Teadmiste formaliseerimine 2023
Name: Knowlege representation |
Sisukord
- 1 NB! See on 2023 aasta arhiiv, mitte hetkel kehtivad materjalid!
- 2 Eksamitulemused
- 3 Eksamiajad ja kohad
- 4 Time, place, result
- 5 Contents overview: what the course is about
- 6 Links to the teams group and lecture videos
- 7 Practical work
- 8 Books to use
- 9 Blocks and lectures: the main content of the course
- 9.1 Block 1: knowledge in SQL, RDF and JSON
- 9.2 Block 2: handling simple facts and rules in symbolic AI and logic
- 9.3 Block 3: General-knowledge databases
- 9.4 Block 4: natural language and question answering
- 9.5 Block 5: uncertain knowledge and hybrid systems
- 9.5.1 Lecture: third lab, neurosymbolic reasoning, open/closed world, planning, frame problem, blocks world: 28 March
- 9.5.2 Reasoning with uncertainty: 4 April
- 9.5.3 Lecture: initial reviews of GPT4 + more on 3rd pract work + semantic parsing, 11 April
- 9.5.4 Lecture: research in hybrid systems: 18 aprill
- 9.5.5 Lecture: further details for semantic parsing: 25 aprill
- 9.5.6 Reasoning with uncertainty: discrete reasoning options: 2. mai
- 9.5.7 Reasoning with uncertainty: combining discrete and numeric + context: 9 mai
- 9.5.8 Konsultatsioon eksamiks: 16 mai
NB! See on 2023 aasta arhiiv, mitte hetkel kehtivad materjalid!
Eksamitulemused
Esimene, 31 mai eksam:
Eesnime esitäht, tudengikood, eksamipunktid (0-50), kokku punktid (0-100), hinne: O 211913 42 78 3 A 221494 42 86 4 M 221613 30 74 3 K 211809 31 68 2 T 211539 40 81 4 R 221523 45 92 5 T 221526 44 88 4 K 211832 37 74 3 G 221346 46 97 5
Teine, 5 juuni eksam:
Eesnime esitäht, tudengikood, eksamipunktid (0-50), kokku punktid (0-100), hinne: H 221662 30 74 3
Eksamiajad ja kohad
- 31 mai kolmap kell 13-16, ruumis SOC-414 (sotsiaalteaduste maja)
- 5 juuni esmasp kell 11-14, ruumis U04-103 (IV korpus, pikast koridorist)
- 8 juuni neljap kell 12:15-15, ruumis SOC-414 (sotsiaalteaduste maja)
Eksamiks on kokku aega 2.5 tundi, aga enamik peaks saama hakkama ca 1.5 tunniga.
Eksam on kirjalik, samas ruumis/ajal toimub ka hajussüsteemide kirjalik eksam.
Vaata ka: 2023 teadmiste kursuse prakside punktid
Time, place, result
Lectures: Tuesday 13:45-15:15 room U05-103
Practical work: Tuesday 15:30-17:00 room U05-103
Plaan on teha osa loengutest kohapeal (esialgu kindlasti kohapeal) ja osa distantsilt. Loenguid salvestame ja salvestuste lingid on allpool blokkide/loengute juures.
Praksidega samamoodi: algul kindlasti kohapeal, samas üritame salvestada / üle kanda, edaspidi tõenäoliselt osa prakse distantsilt (teamsis).
Salvestuste lingid leiad allpool kas vastava loengu või praksi peatüki all.
Moodles materjale ei ole: kogu info, materjalid ja ülesanded on lambda lehel.
Practical work will give 50%, exam 50% of points, and weekly tasks additional extra up to 10%, underlying the final grade. The exam will consist of several small excercises.
To finish the course successfully, you need to
- successfully pass three practical works
- receive at least 1/3 of the max points at exam
- get practice work + weekly tasks + exam at least 50% points altogehter.
Contents overview: what the course is about
The theme of the course: from SQL to natural language.
Hence the main focus of the course is on hybrid methods for knowledge representation and reasoning: symbolic AI, machine learning / neural methods and their combinations. We look at this spectrum from simple (representing and using knowledge in databases) to complex (meaning of sentences in natural language and commonsense knowledge) tasks. A closely related subject is commonsense reasoning.
