory-specific…
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…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
The symbolic-heap fragment of separation logic has been actively developed and advocated for verifying the memory-safety property of computer programs. At present, one of its biggest challenges is to effectively prove entailments containing…
This paper tackles the problem of formulating and proving the completeness of focused-like proof systems in an automated fashion. Focusing is a discipline on proofs which structures them into phases in order to reduce proof search…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
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…
Argument Mining(AM) aims to uncover the argumentative structures within a text. Previous methods require several subtasks, such as span identification, component classification, and relation classification. Consequently, these methods need…
Recently, it is often said that the data used for the pre-training of large language models (LLMs) have been exhausted. This paper proposes a solution to the problem: Automated generation of massive reasonable empirical theorems by forward…
We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is…
Definition Modeling, the task of generating definitions, was first proposed as a means to evaluate the semantic quality of word embeddings-a coherent lexical semantic representations of a word in context should contain all the information…
We introduce LeanConjecturer, a pipeline for automatically generating university-level mathematical conjectures in Lean 4 using Large Language Models (LLMs). Our hybrid approach combines rule-based context extraction with LLM-based theorem…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…