Related papers: Learning from {\L}ukasiewicz and Meredith: Investi…

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…

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…

Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…

This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…

Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…

Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…

Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…

We consider the problem of automated reasoning about dynamically manipulated data structures. The state-of-the-art methods are limited to the unfold-and-match (U+M) paradigm, where predicates are transformed via (un)folding operations…

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…

We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…

Since the advent of Large Language Models (LLMs), efforts have largely focused on improving their instruction-following and deductive reasoning abilities, leaving open the question of whether these models can truly discover new knowledge.…

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…

Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we…

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some…

The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…

In this paper we introduce the convex fragment of {\L}ukasiewicz Logic and discuss its possible applications in different learning schemes. Indeed, the provided theoretical results are highly general, because they can be exploited in any…

We exhibit how the Rasiowa-Sikorski Lemma simplifies, in a sense, proofs of results that make use of the technique known as back-and-forth, often resulting in not very illustrative arguments. The first two sections seek to show one simple…