The course contains the following blocks:
- Knowledge in SQL, RDF and JSON
- Handling simple facts and rules in symbolic AI and logic
- General-knowledge databases
- Natural language and question answering
- Uncertain knowledge and hybrid systems
Links to the teams group and lecture videos
The links to saved lecture videos are and will be visible among the materials of corresponding lectures below.
NB! In case you run into trouble (cannot join or no sound etc) please write via fb messenger or email tanel.tammet at taltech.ee.
Practical work
There are three labs. They are all steps in a single project: build a simple natural-language question-answering system a la classic Watson. There is also an alternative option to do one larger practical research project instead of these three labs: details of this project have to be discussed and agreed with Tanel.
The labs have to be presented (as a demo + small overview of the software and principles) to the course teachers and all students present at labwork time, either in the auditorium or over MS teams. The labs can be prepared alone or by teams of two or three people.
Each lab is evaluated independently and gives the same number of points.
NB! When you do not meet the lab deadline, you will be awarded half of the points for this lab.
First lab
2023 task for the first lab is an intro to the world of large knowledge bases and a preparation for the following labs where we will use this data to experiment with some nontrivial question answering.
Deadline: 28 February.
Second lab
Deadline: 11. April 2022.
See Details of the KR second lab in 2023
Third lab: questions in NLP
Deadline: 9. May.
The tasks for 2023:
- Experiment with natural language rules, ChatGPT and ProofWriter (less technical): this gives 2/3 of full points.
- Use a semantic parser and a reasoner to solve questions posed in natural language (more technical): this gives full points.
Details under the separate pages linked to above. An intro and initial explanations will be given during the lectures, starting with the 28 March lecture.
Since the tasks are conceptually nontrivial, everybody is encouraged to use the teams group for the course to ask for help whenever you run into trouble: starting from April both teachers will monitor the teams daily and try to help you out.
Books to use
Main materials:
- Get the basic background about classical automated reasoning from the book chapter pages 297-345 by Tanel Tammet and optionally more details from the set of course notes from Geoff Sutcliffe.
- The book for natural language (NLP): Speech and Language Processing by Dan Jurafsky and James H. Martin. here is the 2nd edition and (suggested) here the web page for the draft 3rd edition. Recommendation: read from the beginning up to an including chapter 6: Vector Semantics and Embeddings, then skip and read a few chapters starting from 15: Logical Representations of Sentence Meaning. You do not need to understand all the details of math, for example. It is OK if you understand the main principles of representations and algorithms.
Other useful books and tools for symbolic K&R:
- logictools.org for experimenting with classical automated reasoning
- Symbolic reasoning themes are covered in this book with freely accessible pdf-s.
- Similarly, the freely accessible pdf of the handbook of knowledge representation gives a detailed and thorough coverage of the subject; far more than necessary for the course.
- You may want to get a small intro to Prolog by reading the first 100 pages of a classic Art of Prolog book: pdf is freely downloadable under the "Open Access" tab. It is not strictly necessary for the course (we will not be using Prolog) but it surely helps. Besides, the book is interesting, quite easy to read and works out a lot of interesting examples.
Other useful material for neural NLP:
- Andrej Karpathy nanoGPT and neural networks zero to hero course
- GPT architecture and chatgpt cheatsheet
Observe that a noticeable part of the course contents are not covered by these books: use the course materials and links to papers, standards and tutorials provided.
Blocks and lectures: the main content of the course
Allpool olev blokkide struktuur on sarnane, aga mitte sama, kui 2022 aastal. Transformerite (BERT, GPT) ja hübriidsüsteemide osa muutub mahukamaks.
Toimunud loengute materjalid ja salvestused osaliselt uuendatakse/muudetakse: kogu info veel mitte toimunud loengute ja prakside kohta on pärit peamiselt 2022 aastast ja on esialgne indikatsioon.
