In this third session of the Elements of AI Luxembourg series of webinars, our guest speaker Dr. Alexander Steen talks about Logic and Automated Reasoning. More information, and a recording of the session, can be found on our reddit page:
eofai.lu/reddit
In this sixth and last session of the Elements of AI Luxembourg series of webinars, our guest speaker Prof. Dov Gabbay talks about Logic and Artificial Intelligence. More information, and a recording of the session, can be found on our reddit page:
eofai.lu/reddit
From embodied Artificial Intelligence to Artificial LifeKrzysztof Pomorski
The methodological stages presented in embodied Artificial Intelligence are given. Systematically we broaden the concept AI so finally we can approach systems related to Artificial Life.
The Unreasonable Benefits of Deep Learningindico data
Dan Kuster led a talk at Sentiment Analysis Symposium discussing why businesses should consider adopting deep learning solutions. Key takeaways include simplicity, accuracy, flexibility, and some hacks for working with the tech.
About the Session:
Machine learning is becoming the tool of choice for analyzing text and image data. While traditional text processing solutions rely on the ability of experts to encode domain knowledge, machine learning models learn this directly from the data. Deep learning is a branch of machine learning that like the human brain quickly learns hierarchical representations of concepts, and it has been key to unlocking state-of-the-art results on a range of text and image classification tasks such as sentiment analysis and beyond.
In this session, we will show the impact of a deep learning based approach over NLP and traditional machine learning based methods for text analysis across key dimensions such as accuracy, flexibility, and the amount of required training data. Specifically, we will discuss how deep learning models are now setting the records for state-of-the-art accuracy in sentiment analysis. We will also demonstrate the flexibility of this approach by showing how the features learned by one model can be easily reused in different domains (e.g., handling additional languages, or predicting new categories) to drastically reduce the time to deployment. Finally, we will touch on the ability of this method to handle additional types of data beyond text, e.g, images, for maximum insight.
In this sixth and last session of the Elements of AI Luxembourg series of webinars, our guest speaker Prof. Dov Gabbay talks about Logic and Artificial Intelligence. More information, and a recording of the session, can be found on our reddit page:
eofai.lu/reddit
From embodied Artificial Intelligence to Artificial LifeKrzysztof Pomorski
The methodological stages presented in embodied Artificial Intelligence are given. Systematically we broaden the concept AI so finally we can approach systems related to Artificial Life.
The Unreasonable Benefits of Deep Learningindico data
Dan Kuster led a talk at Sentiment Analysis Symposium discussing why businesses should consider adopting deep learning solutions. Key takeaways include simplicity, accuracy, flexibility, and some hacks for working with the tech.
About the Session:
Machine learning is becoming the tool of choice for analyzing text and image data. While traditional text processing solutions rely on the ability of experts to encode domain knowledge, machine learning models learn this directly from the data. Deep learning is a branch of machine learning that like the human brain quickly learns hierarchical representations of concepts, and it has been key to unlocking state-of-the-art results on a range of text and image classification tasks such as sentiment analysis and beyond.
In this session, we will show the impact of a deep learning based approach over NLP and traditional machine learning based methods for text analysis across key dimensions such as accuracy, flexibility, and the amount of required training data. Specifically, we will discuss how deep learning models are now setting the records for state-of-the-art accuracy in sentiment analysis. We will also demonstrate the flexibility of this approach by showing how the features learned by one model can be easily reused in different domains (e.g., handling additional languages, or predicting new categories) to drastically reduce the time to deployment. Finally, we will touch on the ability of this method to handle additional types of data beyond text, e.g, images, for maximum insight.
Striving to Demystify Bayesian Computational ModellingMarco Wirthlin
Abstract
Bayesian approaches to computational modelling have experienced a slow, but steady gain in recognition and
usage in academia and industry alike, accompanying the growing availability of evermore powerful computing
platforms at shrinking costs. Why would one use such techniques? How are those models conceived and
implemented? Which is the recommended workflow? Why make life hard when there are P-values?
In his talk, Marco Wirthlin will first attempt an introduction to statistical notions supporting Bayesian computation and
explain the difference to the Frequentist framework. In the second half, an example of a recommended workflow is
outlined on a simple toy model, with simulated data. Live coding will be used as much as possible to illustrate
concepts on an implementational level in the R language. Ample literature and media references for self-learning
will be provided during the talk.
Context and Licence
This talk was performed in the context of the “R Lunch” on the 29 of October 2019 at the University of Geneva and
was organized by Elise Tancoigne (@tancoigne) & Xavier Adam (@xvrdm). Many thanks for inviting me! :D
Code (if any) is licenced under the BSD (3 clause), while the text licence is CC BY-NC 4.0. Any derived work has
been cited. Please contact me if you see non-attributed work (marco.wirthlin@gmail.com).
1.0 Introduction
1.1 Objectives
1.2 Some Simple Definition of A.I.
1.3 Definition by Eliane Rich
1.4 Definition by Buchanin and Shortliffe
1.5 Another Definition by Elaine Rich
1.6 Definition by Barr and Feigenbaum
1.7 Definition by Shalkoff
1.8 Summary
1.9 Further Readings/References
CSC375CSCM75Logic for Computer ScienceUlrich Berger.docxfaithxdunce63732
CSC375/CSCM75
Logic for Computer Science
Ulrich Berger
Department of Computer Science
Swansea University
Fall 2015
[email protected]
http://www.cs.swan.ac.uk/∼csulrich/
tel 513380, fax 295708, room 306, Faraday Tower
1 Introduction
The aim of this course is to give the student a working knowledge in logic and its
applications in Computer Science. Rather than trying to cover logic in its full breadth,
which, given the diversity and complexity of the subject, would be an impossible task
for a one-semester course, we will focus on the most fundamental concepts which
every computer scientists should be familiar with, be it as a practitioner in industry
or as a researcher at university. Although the selection of topics reflects to some
extent my personal view and taste of logic, I will aim at a balanced presentation that
also takes into account aspects of logic are not so close to my own research interests.
