Related papers: Automating the Generation of High School Geometry …
We report on a new, simple, modular, and flexible approach for automated generation of illustrations for (readable) synthetic geometry proofs. The underlying proofs are generated using the Larus automated prover for coherent logic, and…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we…
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…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…
The study of propositional logic -- fundamental to the theory of computing -- is a cornerstone of the undergraduate computer science curriculum. Learning to solve logical proofs requires repeated guided practice, but undergraduate students…
We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus. The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
This paper presents an intelligent tutoring system, GeoTutor, for Euclidean Geometry that is automatically able to synthesize proof problems and their respective solutions given a geometric figure together with a set of properties true of…
Large Language Models (LLMs) have upended decades of pedagogy in computing education. Students previously learned to code through \textit{writing} many small problems with less emphasis on code reading and comprehension. Recent research has…
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…
The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other…
Proof Blocks is a software tool which enables students to write proofs by dragging and dropping prewritten proof lines into the correct order. These proofs can be graded completely automatically, enabling students to receive rapid feedback…
Providing valuable and personalized feedback is essential for effective learning, but delivering it promptly can be challenging in large-scale courses. Recent research has explored automated feedback mechanisms across various programming…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
The introduction of automated deduction systems in secondary schools face several bottlenecks, the absence of the subject of rigorous mathematical demonstrations in the curricula, the lack of knowledge by the teachers about the subject and…