Block 1: knowledge in SQL, RDF and JSON
Lecture: Intro and background, 31. Jan
Sissejuhatuse presentatsioon:
Soovitav (mitte kohustuslik) kuulamine:
- Marcus episode on the Lex Fridman podcast https://lexfridman.com/gary-marcus/
- Gary Marcus (KR&R commonsense proponent) & Joshua Bengio (ML proponent) https://www.facebook.com/watch/live/?v=498403850881660&ref=watch_permalink read also the related Marcus paper https://arxiv.org/ftp/arxiv/papers/1801/1801.00631.pdf
- David Ferrucci (IBM Watson team leader) on the Lex Fridman podcast https://lexfridman.com/david-ferrucci/
- Tim Rocktäschel (Facebook A.I.) episode https://towardsdatascience.com/language-models-symbolic-learning-and-the-road-to-agi-75725985cdf7
- Reading, not listening: on Hybrid A.I. in image analysis https://knowablemagazine.org/article/technology/2020/what-is-neurosymbolic-ai
Lecture: Nosql, json and rdf in databases: 7. Feb
Lecture materials:
- We cover Background: relations of sql and logic E1
- and start with schemaless databases, RDF and RDFS E1 (also important for practice work)
See also
- Json in Postgresql: json datatype and functions for json
- notes about schema for rdf / first lab
The weekly homework will be about trying out small things in logic: please try out logictools from "basics" to "equality" in simple examples selectbox. Details will appear after the lecture.
Block 2: handling simple facts and rules in symbolic AI and logic
Lecture: simple rules in rdfs, logic and owl: 14 feb
- Main lecture material: schemaless databases, RDF and RDFS looked at rdfs rule meanings in logic and sparql (up to page 30 in the presentation).
- Loengusalvestuse link.
- Praksi salvestuse link.
- Rdf example developed during lecture
Have a brief a look at this, no need to read thoroughly:
- Official w3c rdf and rdfs primer E2
The main materials covered in the lecture:
- json-ld (check out playground examples) E1 currently most popular triple representation language on top of json. see also wikipedia and w3c standard: for the latter, read the basic concepts chapter E2.
- rdfa E2 triple markup language suited for html, see also wikipedia
- schema.org (E2 you can surf on the schema.org site and understand/find answers there)) we looked at in the last lecture: property markup vocabulary suggested by Google, Microsoft and others.
And then have brief look (skim through) at:
- Official w3c owl primer but it is better to look at this intro presentation and continue with the owl rules presentation
- sparql tutorial and wikipedia take on sparql.
Certainly read:
We will also start at looking and understanding the examples in logictools.org
More resources:
- sparql implementations in wikipedia
- various rdf tools listed at the bottom of the page
Lecture: rules in logic with provers to answer questions: Feb 21
We will consider the reasoning part of K&R to understand what provers do:
- rules, logic, provers E1
- logictools system running gkc reasoner in the browser: try out the "simple" and "complex" examples, read explanatory texts and the manual about predicate logic
- Have a look at the gkc github repo, including precompiled binaries for command line in the release 0.6.0 and the tutorial Examples/Readme.md.
- Travel examples from lecture 2021
You may want to have a look at the additional materials - from easier to harder - from the book chapter pages 297-345 by Tanel Tammet, the the set of course notes from Geoff Sutcliffe, the implementation presentation from Stephan Schulz and the readable-and-hackable PyRes reasoner for educational use.
Lecture: what the reasoner does: 28 Feb
We will continue with the same presentation:
along with doing/explaining experiments using logictools.
Block 3: General-knowledge databases
Lecture: looking into main large knowledge bases: 7. March
E2: you can search/investigate what kind of data is available and you can find out actual data from these databases with some work, by surfing on the web pages of the systems.
We will have a look at the goals, main content and differences between:
- wordnet see tptp axioms
- dbpedia, see also classes and dbpedia wiki
- wikidata
- yago old page and new page
- babelnet described in wikipedia
- conceptnet described in wikipedia
- nell website (sometimes down) and in wiki and a good paper.
- framenet described in wikipedia, see example
- cyc but just read wikipedia and see whitepaper also tptp small random selection of axioms
- adimen-sumo see sumo in wikipedia and tptp axioms
- tptp: a large set of axioms and problems in logic usable for automated reasoners
- schema.org: property markup vocabulary suggested by Google, Microsoft and others.
- Wolfram alpha stuff
Block 4: natural language and question answering
Lecture: Intro to NLP, n-grams, word vectors: 14 March
- These three wikipages give useful introductory details:Natural language processing, Knowledge extraction, Natural language understanding.
- Väga hea õpik: 3. variandi draft või 2. variandi terve pdf.
- Hea mõte on hakatuseks lugeda läbi 2. variandi sissejuhatus.