Throughout the course I will emphasize that logic is something one does : one models
a computing system, specifies a data type or a program, checks or proves that a
system satisfies a certain property. We will do a lot of exercises where these logical
activities will be trained, mostly on the blackboard or with pencil and paper, and
occasionally using the computer. The aim is to provide the student with active logic
skills to solve computing problems.
1
Abdullah
Highlight
Abdullah
Highlight
October 13, 2015 CSC375/CSCM75 Logic for Computer Science 2
Besides its practical applications we will also look into the historical development
of logic. What were the main philosophical and mathematical questions that led to
modern logic as we know it today? We will see that these questions and their answers
did shape not only logic, but also large parts of Computer Science.
The main prerequisites for this course are curiosity and a good appetite for solving
problems . No prior knowledge of logic is required. However, I take it for granted
that the student is able to digest formal definitions of syntactic entities such as terms
or formulas. For a Computer Science student, who is familiar with formal syntactic
objects such as computer programs, this will not be a problem at all.
“Logic for Computer Science” is a stand-alone course, but it is also intended to sup-
port other Computer Science modules offered, in particular the modules on Embedded
Systems, High Integrity Systems, Software Testing, Big Data and Machine Learning,
and Modeling and Verification Techniques. Our course does not follow a particular
textbook, but it will use material from several books and lectures on logic. Some of
the main sources are:
[1] D van Dalen, Logic and Structure, 3rd edition, Springer, 1994.
[2] J H Gallier, Logic for Computer Science, John Wiley & Sons, 1987.
[3] Handbook of Logic in Computer Science, Vol. 1-6, S Abramsky, D M
Gabbay, T S E Maibaum, eds, OUP, 1994.
[4] J R Shoenfield, Mathematical Logic, Addison-Wesley, 1967.
[5] D B Plummer, J Barw.
What is Computer Science?
Computer Science and the Liberal Arts
The Apollo Guidance Computer
Recursive Definitions and hippopotomonstrosesquipedaliophobia
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Striving to Demystify Bayesian Computational ModellingMarco Wirthlin
Abstract
Bayesian approaches to computational modelling have experienced a slow, but steady gain in recognition and
usage in academia and industry alike, accompanying the growing availability of evermore powerful computing
platforms at shrinking costs. Why would one use such techniques? How are those models conceived and
implemented? Which is the recommended workflow? Why make life hard when there are P-values?
In his talk, Marco Wirthlin will first attempt an introduction to statistical notions supporting Bayesian computation and
explain the difference to the Frequentist framework. In the second half, an example of a recommended workflow is
outlined on a simple toy model, with simulated data. Live coding will be used as much as possible to illustrate
concepts on an implementational level in the R language. Ample literature and media references for self-learning
will be provided during the talk.
Context and Licence
This talk was performed in the context of the “R Lunch” on the 29 of October 2019 at the University of Geneva and
was organized by Elise Tancoigne (@tancoigne) & Xavier Adam (@xvrdm). Many thanks for inviting me! :D
Code (if any) is licenced under the BSD (3 clause), while the text licence is CC BY-NC 4.0. Any derived work has
been cited. Please contact me if you see non-attributed work (marco.wirthlin@gmail.com).
1.0 Introduction
1.1 Objectives
1.2 Some Simple Definition of A.I.
1.3 Definition by Eliane Rich
1.4 Definition by Buchanin and Shortliffe
1.5 Another Definition by Elaine Rich
1.6 Definition by Barr and Feigenbaum
1.7 Definition by Shalkoff
1.8 Summary
1.9 Further Readings/References
CSC375CSCM75Logic for Computer ScienceUlrich Berger.docxfaithxdunce63732
CSC375/CSCM75
Logic for Computer Science
Ulrich Berger
Department of Computer Science
Swansea University
Fall 2015
[email protected]
http://www.cs.swan.ac.uk/∼csulrich/
tel 513380, fax 295708, room 306, Faraday Tower
1 Introduction
The aim of this course is to give the student a working knowledge in logic and its
applications in Computer Science. Rather than trying to cover logic in its full breadth,
which, given the diversity and complexity of the subject, would be an impossible task
for a one-semester course, we will focus on the most fundamental concepts which
every computer scientists should be familiar with, be it as a practitioner in industry
or as a researcher at university. Although the selection of topics reflects to some
extent my personal view and taste of logic, I will aim at a balanced presentation that
also takes into account aspects of logic are not so close to my own research interests.
Throughout the course I will emphasize that logic is something one does : one models
a computing system, specifies a data type or a program, checks or proves that a
system satisfies a certain property. We will do a lot of exercises where these logical
activities will be trained, mostly on the blackboard or with pencil and paper, and
occasionally using the computer. The aim is to provide the student with active logic
skills to solve computing problems.
1
Abdullah
Highlight
Abdullah
Highlight
October 13, 2015 CSC375/CSCM75 Logic for Computer Science 2
Besides its practical applications we will also look into the historical development
of logic. What were the main philosophical and mathematical questions that led to
modern logic as we know it today? We will see that these questions and their answers
did shape not only logic, but also large parts of Computer Science.
The main prerequisites for this course are curiosity and a good appetite for solving
problems . No prior knowledge of logic is required. However, I take it for granted
that the student is able to digest formal definitions of syntactic entities such as terms
or formulas. For a Computer Science student, who is familiar with formal syntactic
objects such as computer programs, this will not be a problem at all.
