Related papers: Object-Oriented Theorem Proving (OOTP): First Thou…
Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…
Dependently-typed proof assistants furnish expressive foundations for mechanised mathematics and verified software. However, automation for these systems has been either modest in scope or complex in implementation. We aim to improve the…
Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe…
We propose some slight additions to O-O languages to implement the necessary features for using Deductive Object Programming (DOP). This way of programming based upon the manipulation of the Production Tree of the Objects of Interest,…
Neural symbolic processing aims to combine the generalization of logical learning approaches and the performance of neural networks. The Neural Theorem Proving (NTP) model by Rocktaschel et al (2017) learns embeddings for concepts and…
The broader goal of this research, on the one hand, is to obtain the State of the Art in Automated Test Production (ATP), to find the open questions and related problems and to track the progress of researchers in the field, and on the…
The TPTP World is the well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The TPTP World supports a range of classical logics, and since release v9.0.0 has…
We present a novel class of proof-of-position algorithms: Tree-Proof-of-Position (T-PoP). This algorithm is decentralised, collaborative and can be computed in a privacy preserving manner, such that agents do not need to reveal their…
Proving lemmas in synthetic geometry is often a time-consuming endeavour since many intermediate lemmas need to be proven before interesting results can be obtained. Improvements in automated theorem provers (ATP) in recent years now mean…
Auto-active verifiers provide a level of automation intermediate between fully automatic and interactive: users supply code with annotations as input while benefiting from a high level of automation in the back-end. This paper presents…
In some theory development tasks, a problem is satisfactorily solved once it is shown that a theorem (conjecture) is derivable from the background theory (premises). Depending on one's motivations, the details of the derivation of the…
Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly…
The evolution of programming languages from low-level assembly to high-level abstractions demonstrates a fundamental principle: by constraining how programmers express computation and enriching semantic information at the language level, we…
Theorem proving is fundamental to program verification, where the automated proof of Verification Conditions (VCs) remains a primary bottleneck. Real-world program verification frequently encounters hard VCs that existing Automated Theorem…
Object-oriented programming (OOP) is one of the most popular paradigms used for building software systems. However, despite its industrial and academic popularity, OOP is still missing a formal apparatus similar to \(\lambda\)-calculus,…
The main goal of concept-oriented programming (COP) is describing how objects are represented and accessed. It makes references (object locations) first-class elements of the program responsible for many important functions which are…
This work explores the application of deep learning, a machine learning technique that uses deep neural networks (DNN) in its core, to an automated theorem proving (ATP) problem. To this end, we construct a statistical model which…
This article is an attempt to combine different ways of working with sets of objects and their classes for designing and development of artificial intelligent systems (AIS) of analysis information, using object-oriented programming (OOP).…
Neural models combining representation learning and reasoning in an end-to-end trainable manner are receiving increasing interest. However, their use is severely limited by their computational complexity, which renders them unusable on real…
Non-classical logics are used in a wide spectrum of disciplines, including artificial intelligence, computer science, mathematics, and philosophy. The de-facto standard infrastructure for automated theorem proving, the TPTP World, currently…