- Vektorsemantikast arusaamiseks loe 3. variandi ptk 3. N-gram Language Models ja siis chapter 6: Vector Semantics and Embeddings E2. Vektorsemantika kasutamine närvivõrkudes a la Bert ja GPT on hästi kirjas ptks 7: Neural Networks and Neural Language Models
- Slaidid eelmiste peatükkide kohta: Ngrams ja word vectors.
- Google ngrams ja reaalne data.
- GloVE: a relatively simple vector representation
- ChatGPT: katseta!
- Kui tahad katsetada toore Wikipedia dataga, siis saab loengus vaadatud töödeldud variante siit (tarballid sisaldavad datat, selgitavat README-d ja tarkvara selle ise ehitamiseks): a compacted pure-text version of full wikipedia, A lemmatized version of wikipedia texts, Several co-occurrence matrices and lists of top-co-occurring words for wikipedia
- Online demo of NTLK running some basic NLP tasks
Recommended listening:
- A cool 14-minute philosophy podcast episode to listen: Jonathan Webber on deceiving with words plus a a direct audio link (may expire at some point)
- NLP highlights podcast series from the Allen institute for AI. Makes sense to start from the very first ones and pick these which have a title looking interesting to you. World-leading stuff and quite understandable.
Lecture: large language models (LLM), BERT and GPT families: 21 märts
Iseõppe nädal, loengut ei toimu (õppejõud peab olema sama ajal senati istungil).
Eesmärk: saada pinnaliselt aru LLM ja transformerite (NLP masinõppe põhiasjad) peamistest ideedest. Detailid on tegelikult keerulised ja nendest arusaamine võtab hulga rohkem aega, kui meil kursuses on, sestap lepime vähesega. Samas, kui sul endal huvi, siis loomulikult on teretulnud detailsem iseõpe.
Enne järgmisse materjali süvenemist tutvu kindlasti vektorsemantikaga, mida seletasime 14 märtsi loengus.
Mida vaadata ja lugeda:
Kindlasti
- Andrej Karpathy progemisega-koos loeng: vaata see süvenemisega läbi!
Paratamatult jääb enamus detaile loengus vähearusaadavaks (kui ise ei kuluta hulga aega järele katsetamiseks), aga sellegipoolest on see tõenäoliselt kõige parem loeng transformeritest: mingi tunnetuse sellest, et mis toimub, saab.
Optsionaalselt üldisem arusaam klassikutelt:
- Wolframi pikk jutt lugemiseks koos närvivõrkudega üldisema taustaga
- Rodney Brooksi ennustused transformerite kohta
Optsionaalselt diipim arusaam:
- nanoGPT: Karpathy reaalne näitekood GPT ise-ehitamiseks (otse eelmise loenguga seotud) : seda saab ilma suuremate pingutusteta käima linuxil ja macil, windowsil tekib aga suuremaid probleeme (proovisin ise linuxil järgi).
- Taustaks: Karpathy terve loenguseeria, kui sul tekib sügavam huvi
- Jurafsky & Martin ptk 10 Transformers and Pretrained Language Models kui tahad ise juurde lugeda.
Block 5: uncertain knowledge and hybrid systems
We will focus on (a) uncertainty in KR (open/closed world, frame problem, probabilities, exceptions) and (b) current research on building hybrid systems
Lecture: third lab, neurosymbolic reasoning, open/closed world, planning, frame problem, blocks world: 28 March
We will first have a brief look at the 3. lab: Experiment with natural language rules, ChatGPT and ProofWriter and an alternative Use a semantic parser and a reasoner to solve questions posed in natural language.
We will then give a brief overview of the work/tasks in hybrid neurosymbolic AI.
For the main part of the lecture we consider planning and the frame problem. The standard example for these is a blocks world: some blocks are on the table and the robot arm can lift single blocks and put them on other blocks or on the table. The arm cannot lift several blocks or a tower of blocks. Then, given a position of blocks at initial situation, can the robot arm create a required new position of blocks? Can we get the steps required? For getting the steps we use the $ans predicate.
One hard issue arising is that how do we know that doing some action like lifting a block does not create side effects like stumbling existing towers, moving other blocks etc? This issue is called the frame problem and it has no easy solutions.
Importantly, the frame problem arises since normal first order logic has
- the open world assumption E1 (must read): if we do not have (and cannot derive) a positive fact like P(a) and neither a negative fact like -P(a), we assume we simply do not know which holds.