“Logic for Computer Science” is a stand-alone course, but it is also intended to sup-
port other Computer Science modules offered, in particular the modules on Embedded
Systems, High Integrity Systems, Software Testing, Big Data and Machine Learning,
and Modeling and Verification Techniques. Our course does not follow a particular
textbook, but it will use material from several books and lectures on logic. Some of
the main sources are:
[1] D van Dalen, Logic and Structure, 3rd edition, Springer, 1994.
[2] J H Gallier, Logic for Computer Science, John Wiley & Sons, 1987.
[3] Handbook of Logic in Computer Science, Vol. 1-6, S Abramsky, D M
Gabbay, T S E Maibaum, eds, OUP, 1994.
[4] J R Shoenfield, Mathematical Logic, Addison-Wesley, 1967.
[5] D B Plummer, J Barw.
What is Computer Science?
Computer Science and the Liberal Arts
The Apollo Guidance Computer
Recursive Definitions and hippopotomonstrosesquipedaliophobia
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Unit 8 - Information and Communication Technology (Paper I).pdf
Elements of AI Luxembourg - session 3
1. Logic and Automated Reasoning
Or: Machine languages for everything?
Alexander Steen
University of Luxembourg
Elements of AI, Webinar III, 2021
2. C.
B.
Francke,
Herzog
Anton
Ulrich-Museum
”If we had it [a characteristica unversalis],
we should be able to reason in metaphysics
and morals in much the same way as in
geometry and analysis.”
— G.W. Leibniz, 1677
(translated by Russell, 1900)
3. C.
B.
Francke,
Herzog
Anton
Ulrich-Museum
”If we had it [a characteristica universalis],
we should be able to reason in metaphysics
and morals in much the same way as in
geometry and analysis.”
— G.W. Leibniz, 1677
(translated by Russell, 1900)
4. Leibniz’ Vision
”[...] quando orientur controversiae, non magis disputatione opus erit inter duos philosophus, quam inter duos
computistas. Sufficiet enim calamos in manus sumere sedereque ad abacos, et sibi mutuo [...] dicere: calcule-
mus”
— G.W. Leibniz, 1684
”[...] if controversies were to arise, there would be no more need of disputation between two
philosophers than between two calculators. For it would suffice for them to take their pencils in
their hands and to sit down at the abacus, and to say to each other [...]: Let us calculate.”
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 3
5. Leibniz’ Vision
”[...] quando orientur controversiae, non magis disputatione opus erit inter duos philosophus, quam inter duos
computistas. Sufficiet enim calamos in manus sumere sedereque ad abacos, et sibi mutuo [...] dicere: calcule-
mus”
— G.W. Leibniz, 1684
”[...] if controversies were to arise, there would be no more need of disputation between two
philosophers than between two calculators. For it would suffice for them to take their pencils in
their hands and to sit down at the abacus, and to say to each other [...]: Let us calculate.”
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 3
6. Leibniz’ Vision
”[...] quando orientur controversiae, non magis disputatione opus erit inter duos philosophus, quam inter duos
computistas. Sufficiet enim calamos in manus sumere sedereque ad abacos, et sibi mutuo [...] dicere: calcule-
mus”
— G.W. Leibniz, 1684
”[...] if controversies were to arise, there would be no more need of disputation between two
philosophers than between two calculators. For it would suffice for them to take their pencils in
their hands and to sit down at the abacus, and to say to each other [...]: Let us calculate.”
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 3
7. Leibniz’ Vision (2)
The ultimate goal
”[...] it would suffice [...] to say [...]: Let us calculate”
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 4
8. Leibniz’ Vision (2)
The ultimate goal
”[...] it would suffice [...] to say [...]: Let us calculate”
Dispute
Â
National
Gallery
of
Victoria,
Melbourne/Felton
Bequest,
via
NGV
Formalization
Â
Calculation
Â
Result
Â
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 4
9. Leibniz’ Vision (2)
The ultimate goal
”[...] it would suffice [...] to say [...]: Let us calculate”
Dispute
Â
National
Gallery
of
Victoria,
Melbourne/Felton
Bequest,
via
NGV
Formalization
Â
Calculation
Â
Result
Â
↑
Characteristica universalis
↑
Calculus ratiocinator
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 4
10. Leibniz’ Vision (2)
The ultimate goal
”[...] it would suffice [...] to say [...]: Let us calculate”
Dispute
Â
National
Gallery
of
Victoria,
Melbourne/Felton
Bequest,
via
NGV
Formalization
Â
Calculation
Â
Result
Â
↑
Characteristica universalis
↑
Calculus ratiocinator
≈ Logic ≈ (Automated) Reasoning
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 4
11. Leibniz’ Vision (2)
The ultimate goal
”[...] it would suffice [...] to say [...]: Let us calculate”
Dispute
Â
National
Gallery
of
Victoria,
Melbourne/Felton
Bequest,
via
NGV
Formalization
Â
Calculation
Â
Result
Â
↑
Characteristica universalis
↑
Calculus ratiocinator
≈ Logic (?) ≈ (Automated) Reasoning (?)
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 4
12. AI and Logic
What does this has to do with AI?
Automated Reasoning is a core subfield of Artificial Intelligence
also: ”good old-fashioned AI (GOFAI)”
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 5
13. AI and Logic
What does this has to do with AI?
A ”dispute” can be anything:
É Internal decision processes of banks for loans Is this person eligible for a loan?
É Emergency actions of autonomous vehicles Which action should be taken?
É Facial recognition Does this picture show person X?
É Planning Which route is the fastest/shortest?
É ... and much more ...
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 5
14. AI and Logic
What does this has to do with AI?
A ”dispute” can be anything:
É Internal decision processes of banks for loans Is this person eligible for a loan?
É Emergency actions of autonomous vehicles Which action should be taken?
É Facial recognition Does this picture show person X?
É Planning Which route is the fastest/shortest?
É ... and much more ...
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 5
15. Formal Logic and Reasoning
What is a Logic?
