Related papers: Object-Oriented Theorem Proving (OOTP): First Thou…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
OWLOOP is an Application Programming Interface (API) for using the Ontology Web Language (OWL) by the means of Object-Oriented Programming (OOP). It is common to design software architectures using the OOP paradigm for increasing their…
Currently, there is a lack of rigorous theoretical system for systematically generating non-trivial and logically valid theorems. Addressing this critical gap, this paper conducts research to propose a novel automated theorem generation…
We report on several scenarios of using automated theorem proving software in university education. In particular, we focus on using the Theorema system in a software-enhanced logic-course for students in computer science or artificial…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that…
Operational semantics has established itself as a flexible but rigorous means to describe the meaning of programming languages. Oftentimes, it is felt necessary to keep a semantics small, for example to facilitate its use for model checking…
The demand for synthetic data in mathematical reasoning has increased due to its potential to enhance the mathematical capabilities of large language models (LLMs). However, ensuring the validity of intermediate reasoning steps remains a…
A new theory of programming is proposed. The theory consists of OE (Operation Expression), SP (Semantic Predicate) and A (Axiom), abbreviated as OESPA. OE is for programming: its syntax is given by BNF formulas and its semantics is defined…
Context-oriented programming (COP) is a new technique for programming that allows changing the context in which commands execute as a program executes. Compared to object-oriented programming (aspect-oriented programming), COP is more…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
The Operational Transformation (OT) approach, used in many collaborative editors, allows a group of users to concurrently update replicas of a shared object and exchange their updates in any order. The basic idea of this approach is to…
Real-world processes often involve interdependent objects that also carry data values, such as integers, reals, or strings. However, existing process formalisms fall short to combine key modeling features, such as tracking object…
Online Analytical Processing (OLAP) comprises tools and algorithms that allow querying multidimensional databases. It is based on the multidimensional model, where data can be seen as a cube, where each cell contains one or more measures…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in…
A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by alternating between LLM generating proofs and…
Much mathematical writing exists that is, explicitly or implicitly, based on set theory, often Zermelo-Fraenkel set theory (ZF) or one of its variants. In ZF, the domain of discourse contains only sets, and hence every mathematical object…
Much of the current research and development in the field of automated reasoning builds on the infrastructure provided by the TPTP World. The TPTP language for logical formulae is central to the far-reaching adoption of the TPTP World. This…