Related papers: Automated Planning Techniques for Elementary Proof…
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…
I introduce an approach for automated reasoning in first order set theories that are not finitely axiomatizable, such as $ZFC$, and describe its implementation alongside the automated theorem proving software E. I then compare the results…
Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…
We formulate learning guided Automated Theorem Proving as Partial Label Learning, building the first bridge across these fields of research and providing a theoretical framework for dealing with alternative proofs during learning. We use…
This paper surveys and organizes research works in an under-studied area, which we call automated evaluation for student argumentative writing. Unlike traditional automated writing evaluation that focuses on holistic essay scoring, this…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the…
Automated Machine Learning (AutoML) is an area of research that focuses on developing methods to generate machine learning models automatically. The idea of being able to build machine learning models with very little human intervention…
This essay examines how automation has reconfigured mathematical proof and labor, and what might happen in the future. It discusses practical standards of proof, distinguishes between prominent forms of automation in research, provides…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
The intention of the present study is to establish the mathematical fundamentals for automated problem solving essentially targeted for robotics by approaching the task universal algebraically introducing knowledge as realizations of…
Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…
The introduction of automated deduction systems in secondary schools face several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers…
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),…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify…
Automated planning is concerned with developing efficient algorithms to generate plans or sequences of actions to achieve a specific goal in a given environment. Emerging Large Language Models (LLMs) can answer questions, write high-quality…
Task and motion planning (TAMP) frameworks address long and complex planning problems by integrating high-level task planners with low-level motion planners. However, existing TAMP methods rely heavily on the manual design of planning…
In this paper we examine the potential of computer-assisted proof methods to be applied much more broadly than commonly recognized. More specifically, we contend that there are vast opportunities to derive useful mathematical results and…