(1) A language
Composed by number of building blocks:
É not A (¬A)
É A and B (A ∧ B)
É A or B (A ∨ B)
É if A then B (A → B)
É ... many more possible
(2) Collection of reasoning patterns
Recipes for processing information
(rules for argumentation):
É If A → B holds and A holds
then B follows (modus ponens)
É If A ∨ B holds and ¬A holds
then B follows (modus tollens)
É ...
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 6
16. Formal Logic and Reasoning
What is a Logic?
(1) A language
Composed by number of building blocks:
É not A (¬A)
É A and B (A ∧ B)
É A or B (A ∨ B)
É if A then B (A → B)
É ... many more possible
(2) Collection of reasoning patterns
Recipes for processing information
(rules for argumentation):
É If A → B holds and A holds
then B follows (modus ponens)
É If A ∨ B holds and ¬A holds
then B follows (modus tollens)
É ...
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 6
17. Formal Logic and Reasoning
What is a Logic?
(1) A language
Composed by number of building blocks:
É not A (¬A)
É A and B (A ∧ B)
É A or B (A ∨ B)
É if A then B (A → B)
É ... many more possible
(2) Collection of reasoning patterns
Recipes for processing information
(rules for argumentation):
É If A → B holds and A holds
then B follows (modus ponens)
É If A ∨ B holds and ¬A holds
then B follows (modus tollens)
É ...
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 6
18. Formal Logic and Reasoning
What is a Logic?
(1) A language
Composed by number of building blocks:
É not A (¬A)
É A and B (A ∧ B)
É A or B (A ∨ B)
É if A then B (A → B)
É ... many more possible
(2) Collection of reasoning patterns
Recipes for processing information
(rules for argumentation):
É If A → B holds and A holds
then B follows (modus ponens)
É If A ∨ B holds and ¬A holds
then B follows (modus tollens)
É ...
Important property: Unambiguous
Consider the sentence ”Time flies like an arrow”
What do we mean?
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 6
19. Formal Logic and Reasoning
What is a Logic?
(1) A language
Composed by number of building blocks:
É not A (¬A)
É A and B (A ∧ B)
É A or B (A ∨ B)
É if A then B (A → B)
É ... many more possible
(2) Collection of reasoning patterns
Recipes for processing information
(rules for argumentation):
É If A → B holds and A holds
then B follows (modus ponens)
É If A ∨ B holds and ¬A holds
then B follows (modus tollens)
É ...
Important property: Unambiguous
Consider the sentence ”Time flies like an arrow”
What do we mean? (1) There is species of flies, called time flies, that like a specific arrow
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 6
20. Formal Logic and Reasoning
What is a Logic?
(1) A language
Composed by number of building blocks:
É not A (¬A)
É A and B (A ∧ B)
É A or B (A ∨ B)
É if A then B (A → B)
É ... many more possible
(2) Collection of reasoning patterns
Recipes for processing information
(rules for argumentation):
É If A → B holds and A holds
then B follows (modus ponens)
É If A ∨ B holds and ¬A holds
then B follows (modus tollens)
É ...
Important property: Unambiguous
Consider the sentence ”Time flies like an arrow”
What do we mean? (2) Time (considered as an ”object”) flies through space like an arrow
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 6
21. Formal Logic and Reasoning
What is a Logic?
(1) A language
Composed by number of building blocks:
É not A (¬A)
É A and B (A ∧ B)
É A or B (A ∨ B)
É if A then B (A → B)
É ... many more possible
(2) Collection of reasoning patterns
Recipes for processing information
(rules for argumentation):
É If A → B holds and A holds
then B follows (modus ponens)
É If A ∨ B holds and ¬A holds
then B follows (modus tollens)
É ...
Important property: Unambiguous
Consider the sentence ”Time flies like an arrow”
What do we mean? (3) Time passes quite quickly
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 6
22. Formal Logic and Reasoning
What is a Logic?
(1) A language
Composed by number of building blocks:
É not A (¬A)
É A and B (A ∧ B)
É A or B (A ∨ B)
É if A then B (A → B)
É ... many more possible
(2) Collection of reasoning patterns
Recipes for processing information
(rules for argumentation):
É If A → B holds and A holds
then B follows (modus ponens)
É If A ∨ B holds and ¬A holds
then B follows (modus tollens)
É ...
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 6
23. Formal Logic and Reasoning
What is a Logic?
(1) A language
Composed by number of building blocks:
É not A (¬A)
É A and B (A ∧ B)
É A or B (A ∨ B)
É if A then B (A → B)
É ... many more possible
(2) Collection of reasoning patterns
Recipes for processing information
(rules for argumentation):
É If A → B holds and A holds
then B follows (modus ponens)
É If A ∨ B holds and ¬A holds
then B follows (modus tollens)
É ...
Example:
1. It’s daytime or it’s nighttime (day ∨ night)
2. If the sun is shining, it is not nighttime (sun → ¬night)
3. The sun is shining (sun)
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 6
24. Formal Logic and Reasoning
What is a Logic?
(1) A language
Composed by number of building blocks:
É not A (¬A)
É A and B (A ∧ B)
É A or B (A ∨ B)
É if A then B (A → B)
É ... many more possible
(2) Collection of reasoning patterns
Recipes for processing information
(rules for argumentation):
É If A → B holds and A holds
then B follows (modus ponens)
É If A ∨ B holds and ¬A holds
then B follows (modus tollens)
É ...
Example:
1. It’s daytime or it’s nighttime (day ∨ night)
2. If the sun is shining, it is not nighttime (sun → ¬night)
3. The sun is shining (sun)
It follows: It’s daytime
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 6
25. Logical Reasoning in AI
Reasoning: How is this useful in AI?
