Related papers: Goal-Oriented Conjecturing for Isabelle/HOL
Automatic (i.e., computer-assisted) theorem proving (ATP) can come in many flavors. This document presents early steps in our effort towards defining object-oriented theorem proving (OOTP) as a new style of ATP. Traditional theorem proving…
Goal models have been widely used in Computer Science to represent software requirements, business objectives, and design qualities. Existing goal modelling techniques, however, have shown limitations of expressiveness and/or tractability…
A Forensic Lucid intensional programming language has been proposed for intensional cyberforensic analysis. In large part, the language is based on various predecessor and codecessor Lucid dialects bound by the higher-order intensional…
We formalise and mechanise a construtive, proof theoretic proof of Craig's Interpolation Theorem in Isabelle/HOL. We give all the definitions and lemma statements both formally and informally. We also transcribe informally the formal…
General-purpose object placement is a fundamental capability of an intelligent generalist robot: being capable of rearranging objects following precise human instructions even in novel environments. This work is dedicated to achieving…
This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in…
This article describes a formal strategy of geometric complexity theory (GCT) to resolve the {\em self referential paradox} in the $P$ vs. $NP$ and related problems. The strategy, called the {\em flip}, is to go for {\em explicit proofs} of…
While Large Language Models (LLMs) have emerged as powerful foundational models to solve a variety of tasks, they have also been shown to be prone to hallucinations, i.e., generating responses that sound confident but are actually incorrect…
Recent announcements from frontier AI model labs have highlighted strong results on high-school and undergraduate math competitions. Yet it remains unclear whether large language models can solve new, simple conjectures in more advanced…
We present a formal framework for the development of a family of discriminative learning algorithms for Probabilistic Context-Free Grammars (PCFGs) based on a generalization of criterion-H. First of all, we propose the H-criterion as the…
This letter introduces an abstract learning problem called the "set embedding": The objective is to map sets into probability distributions so as to lose less information. We relate set union and intersection operations with corresponding…
We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original…
Hammers are tools that provide general purpose automation for formal proof assistants. Despite the gaining popularity of the more advanced versions of type theory, there are no hammers for such systems. We present an extension of the…
Goedel's explicit thesis was that his undecidable formula GUS is a well-formed, well-defined formal sentence in any formalisation of Intuitive Arithmetic IA in which the axioms and rules of inference are recursively definable. His implicit…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
This paper tackles the problem of learning a questioner in the goal-oriented visual dialog task. Several previous works adopt model-free reinforcement learning. Most pretrain the model from a finite set of human-generated data. We argue…
While state-of-the-art language models (LMs) surpass the vast majority of humans in certain domains, their reasoning remains largely opaque, undermining trust in their output. Furthermore, while autoregressive LMs can output explicit…
In this work, we further develop multigoal-oriented a posteriori error estimation with two objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals of interest for nonlinear problems in which both the…
We introduce Tinker, a tool for designing and evaluating proof strategies based on proof-strategy graphs, a formalism previously introduced by the authors. We represent proof strategies as open-graphs, which are directed graphs with…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…