Prolog and databases operate under the
- closed world assumption E1 (must read): if we do not have (and cannot derive) a positive fact like P(a), we automatically assume that -P(a) must be true. For example, Prolog "negation" really means "cannot prove". One consequence of this assumption is that we cannot represent real negation and disjunction in an OK manner (Prolog does not contain these) and cannot satisfactorily speak about "true", "false" and "unknown". See also negation as failure in prolog
Please look at and read these materials about the frame problem:
- tiny video of the Boston Dynamics robot failing: looks like a frame problem in the blocks world :)
- overview presentation: E1 must read.
- a classic AI philosophy paper about the frame problem: must read the first three pages (rest is optional).
- wikipedia about frame problem: E2 skim it through (no need to read all the details) to get a rough idea about different approaches to the frame problem. None of these are really good.
These two readings are optional:
- frame problem at the Stanford Encyclopedia of philosophy: not obligatory, but a good read to get a better understanding.
- another classic about frame problem: read this only if you became really really interested about the whole issue: it goes quite deep, although it is not especially technical.
You may also want to have a look at the algorithmic complexity and efficient solution algorithms, regardless of how we formalize the problem: see this article.
Next, importantly, you should experiment yourself with gkc and both of the following files. Please copy and read the files and understand the encoding. At the end of the files are several queries to experiment with: instructions are also there.
In both of them the predicate holds(X,Y) is used to describe something X about the blocks world (like, one block is on another or robot holds some block) and the second argument Y describes the state we have arrived to via robot actions from the original state (like, picked up a block in the initial state and then did put the block down on top of another).
- Simple axiomatization of the blocks world: E2 please also read through the comments explaining the axiomatization and queries!
- More complex blocks world axiomatization taken from the TPTP problem set for first order logic, concretely by concatenanting and commenting axiom sets PLA001-0.ax, PLA001-1.ax and queries PLA004-1.p, PLA005-1.p, PLA019-1.p
To get a simple visualization of the blocks world, have a look at this tiny video.
Reasoning with uncertainty: 4 April
- Loengusalvestus 2022: siit vaata esimest 30 minutit.
- Loengusalvestus 2023: uuem variant pärast eelmise 30 minutit ja edasi
Loengu sissejuhatava osa presentatsioon: Reasoning_with_uncertainty.pdf E1.
Almost all the knowledge we have is uncertain: there are many exceptions to a rule or a fact/rule holds with some vague probability. Notice that, in contrast, typical databases in companies contain facts with very high certainty, but they do not contain rule or commonsense knowledge: the latter is built into brittle software code of systems using these databases.
We will consider two different ways to tackle uncertainty:
- Numeric methods: uncertainty is estimated with probability-like numbers of various kinds.
- Discrete methods: no numbers used. Instead, uncertainty is described as exceptions or beliefs of people.
NB! Both of these ways are hard to actually implement, neither have they been understood very well, despite an immense amount of research and papers. For example, typical machine learning methods operate with extremely vague probability-like numbers and do not attempt to put these numbers into a real properly-theoretical-and-correct probabilities framework.
The main material for reading about numeric methods is an overview-followed-in-depth by the lecturer Numeric uncertainty: (E2 up to and including the chapter 3, see also E2 tags inside)
- Read carefully up to and including the chapter 4 "Different ways to encode confidences in logic" and have a quick look at all the wikipedia links.
- Skim through the later parts and look only into these subchapters which you found interesting.
Next,
- Read the paper E2. containing intro, alorithms and experiments.
- Look at the web page with the confer reasoner and a wealth of examples.
Next, have a brief look at a good example system doing some specific kinds of probability reasoning:
Lecture: initial reviews of GPT4 + more on 3rd pract work + semantic parsing, 11 April
Materials accompanying the lecture:
- Paper "Sparks of Artificial General Intelligence: Early experiments with GPT-4"
- nlpsolver and Media:nlp_reasoning_pipeline.pdf
- nlpsolver knowledge representation principles: draft
Additionally recommended to listen and read in this order:
- Listen to the episode David Ferrucci: IBM Watson, Jeopardy & Deep Conversations with AI in a very popular ai podcast.
- Read a good presentation <! about a history of semantic parsing: this won't tell you much about how to do it, though.
Also, check out a very useful demo:
- Ascent from Max Planck.