Deduction
From
A → B
and
A
to
B
Given: Rules, Situation
Search: Conclusions
⇒ Decide on actions
Induction
From
A
and
B
to
A → B
Given: Situation, Conclusions
Search: Rules
⇒ Learn principles
Abduction
From
A → B
and
B
to
A
Given: Rules, Conclusions
Search: Situation
⇒ Explain actions
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 7
26. Logical Reasoning in AI
Reasoning: How is this useful in AI?
Deduction
From
A → B
and
A
to
B
Given: Rules, Situation
Search: Conclusions
⇒ Decide on actions
Induction
From
A
and
B
to
A → B
Given: Situation, Conclusions
Search: Rules
⇒ Learn principles
Abduction
From
A → B
and
B
to
A
Given: Rules, Conclusions
Search: Situation
⇒ Explain actions
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 7
27. Logical Reasoning in AI
Reasoning: How is this useful in AI?
Deduction
From
A → B
and
A
to
B
Given: Rules, Situation
Search: Conclusions
⇒ Decide on actions
Induction
From
A
and
B
to
A → B
Given: Situation, Conclusions
Search: Rules
⇒ Learn principles
Abduction
From
A → B
and
B
to
A
Given: Rules, Conclusions
Search: Situation
⇒ Explain actions
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 7
28. Logical Reasoning in AI
Reasoning: How is this useful in AI?
Deduction
From
A → B
and
A
to
B
Given: Rules, Situation
Search: Conclusions
⇒ Decide on actions
Induction
From
A
and
B
to
A → B
Given: Situation, Conclusions
Search: Rules
⇒ Learn principles
Abduction
From
A → B
and
B
to
A
Given: Rules, Conclusions
Search: Situation
⇒ Explain actions
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 7
29. Logical Reasoning in AI
Reasoning: How is this useful in AI?
Deduction
From
A → B
and
A
to
B
Given: Rules, Situation
Search: Conclusions
⇒ Decide on actions
Induction
From
A
and
B
to
A → B
Given: Situation, Conclusions
Search: Rules
⇒ Learn principles
Abduction
From
A → B
and
B
to
A
Given: Rules, Conclusions
Search: Situation
⇒ Explain actions
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 7
30. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
31. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
32. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
É Example 1: A bag of coins, pick some:
É First pick: A penny
É Second pick: ... penny
É Third pick: ... penny
É
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
33. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
É Example 1: A bag of coins, pick some:
É First pick: A penny
É Second pick: ... penny
É Third pick: ... penny
É
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
34. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
É Example 1: A bag of coins, pick some:
É First pick: A penny
É Second pick: ... penny
É Third pick: ... penny
É
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
35. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
É Example 1: A bag of coins, pick some:
É First pick: A penny
É Second pick: ... penny
É Third pick: ... penny
É
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
36. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
É Example 1: A bag of coins, pick some:
É First pick: A penny
É Second pick: ... penny
É Third pick: ... penny
É Therefore, every coin is a penny (prediction)
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
37. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
É Example 1: A bag of coins, pick some:
É First pick: A penny
É Second pick: ... penny
É Third pick: ... penny
É Therefore, every coin is a penny (prediction)
Shortcoming: Sample set may be too small
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
38. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
É Example 2: Considering ancestry:
É My grandfather is bald
É Jeremie’s grandfather is bald
É
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
39. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
É Example 2: Considering ancestry:
É My grandfather is bald
É Jeremie’s grandfather is bald
É
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
40. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
É Example 2: Considering ancestry:
É My grandfather is bald
É Jeremie’s grandfather is bald
É
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
41. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
É Example 2: Considering ancestry:
É My grandfather is bald
É Jeremie’s grandfather is bald
É Therefore, all grandfathers are bald
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
42. Automated Deduction: Introduction
Automated Deduction: What is it not?
É Autom. Deduction is not machine learning (ML) as such
É Usually associated un-/supervised (deep) learning, neural
networks, ...
Key difference: ML is related to inductive reasoning
É Arguing using empirical evidence
É Observations do not necessarily imply actual causality
É Example 2: Considering ancestry:
É My grandfather is bald
É Jeremie’s grandfather is bald
É Therefore, all grandfathers are bald
Shortcoming: Learning set may be biased
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 8
43. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
44. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
45. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
É Example 1:
É If X is human, then X is mortal.
É Socrates is human
É
Sting/Wikimedia
Commons,
CC
BY-SA
2.5
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
46. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
É Example 1:
É If X is human, then X is mortal.
É Socrates is human
É
Sting/Wikimedia
Commons,
CC
BY-SA
2.5
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
47. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
É Example 1:
É If X is human, then X is mortal.
É Socrates is human
É
Sting/Wikimedia
Commons,
CC
BY-SA
2.5
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
48. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
É Example 1:
É If X is human, then X is mortal.
É Socrates is human
É Question: Therefore, Socrates is mortal?
Sting/Wikimedia
Commons,
CC
BY-SA
2.5
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
49. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
É Example 1:
É If X is human, then X is mortal.
É Socrates is human
É Question: Therefore, Socrates is mortal?
AR can derive this conclusion; it is implicitly contained in the
rules already
Sting/Wikimedia
Commons,
CC
BY-SA
2.5
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
50. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
É Example 2:
É If X is human, then X is mortal.
É Socrates is human
É
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
51. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
É Example 2:
É If X is human, then X is mortal.
É Socrates is human
É
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
52. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
É Example 2:
É If X is human, then X is mortal.
É Socrates is human
É
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
53. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
É Example 2:
É If X is human, then X is mortal.
É Socrates is human
É Question: Therefore, Plato is mortal?
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
54. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
É Example 2:
É If X is human, then X is mortal.
É Socrates is human
É Question: Therefore, Plato is mortal?
Not necessarily.
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
55. Automated Deduction: Introduction (2)
Automated Deduction: What is it then?
