Automated Theorem Proving (Automated Deduction)

Notes:

Automated theorem proving and automated deduction are closely related concepts in the field of computer science and artificial intelligence. Both involve the use of computers to automatically prove or verify mathematical or logical statements based on a set of rules or axioms.

Automated theorem proving is the process of using a computer program to automatically prove or verify the validity of a mathematical or logical statement based on a set of given axioms or rules. It is a branch of automated deduction that focuses specifically on proving theorems or other statements.

Automated deduction, on the other hand, is a broader concept that encompasses a range of techniques and methods for using computers to automatically reason about and solve problems in logic and mathematics. This includes the use of automated theorem proving, as well as other techniques such as model checking and satisfiability modulo theories (SMT) solvers.

Resources:

Conferences:

Wikipedia:

References:

  • Architectural Refinement in HETS (2012)
  • Reasoning in the OWL 2 full ontology language using first-order automated theorem proving (2011)
  • Coupling Ontology with Rule-Based Theorem Proving for Knowledge Representation and Reasoning (2010)
  • Logical Ontology Validation Using an Automatic Theorem Prover (2010)

See also:

Abduction & Dialog Systems | Automated Reasoning & Dialog Systems | Best Theorem Prover Videos | GATE & Dialog Systems | NLTK & Chatbots

Lakatos-style collaborative mathematics through dialectical, structured and abstract argumentation
A Pease, J Lawrence, K Budzynska, J Corneli… – Artificial Intelligence, 2017 – Elsevier
… We draw on two areas in which Automated Theorem Proving … and develop a formal dialogue system from Lakatos’s model of … from a formal dialogue system to Argument Interchange …

The QMLTP problem library for first-order modal logics
T Raths, J Otten – International Joint Conference on Automated …, 2012 – Springer
… The Quantified Modal Logic Theorem Proving (QMLTP) library provides a platform for testing and evaluating automated theorem proving (ATP) systems for first-order modal logics. The …

Optimising spoken dialogue systems using Gaussian process reinforcement learning for a large action set
TFW Nicholson, M Gaši? – mlmi.eng.cam.ac.uk
In dialogue management for statistical dialogue systems we seek to learn a policy that can select the optimal action for the system to perform. This dissertation looks at how by defining …

Students’ language in computer-assisted tutoring of mathematical proofs
MA Wolska – 2015 – publikationen.sulb.uni-saarland.de
… of tutorial dialogue systems. On the one … automated deduction system, however, the detailed task specification is dependent on the scenario and its requirements. Automated deduction …

Preliminary Research and Development on the Problem-Solving Humanoid Machine for K-12 Education
X Yu, D Yang, W Ding, W Gan – 2014 International Conference …, 2014 – ieeexplore.ieee.org
… -problem solver, automated theorem proving machine and Deep … The automated theorem proving machines are the … to Q&A intelligent interactive dialogue systems for commercial and …

Neurosymbolic Programming
S Chaudhuri, K Ellis, O Polozov, R Singh… – … and Trends® in …, 2021 – nowpublishers.com
… methods like heuristic search and automated deduction to construct inferences and plans. … Dialog Systems. Task-oriented dialog systems assist users with specific goals through a …

Granularity analysis for mathematical proofs
MRG Schiller – Topics in cognitive science, 2013 – Wiley Online Library
… built on existing automated theorem-proving systems and … to aid the design of the Dialog system and the development of … who helped simulate the dialog system were analyzing and …

Sinhala chatbot for train information
S Harshani – 2021 – dl.ucsc.cmb.ac.lk
… and automated theorem proving[10] … dialogue systems, including black box and glass box, comparative, quantitative, and qualitative evaluation. Four aspects of NLP dialogue system …

In Pursuit of Decidable’Logical Form’
M Minock – The Fifth Swedish Language Technology Conference …, 2014 – diva-portal.org
… While the work has been in the context of NLIs to databases, we are considering an extension of the work to dialogue systems. To achieve this it is necessary to allow for the …

Survey on frontiers of language and robotics
T Taniguchi, D Mochihashi, T Nagai, S Uchida… – Advanced …, 2019 – Taylor & Francis
… distributed representations: automated theorem proving and knowledge base embedding. … In addition, a dialogue system was also enabled to utilize sequential contextual information as …

Postmortem: MKULTRA, an experimental AI-based game
ID Horswill – Fourteenth Artificial Intelligence and Interactive Digital …, 2018 – aaai.org
Games are inherently situated within the cultures of their players. Players bring a wide range of knowledge and expectations to a game, and the more the game suggests connections to …

Logic-based artificial intelligence
J Minker – 2012 – books.google.com
… He has contributed to: automated deduction, nonmonotonic reasoning, diagnostic reasoning… representation, computational semantics, and dialogue systems. He was an Alexander von …

What is a logical system? An evolutionary view: 1964-2014.
DM Gabbay – Computational Logic, 2014 – books.google.com
… The relative importance of automated deduction is on the increase, in view of its wide applicability. New automated deduction methods have been developed for non-classical logics, …

