Related papers: An alternative to back-and-forth
Using reinforcement learning for automated theorem proving has recently received much attention. Current approaches use representations of logical statements that often rely on the names used in these statements and, as a result, the models…
Some natural inequalities related to rearrangement in matrix products can also be regarded as extensions of classical inequalities for sequences or integrals. In particular, we show matrix versions of Chebyshev and Kantorovich type…
The static dependency pair method is a method for proving the termination of higher-order rewrite systems a la Nipkow. It combines the dependency pair method introduced for first-order rewrite systems with the notion of strong computability…
In this paper, we give a new proof of an arithmetic analogue of the Riemann-Roch Theorem, due originally to Serge Lang. Lang's result was first proved using the lattice point geometry of Minkowski. By contrast, our proof is completely…
The technique of symmetric extensions is derived from forcing and it is one of the most important tools for studying models without the Axiom of Choice. Despite being incredibly successful since the 1960s, our understanding of the technique…
Razborov's flag algebra forms a powerful framework for deriving asymptotic inequalities between induced subgraph densities, underpinning many advances in extremal graph theory. This survey introduces flag algebra to computer scientists…
Self-Consistency samples diverse reasoning chains with answers and chooses the final answer by majority voting. It is based on forward reasoning and cannot further improve performance by sampling more reasoning chains when saturated. To…
We present a comprehensive introduction to the kinematics of special relativity based on Minkowski diagrams and provide a graphical alternative to each and every topic covered in a standard introductory sequence. Compared to existing…
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
In previous work, the second author introduced a topology, for spaces of irreducible representations, that reduces to the classical Zariski topology over commutative rings but provides a proper refinement in various noncommutative settings.…
We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or {\L}ojasiewicz properties. These geometrical notions are usually local by nature, and may…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
We present a novel treatment of set theory in a four-valued paraconsistent and paracomplete logic, i.e., a logic in which propositions can be both true and false, and neither true nor false. Our approach is a significant departure from…
Algebras of relations form an algebraic framework for the study of logical systems, extending the correspondence between Boolean algebras and propositional logic. Tarski's representable cylindric algebras $RCA_{\alpha}$, and Halmos'…
This paper introduces a new theory which encompasses concepts and ideas from set theory, type theory, and Le\'{s}niewski's mereology and describes its possibility as an alternative foundation for mathematics. In the introduction section I…
In deriving their characterization of the perfect matchings polytope, Edmonds, Lov\'asz, and Pulleyblank introduced the so-called {\em Tight Cut Lemma} as the most challenging aspect of their work. The Tight Cut Lemma in fact claims {\em…
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…
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…
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…
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.