É Could also call it ”information discovery”
É Of course, this is also a form of learning
Key difference to ML: It represents deductive reasoning
É Arguing using logical inferences
É Deductive conclusions are sound and reliable
Advantages: No false negatives, no false positives, explainable.
Disadvantages: Translation of domain knowledge is expensive
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 9
56. Automated Reasoning
How does automated reasoning work?
1. Translate problem to logic
É Rules: Knowledge about the world (axioms)
É Goal: What is to be to solved (conjecture)
2. Run reasoner for obtaining a solution
É Certificate: Describes the solution (proof)
— or —
É Counter example: Explanation why there
is no solution (model)
3. Translate solution to world
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 10
57. Automated Reasoning
How does automated reasoning work?
1. Translate problem to logic
É Rules: Knowledge about the world (axioms)
É Goal: What is to be to solved (conjecture)
2. Run reasoner for obtaining a solution
É Certificate: Describes the solution (proof)
— or —
É Counter example: Explanation why there
is no solution (model)
3. Translate solution to world
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 10
58. Automated Reasoning
How does automated reasoning work?
1. Translate problem to logic
É Rules: Knowledge about the world (axioms)
É Goal: What is to be to solved (conjecture)
2. Run reasoner for obtaining a solution
É Certificate: Describes the solution (proof)
— or —
É Counter example: Explanation why there
is no solution (model)
3. Translate solution to world
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 10
59. Automated Deduction
How does automated deduction work?
É Usage of formal inference rules
É Iterative deduction of facts
É Formalization acts as assumptions
É A derivation of a goal forms a
mathematical proof
É Proofs can be verified externally
É Act as explicit justification
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 11
60. Automated Deduction
How does automated deduction work?
É Usage of formal inference rules
É Iterative deduction of facts
É Formalization acts as assumptions
É A derivation of a goal forms a
mathematical proof
É Proofs can be verified externally
É Act as explicit justification
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 11
61. Automated Reasoning: Systems
State of the art system output
É System output may be (very) large
É often unreadable, machine-oriented
Small sample proof:
(TPTP THF format, widely accepted standard format for proofs)
thf(6,axiom,((! [A:(nat > $o)]: (((A @ zero) & ! [B:nat]: ((A @ B) => (A
thf(18,plain,((! [A:(nat > $o)]: (((A @ zero) & ! [B:nat]: ((A @ B) => (
thf(24,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (A @ (sk2 @ (A)
thf(1,axiom,((? [A:nat]: ~ (p @ A))),file(’oded_2.p’,8)).
thf(7,plain,((? [A:nat]: ~ (p @ A))),inference(defexp_and_simp_and_etaex
thf(8,plain,((~ (! [A:nat]: (p @ A)))),inference(miniscope,[status(thm)]
thf(9,plain,((~ (p @ sk1))),inference(cnf,[status(esa)],[8])).
thf(506,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (A @ (sk2 @ (A
thf(660,plain,((~ (p @ zero)) | (p @ (sk2 @ (p)))),inference(pre_uni,[st
thf(5,axiom,((p @ zero)),file(’oded_2.p’,4)).
thf(17,plain,((p @ zero)),inference(defexp_and_simp_and_etaexpand,[statu
thf(716,plain,(~ ($true) | (p @ (sk2 @ (p)))),inference(rewrite,[status(
thf(717,plain,((p @ (sk2 @ (p)))),inference(simp,[status(thm)],[716])).
thf(3,axiom,((! [A:nat]: ((p @ (succ @ A)) = ((p @ A) & (q @ A))))),file
thf(13,plain,((! [A:nat]: ((p @ (succ @ A)) = ((p @ A) & (q @ A))))),inf
thf(14,plain,(! [A:nat] : (((p @ (succ @ A)) = ((p @ A) & (q @ A))))),in
thf(15,plain,(! [A:nat] : ((((p @ A) & (q @ A)) = (p @ (succ @ A))))),in
thf(844,plain,(! [A:nat] : (((q @ A) = (p @ (succ @ A))) | ((p @ (sk2 @
thf(845,plain,(((q @ (sk2 @ (p))) = (p @ (succ @ (sk2 @ (p)))))),inferen
thf(23,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (~ (A @ (succ @
thf(33,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (~ (A @ (succ @
thf(69,plain,((~ (p @ zero)) | (~ (p @ (succ @ (sk2 @ (p)))))),inference
thf(90,plain,(~ ($true) | (~ (p @ (succ @ (sk2 @ (p)))))),inference(rewr
thf(91,plain,((~ (p @ (succ @ (sk2 @ (p)))))),inference(simp,[status(thm
thf(861,plain,((~ (q @ (sk2 @ (p))))),inference(rewrite,[status(thm)],[8
thf(869,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (A @ (sk2 @ (A
thf(882,plain,((~ (q @ zero)) | (q @ (sk2 @ (q)))),inference(pre_uni,[st
thf(4,axiom,((q @ zero)),file(’oded_2.p’,5)).
thf(16,plain,((q @ zero)),inference(defexp_and_simp_and_etaexpand,[statu
thf(901,plain,(~ ($true) | (q @ (sk2 @ (q)))),inference(rewrite,[status(
thf(902,plain,((q @ (sk2 @ (q)))),inference(simp,[status(thm)],[901])).
thf(2,axiom,((! [A:nat]: ((q @ (succ @ A)) = ((q @ A) | (r @ A))))),file
thf(10,plain,((! [A:nat]: ((q @ (succ @ A)) = ((q @ A) | (r @ A))))),inf
thf(11,plain,(! [A:nat] : (((q @ (succ @ A)) = ((q @ A) | (r @ A))))),in
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 12
62. Automated Reasoning: Systems
State of the art system output
É System output may be (very) large
É often unreadable, machine-oriented
Small sample proof:
(TPTP THF format, widely accepted standard format for proofs)
thf(6,axiom,((! [A:(nat > $o)]: (((A @ zero) & ! [B:nat]: ((A @ B) => (A
thf(18,plain,((! [A:(nat > $o)]: (((A @ zero) & ! [B:nat]: ((A @ B) => (
thf(24,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (A @ (sk2 @ (A)
thf(1,axiom,((? [A:nat]: ~ (p @ A))),file(’oded_2.p’,8)).
