Related papers: Generating Theorems by Generating Proof Structures
Free theorems are a popular tool in reasoning about parametrically polymorphic code. They are also of instructive use in teaching. Their derivation, though, can be tedious, as it involves unfolding a lot of definitions, then hoping to be…
Program synthesis is the task of constructing a program conforming to a given specification. We focus on deductive synthesis, and in particular on synthesis problems with specifications given as $\forall\exists$-formulas, expressing the…
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 novel document generation process based on hierarchical latent tree models (HLTMs) learned from data. An HLTM has a layer of observed word variables at the bottom and multiple layers of latent variables on top. For each…
Much like sentences are composed of words, words themselves are composed of smaller units. For example, the English word questionably can be analyzed as question+able+ly. However, this structural decomposition of the word does not directly…
Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…
Grammar-based sentence generation has been thoroughly explored for Context-Free Grammars (CFGs), but remains unsolved for recognition-based approaches such as Parsing Expression Grammars (PEGs). Lacking tool support, language designers…
This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…
We focus in this paper on generating models of quantified first-order formulas over built-in theories, which is paramount in software verification and bug finding. While standard methods are either geared toward proving the absence of…
Explanations shed light on a machine learning model's rationales and can aid in identifying deficiencies in its reasoning process. Explanation generation models are typically trained in a supervised way given human explanations. When such…
Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic. The clause selection heuristics in such systems are, however, often evaluating…
We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP). Unlike most learning based approaches, we focus on generalising from very little training data and…
This paper concerns the development of metatheory for extensible languages. It uses as its starting point a view that programming languages tailored to specific application domains are to be constructed by composing components from an open…
This paper from 2012 is the second in a series of three papers. All three papers deal with interpretability logics and related matters. In the first paper a construction method was exposed to obtain models of these logics. Using this…
This study presents a new approach to metaphorical paraphrase generation by masking literal tokens of literal sentences and unmasking them with metaphorical language models. Unlike similar studies, the proposed algorithm does not only focus…
Synthetic data is a standard component in training large language models, yet systematic comparisons across design dimensions, including rephrasing strategy, generator model, and source data, remain absent. We conduct extensive controlled…
We propose Composition Sampling, a simple but effective method to generate diverse outputs for conditional generation of higher quality compared to previous stochastic decoding strategies. It builds on recently proposed plan-based neural…
We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a…
Proofs of the fundamental theorem of algebra can be divided up into three groups according to the techniques involved: proofs that rely on real or complex analysis, algebraic proofs, and topological proofs. Algebraic proofs make use of the…
The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a…