- Ascent online answering demo
You may want to have a look at the AllenAI tutorial
- semantic-parsing-tutorial with a lot of details and fancy stuff.
Additionally you may want to read some papers about semantic parsing:
- Read a paper about building a semantic parser in a relatively simple way.
- Another paper about semantic parsing
There is an interesting specific method for semantic parsing, called AMR, worth having a brief look into:
- Amr site with examples, papers etc.
- A concrete implementation of an AMR parser
- A catalogue of papers about AMR parsing
There is a very good fairly deep NLP-and-commonsense series of podcasts and other interesting stuff from the Allen Institute for AI:
- NLP highlights podcasts
- episode 89 about dialog systems
- episode 91 about executable semantic parsing
- episode 59 about semantic parsing
- demos, in partcular Rover demo
Lecture: research in hybrid systems: 18 aprill
Hübriidsüsteemid: loengu käigus tehtud sissjeuhatavad märkmed
Lecture: further details for semantic parsing: 25 aprill
Loengu annab Martin: audikas pluss teamsis.
Loenguslaidid: Media:KR_2023_Parsing_Verrev.pdf E2
Reasoning with uncertainty: discrete reasoning options: 2. mai
Loengusalvestus teamsis 2023.
- Esimest järku loogikas ei ole üldjuhul võimalik välja rehkendada, et mingi asi ei ole järelduv. Lausearvutuses samas on. Sestap on olemas selline tore valdkond nagu answer set programming, E2 kus esimest järku muutujatega valem teisendatakse lausearvutuseks, tekitades muutujatega reeglitest hästi palju konstante sisaldavaid reegleid. Siis muutuvad blokkerite arvutamised võimalikuks. Võid tahta lugeda päris head introt teemasse, mille on kirjutanud Aalto ülikooli rektor Niemelä. Samas ei ole see lausearvutuseks-teisendamine mittetriviaalsetel juhtudel võimalik. Üks paremaid süsteeme seal on DLV (DLV wikis), vaata DLV manuaali Kui sul tekib rohkem huvi, siis selle answer-set programming lähenemise jaoks on olemas terve kursus videote ja loengumaterjalidega.
- Teine oluline küsimus eranditega reeglite puhul on nende prioriteedid: kui kaks reeglit üksteist blokivad, kas mõnel peaks olema kõrgem prioriteet? Näiteks, "materiaalsed asjad üldiselt ei lenda", "linnud on materiaalsed asjad", "linnud üldiselt lendavad", "pingiviinid on linnud", "pingviinid üldiselt ei lenda". Siin paistab, et taksonoomias allpool olevaid asju kirjeldavad reeglid võiks olla kõrgema prioriteediga kui ülalpool asju kirjeldavad reeglid. Samas "Nixoni kolmnurga" näites "vabariiklased ei ole patsifistid", "kveekerid on patsifistid", "Nixon korraga vabariiklane ja kveeker" oleks loomulik mõelda, et esimesed kaks default reeglit Nixoni jaoks blokeeruvadki ja me ei saa järelda, et Nixon on patsifist, ega ka seda, et ta ei ole patsifist. Prioriteetide teema kohta võib vaadata täeindavalt seda artiklit või seda sarnast artiklit.
- Describing beliefs of various actors. This builds upon modal logic (see intro presentation to understand the basics) and the main method is (auto)epistemic logic: the logic for encoding who knows or believes what. See the long tutorial as an easily read text E2 and additionally tutorial slides Ijcai93.pdf by the same authors to accompany the long text. Read carefully, starting with the long text and also looking at slides at the side.
- Multi-valued logics with belief degrees (a la "very unlikely", "very likely") at different intervals. We will not look into these: we'll investigate the numeric methods instead. Have a very brief look at the wikipedia.
NB! Modal beliefs and multivalued logics are not really used in any kinds of practical systems: they are hard to efficiently implement and they are not understood well enough in practical settings. However, different versions of default logics (and other systems with exceptions) are actually used, including in https://github.com/tammet/nlpsolver
Reasoning with uncertainty: combining discrete and numeric + context: 9 mai
Artikkel default reasoningu kohta.
Artikkel kogu pipeline kohta: parsimine, reasoning, vastused. E2
We will look at a number of small examples using both numeric and discrete
uncertainty, plus context, and will experiment with our new experimental solver in a live session.