Learning inference rules from data
C Sakama, K Inoue, T Ribeiro – KI-Künstliche Intelligenz, 2019 – Springer
… Such systems have been developed in the field of automated theorem proving or logic … To realize this, we assume a simple dialogue system that is able to converse with a human. …

Interactive Learning from Natural Language and Demonstrations using Signal Temporal Logic
S Mohammadinejad, J Thomason… – arXiv preprint arXiv …, 2022 – arxiv.org
Natural language is an intuitive way for humans to communicate tasks to a robot. While natural language (NL) is ambiguous, real world tasks and their safety requirements need to be …

SIGLOG monthly 205
D Petri?an – ACM SIGLOG News, 2020 – dl.acm.org
… dialogue systems, QA and information retrieval systems that use (natural) logic and … automata theory, automated deduction, categorical models and logics, concurrency and distributed …

Artificial Intelligence IV: Methodology, Systems, Applications
P Jorrand, V Sgurev – 2016 – books.google.com
… This book presents results in automated deduction, non-standard logics, commonsense … uni-k!. de Abstract: Automated deduction systems can considerably be improved by replacing …

Int: An inequality benchmark for evaluating generalization in theorem proving
Y Wu, AQ Jiang, J Ba, R Grosse – arXiv preprint arXiv:2007.02924, 2020 – arxiv.org
… , which provides theoretically infinite data and allows us to measure 6 different types of generalization, each reflecting a distinct challenge, characteristic of automated theorem proving. …

Law and logic: A review from an argumentation perspective
H Prakken, G Sartor – Artificial intelligence, 2015 – Elsevier
… At first sight, one might think that such testing and application boils down to the use of techniques for knowledge representation and automated deduction. Once a legal text and a body …

Faculty Members and Labs in Department of Computer Science
M Hagiya – iu-tokyo.ac.jp
… goal, we also need to study and advance many research topics in theoretical computer science, such as type theory, formal languages and automata, and automated theorem proving. It …

Integration of world knowledge for natural language understanding
E Ovchinnikova – 2012 – books.google.com
… example, question answering, information extraction, and dialog systems. In spite of the strong … Unfortunately, the experiments with Nutcracker showed that using automated deduction is …

A review of methodologies for natural-language-facilitated human–robot cooperation
R Liu, X Zhang – International Journal of Advanced Robotic …, 2019 – journals.sagepub.com
Natural-language-facilitated human–robot cooperation refers to using natural language to facilitate interactive information sharing and task executions with a common goal constraint …

Formalization of AMR Inference via Hybrid Logic Tableaux
ET Goldner – 2021 – search.proquest.com
… language data (for instance NLP and dialogue systems for health and mission critical tasks), … so general as to require automated theorem proving techniques for assessing a sentence …

Logic-Based Natural Language Processing Winter Semester 2019/20 Lecture Notes
M Kohlhase – 2020 – kwarc.info
This document contains the course notes for the course “Logic-Based Natural Language Processing”(Logik-Basierte Sprachverarbeitung) held at FAU Erlangen-Nürnberg in the Winter …

Contract No. FP7-ICT247914 Project full title MOLTO-Multilingual Online Translation Deliverable D2. 3 Grammar Tool Manual and Best Practices Distribution …
A Ranta, J Camilleri, G Détrez, R Enache, T Hallgren… – molto-project.eu
… In dialogue systems, dependent types are used to reduce overgeneration, in order to define more restrictive language models and thereby better speech recognition performance (…

Logic-Based Natural Language Processing Winter Semester 2017/18 Provisional Lecture Notes
M Kohlhase – 2018 – kwarc.info
This document contains the course notes for the course “Logic-Based Natural Language Processing”(Logik-Basierte Sprachverarbeitung) held at FAU Erlangen-NÃ?rnberg in the Winter …

Logic-Based Natural Language Processing Winter Semester 2018/19 Lecture Notes
M Kohlhase – 2019 – kwarc.info
This document contains the course notes for the course “Logic-Based Natural Language Processing”(Logik-Basierte Sprachverarbeitung) held at FAU Erlangen-Nürnberg in the Winter …

Representation of case law for argumentative reasoning
LM Al Abdulkarim – 2017 – search.proquest.com
… Dialogue systems were originally introduced into AI and Law as a way of modelling legal … oped using techniques of knowledge representation and automated deduction [93], but it is not. …

Investigating the limitations of transformers with simple arithmetic tasks
R Nogueira, Z Jiang, J Lin – arXiv preprint arXiv:2102.13019, 2021 – arxiv.org
The ability to perform arithmetic tasks is a remarkable trait of human intelligence and might form a critical component of more complex reasoning tasks. In this work, we investigate if the …

Lower bound resource requirements for machine intelligence
T Gilmanov – 2018 – search.proquest.com
… Dialogue systems or conversational agents have been a … Dialogue systems are directly related to the work described … More recent work was done using automated theorem proving …

Logic-based Approaches to the Semantics of Natural
M Kohlhase – kwarc.info
In this Section we will introduce the topic of this course and situate it in the larger field of natural language understanding. But before we do that, let us briefly step back and marvel at the …