thf(7,plain,((? [A:nat]: ~ (p @ A))),inference(defexp_and_simp_and_etaex
thf(8,plain,((~ (! [A:nat]: (p @ A)))),inference(miniscope,[status(thm)]
thf(9,plain,((~ (p @ sk1))),inference(cnf,[status(esa)],[8])).
thf(506,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (A @ (sk2 @ (A
thf(660,plain,((~ (p @ zero)) | (p @ (sk2 @ (p)))),inference(pre_uni,[st
thf(5,axiom,((p @ zero)),file(’oded_2.p’,4)).
thf(17,plain,((p @ zero)),inference(defexp_and_simp_and_etaexpand,[statu
thf(716,plain,(~ ($true) | (p @ (sk2 @ (p)))),inference(rewrite,[status(
thf(717,plain,((p @ (sk2 @ (p)))),inference(simp,[status(thm)],[716])).
thf(3,axiom,((! [A:nat]: ((p @ (succ @ A)) = ((p @ A) & (q @ A))))),file
thf(13,plain,((! [A:nat]: ((p @ (succ @ A)) = ((p @ A) & (q @ A))))),inf
thf(14,plain,(! [A:nat] : (((p @ (succ @ A)) = ((p @ A) & (q @ A))))),in
thf(15,plain,(! [A:nat] : ((((p @ A) & (q @ A)) = (p @ (succ @ A))))),in
thf(844,plain,(! [A:nat] : (((q @ A) = (p @ (succ @ A))) | ((p @ (sk2 @
thf(845,plain,(((q @ (sk2 @ (p))) = (p @ (succ @ (sk2 @ (p)))))),inferen
thf(23,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (~ (A @ (succ @
thf(33,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (~ (A @ (succ @
thf(69,plain,((~ (p @ zero)) | (~ (p @ (succ @ (sk2 @ (p)))))),inference
thf(90,plain,(~ ($true) | (~ (p @ (succ @ (sk2 @ (p)))))),inference(rewr
thf(91,plain,((~ (p @ (succ @ (sk2 @ (p)))))),inference(simp,[status(thm
thf(861,plain,((~ (q @ (sk2 @ (p))))),inference(rewrite,[status(thm)],[8
thf(869,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (A @ (sk2 @ (A
thf(882,plain,((~ (q @ zero)) | (q @ (sk2 @ (q)))),inference(pre_uni,[st
thf(4,axiom,((q @ zero)),file(’oded_2.p’,5)).
thf(16,plain,((q @ zero)),inference(defexp_and_simp_and_etaexpand,[statu
thf(901,plain,(~ ($true) | (q @ (sk2 @ (q)))),inference(rewrite,[status(
thf(902,plain,((q @ (sk2 @ (q)))),inference(simp,[status(thm)],[901])).
thf(2,axiom,((! [A:nat]: ((q @ (succ @ A)) = ((q @ A) | (r @ A))))),file
thf(10,plain,((! [A:nat]: ((q @ (succ @ A)) = ((q @ A) | (r @ A))))),inf
thf(11,plain,(! [A:nat] : (((q @ (succ @ A)) = ((q @ A) | (r @ A))))),in
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 12
63. Automated Reasoning: Systems
State of the art system output
É System output may be (very) large
É often unreadable, machine-oriented
Small sample proof:
(TPTP THF format, widely accepted standard format for proofs)
thf(6,axiom,((! [A:(nat > $o)]: (((A @ zero) & ! [B:nat]: ((A @ B) => (A
thf(18,plain,((! [A:(nat > $o)]: (((A @ zero) & ! [B:nat]: ((A @ B) => (
thf(24,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (A @ (sk2 @ (A)
thf(1,axiom,((? [A:nat]: ~ (p @ A))),file(’oded_2.p’,8)).
thf(7,plain,((? [A:nat]: ~ (p @ A))),inference(defexp_and_simp_and_etaex
thf(8,plain,((~ (! [A:nat]: (p @ A)))),inference(miniscope,[status(thm)]
thf(9,plain,((~ (p @ sk1))),inference(cnf,[status(esa)],[8])).
thf(506,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (A @ (sk2 @ (A
thf(660,plain,((~ (p @ zero)) | (p @ (sk2 @ (p)))),inference(pre_uni,[st
thf(5,axiom,((p @ zero)),file(’oded_2.p’,4)).
thf(17,plain,((p @ zero)),inference(defexp_and_simp_and_etaexpand,[statu
thf(716,plain,(~ ($true) | (p @ (sk2 @ (p)))),inference(rewrite,[status(
thf(717,plain,((p @ (sk2 @ (p)))),inference(simp,[status(thm)],[716])).
