Related papers: A Proof Tree Builder for Sequent Calculus and Hoar…

We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…

We introduce a Three Tier Tree Calculus (3TC) that defines in a systematic way three tiers of tree structures underlying proof search in logic programming. We use 3TC to define a new -- structural -- version of resolution for logic…

The synergy between deep learning models and traditional automation tools, such as built-in tactics of the proof assistant and off-the-shelf automated theorem provers, plays a crucial role in developing robust and efficient neural theorem…

We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…

We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction…

Programming in Prolog is hard for programmers that are used to procedural coding. In this manual the method of drawing search trees is introduced with the aim to get a better understanding of how Prolog works. After giving a first example…

In this work, we present the development of an automated extension tool to assist educators and increase the success and well-being of students by implementing flexible extension policies. Flexible extension policies materialize in many…

We propose to extend property-based testing to substructural logics to overcome the current lack of reasoning tools in the field. We take the first step by implementing a property-based testing system for specifications written in the…

Hoare logic is a foundation of axiomatic semantics of classical programs and it provides effective proof techniques for reasoning about correctness of classical programs. To offer similar techniques for quantum program verification and to…

With recent advancements in large language models, methods like chain-of-thought prompting to elicit reasoning chains have been shown to improve results on reasoning tasks. However, tasks that require multiple steps of reasoning still pose…

Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in…

I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a…

In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set…

We propose a novel method for automatic program synthesis. P-Tree Programming represents the program search space through a single probabilistic prototype tree. From this prototype tree we form program instances which we evaluate on a given…

Programs must be correct with respect to their application domain. Yet, the program specification and verification approaches so far only consider correctness in terms of computations. In this work, we present a two-tier Hoare Logic that…

We introduce proof nets for PiL, an extension of first-order multiplicative additive linear logic with new operators allowing a shallow encoding of processes in the {\pi}-calculus as formulas. We provide correctness criterion,…

Separation logics are a family of extensions of Hoare logic for reasoning about programs that mutate memory. These logics are "abstract" because they are independent of any particular concrete memory model. Their assertion languages, called…

Argumentative essay generation (AEG) aims to generate complete texts on specific controversial topics or debates. Although current AEG methods can generate individual opinions, they often overlook the high-level connections between these…

Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…

There are two kinds of systems that programming language researchers use for their work. Semantics engineering tools let them interactively explore their definitions, while proof assistants can be used to check the proofs of their…