Rigorous deductive argumentation for socially relevant issues
D Wehr – 2015 – search.proquest.com
… The idea to adopt an asymmetric dialog system (author vs critics) came from work on … of metatheorems and simpler programming of automated theorem proving tools (eg if one is …

DEDUCTIVE QUESTION-ANSWERING ON There are two important consequences of this decomposition of
R Reiter – Readings in Artificial Intelligence and Databases, 2014 – books.google.com
The principal concern of this paper is the design of a retrieval system which combines current techniques for query evaluation on relational data bases with a deductive component in …

Refinement of adaptivity by reflection
KP Jantke, HR Beick, Y Brovko… – … Conference on Signal …, 2013 – ieeexplore.ieee.org
… In formal terms, we are facing a problem of automated deduction (see [46] and [47] for a birds-eye perspective and [1] for a particularly reader-friendly introduction). For every relevant …

An artificial intelligence framework for investigative reasoning.
R Ramezani – 2014 – core.ac.uk
… We discussed automated deduction and resolution in §2.2 and §2.4. As resolution is complete, the researchers attempted to invert it in order to construct the inverse entailment operator. …

Artificial Intelligence: Research Directions in Cognitive Science: European Perspectives Vol. 5
D Sleeman, NO Bernsen – 2019 – books.google.com
… automated deduction is not a sharp one and there is always a mutual influence; new results in automated deduction … can improve the field of automated deduction. First Order Predicate …

Dynamic Generation of Interpretable Inference Rules in a Neuro-Symbolic Expert System
N Weir, B Van Durme – arXiv preprint arXiv:2209.07662, 2022 – arxiv.org
We present an approach for systematic reasoning that produces human interpretable proof trees grounded in a factbase. Our solution resembles the style of a classic Prolog-based …

A review on language models as knowledge bases
B AlKhamissi, M Li, A Celikyilmaz, M Diab… – arXiv preprint arXiv …, 2022 – arxiv.org
Recently, there has been a surge of interest in the NLP community on the use of pretrained Language Models (LMs) as Knowledge Bases (KBs). Researchers have shown that LMs …

Cybernetics and Systems’ 86: Proceedings of the Eighth European Meeting on Cybernetics and Systems Research, Organized by the Austrian Society for …
R Trappl – 2012 – books.google.com
This volume contains all papers presented at the Eighth European Meeting on Cybernetics and Systems Research. 169 draft papers were submitted for evaluation. In the process of …

KI 2012: Advances in Artificial Intelligence: 35th Annual German Conference on AI, Saarbrücken, Germany, September 24-27, 2012, Proceedings
B Glimm, A Krüger – 2012 – books.google.com
This book constitutes the refereed proceedings of the 35th Annual German Conference on Artificial Intelligence, KI 2012, held in Saarbrücken, Germany, in September 2012. The 19 …

Artificial Intelligence: What it Was, and What it Should Be?
HA Hameed – … Journal of Advanced Computer Science and …, 2020 – search.proquest.com
… [27] Yoshua Bengio, Chinnadhurai Sankar, Sandeep Subramanian, Chris Pal, SarathChandar, “do neural dialog systems use the conversation history effectively? an empirical study. …

Towards General Natural Language Understanding with Probabilistic Worldbuilding
A Saparov, TM Mitchell – Transactions of the Association for …, 2022 – direct.mit.edu
We introduce the Probabilistic Worldbuilding Model ( PWM ), a new fully symbolic Bayesian model of semantic parsing and reasoning, as a first step in a research program toward more …

KI 2012: Advances in Artificial Intelligence
BGA Krüger – Springer
The yearly German Conference on Artificial Intelligence is the premier forum for German research in artificial intelligence, and attracts numerous international guests, too. The KI …

Advances in Artificial Intelligence and Its Applications: 14th Mexican International Conference on Artificial Intelligence, MICAI 2015, Cuernavaca, Morelos …
OP Lagunas, OH Alcántara, GA Figueroa – 2015 – books.google.com
… Probabilistic Reasoning 8 4 50 % Logic Programming 7 5 71 % Intelligent Interfaces: Multimedia, Virtual Reality 5 2 40 % Intelligent Organizations 4 – – Automated Theorem Proving 3 2 …

Reasoning with transformer-based models: Deep learning, but shallow reasoning
C Helwe, C Clavel, FM Suchanek – 3rd Conference on Automated …, 2021 – openreview.net
… 2020] is a benchmark for automated theorem proving. The dataset evaluates the capabilities of a language model to generate a proof for a given statement. The dataset contains 3 …

Future Research.
RH Reussner, M Goedicke, W Hasselbring… – 2019 – library.oapen.org
The overall result of the priority program, as discussed in the previous chapter, shows that the SPP 1593 projects covered a wide range of aspects regarding evolution. However, the …

Advances in Artificial Intelligence and Soft Computing
G Sidorov, SN Galicia-Haro – 2015 – Springer
The Mexican International Conference on Artificial Intelligence (MICAI) is a yearly international conference series organized by the Mexican Society of Artificial Intelligence (SMIA) since …