thf(3,axiom,((! [A:nat]: ((p @ (succ @ A)) = ((p @ A) & (q @ A))))),file
thf(13,plain,((! [A:nat]: ((p @ (succ @ A)) = ((p @ A) & (q @ A))))),inf
thf(14,plain,(! [A:nat] : (((p @ (succ @ A)) = ((p @ A) & (q @ A))))),in
thf(15,plain,(! [A:nat] : ((((p @ A) & (q @ A)) = (p @ (succ @ A))))),in
thf(844,plain,(! [A:nat] : (((q @ A) = (p @ (succ @ A))) | ((p @ (sk2 @
thf(845,plain,(((q @ (sk2 @ (p))) = (p @ (succ @ (sk2 @ (p)))))),inferen
thf(23,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (~ (A @ (succ @
thf(33,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (~ (A @ (succ @
thf(69,plain,((~ (p @ zero)) | (~ (p @ (succ @ (sk2 @ (p)))))),inference
thf(90,plain,(~ ($true) | (~ (p @ (succ @ (sk2 @ (p)))))),inference(rewr
thf(91,plain,((~ (p @ (succ @ (sk2 @ (p)))))),inference(simp,[status(thm
thf(861,plain,((~ (q @ (sk2 @ (p))))),inference(rewrite,[status(thm)],[8
thf(869,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero)) | (A @ (sk2 @ (A
thf(882,plain,((~ (q @ zero)) | (q @ (sk2 @ (q)))),inference(pre_uni,[st
thf(4,axiom,((q @ zero)),file(’oded_2.p’,5)).
thf(16,plain,((q @ zero)),inference(defexp_and_simp_and_etaexpand,[statu
thf(901,plain,(~ ($true) | (q @ (sk2 @ (q)))),inference(rewrite,[status(
thf(902,plain,((q @ (sk2 @ (q)))),inference(simp,[status(thm)],[901])).
thf(2,axiom,((! [A:nat]: ((q @ (succ @ A)) = ((q @ A) | (r @ A))))),file
thf(10,plain,((! [A:nat]: ((q @ (succ @ A)) = ((q @ A) | (r @ A))))),inf
thf(11,plain,(! [A:nat] : (((q @ (succ @ A)) = ((q @ A) | (r @ A))))),in
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 12
64. Applications: Brief look I
Classical applications: Mathematics/Computer Science and Verification
Mathematics/CS: Analysis of the Pythagorean Triples problem
Approx. 200 terabytes in proofs, 16000 CPU hours used
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 13
65. Applications: Brief look I
Classical applications: Mathematics/Computer Science and Verification
Software verification: Safety-critical and mission-critical components, e.g.
É NASA: Verification of mission components using PVS (NASA Langley)
É SNCF: Verification of train systems using ProMeLa/Spin
É ...
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 13
66. Applications: Brief look II
AI and Law: Normative Reasoning and Computational Law
É Standards for normative/legal languages (e.g. LegalRuleML)
É Tools for business compliance (e.g. Guido Governatori et al.)
É Automation of normative logics
É Own projects: NAI (jww. T. Libal) and Automated Reasoning with Legal Entities (AuReLeE)
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 14
67. Applications: Brief look II
AI and Law: Normative Reasoning and Computational Law
É Standards for normative/legal languages (e.g. LegalRuleML)
É Tools for business compliance (e.g. Guido Governatori et al.)
É Automation of normative logics
É Own projects: NAI (jww. T. Libal) and Automated Reasoning with Legal Entities (AuReLeE)
(c)
Guido
Governatori
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 14
68. Applications: Brief look II
AI and Law: Normative Reasoning and Computational Law
É Standards for normative/legal languages (e.g. LegalRuleML)
É Tools for business compliance (e.g. Guido Governatori et al.)
É Automation of normative logics
É Own projects: NAI (jww. T. Libal) and Automated Reasoning with Legal Entities (AuReLeE)
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 14
69. Applications: Brief look II
AI and Law: Normative Reasoning and Computational Law
É Standards for normative/legal languages (e.g. LegalRuleML)
É Tools for business compliance (e.g. Guido Governatori et al.)
É Automation of normative logics
É Own projects: NAI (jww. T. Libal) and Automated Reasoning with Legal Entities (AuReLeE)
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 14
70. Applications: Brief look II
AI and Law: Normative Reasoning and Computational Law
É Standards for normative/legal languages (e.g. LegalRuleML)
É Tools for business compliance (e.g. Guido Governatori et al.)
É Automation of normative logics
É Own projects: NAI (jww. T. Libal) and Automated Reasoning with Legal Entities (AuReLeE)
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 14
71. Applications: Brief look III
Automated Reasoning in Philosophy [Benzmüller and Woltzenlogel Paleo, since 2013]
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 15
72. Re: Characteristica Universalis
How far have we progressed?
Recall: Initial idea of logic as universal language
Not yet there: Zoo of logics
classical logics, constructive logics, free logics, ...
Dynamic logics, epistemic logics, higher-order logics, ..
Many-valued logics, fuzzy logics, dynamic logics, constructive logics, temporal logic,
...
Multi modal logics, epistemic logics, alethic logics, temporal logics, public announce-
ment logics, dynamic logics, deontic logics, paraconsistent logics, paracomplete log-
ics, ...
Modal logics, deontic logics, epistemic logics, temporal logics, argumentation logics,
dialog logics, I/O logics, paraconsistent logics, ...
...
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 16
73. Summary
Conclusion
É Logical reasoning core part of AI
É Automated reasoning systems
É Applications examples (only partly addressed)
É Software/hardware verification
É Computer Science and Mathematics (also in teaching)
É Legal AI, Computational Law, Normative reasoning
É Reasoning in Metaphysics, Ethics, ...
Thank you!
Questions?
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 17
74. Summary
Conclusion
É Logical reasoning core part of AI
É Automated reasoning systems
É Applications examples (only partly addressed)
É Software/hardware verification
É Computer Science and Mathematics (also in teaching)
É Legal AI, Computational Law, Normative reasoning
É Reasoning in Metaphysics, Ethics, ...
Thank you!
Questions?
,
Logic and Automated Reasoning, Elements of AI, Webinar III, 2021 17
![C.
B.
Francke,
Herzog
Anton
Ulrich-Museum
”If we had it [a characteristica unversalis],
we should be able to reason in metaphysics
and morals in much the same way as in
geometry and analysis.”
— G.W. Leibniz, 1677
(translated by Russell, 1900)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)