A well written summary of the course Knowledge Representation given at the TiU. Two books are covered including a short quiz with their correct answers highlighted. Also, Prolog examples are shown. In addition, it contains a Mock exam at the end of the summary with a practical example.
L book = Hector J. Levesque (2012) Thinking as computation
N book = Gonzalo Nápoles (2020). Lecture notes in Knowledge Representation
With quiz question examples
L1: Chapter 1 N book & L book / Preliminary concepts & Thinking and Computation
Introduction
-AI → simulation of HI in machines programmed to think like humans and mimic their actions
-More interesting to equip machines to think so they can solve problems that humans cannot
What is thinking?
--Sort of process that occurs in our heads over time.
--Observe it in action / Bring what you know to bear on what you doing.
--Thinking can be usefully understood as a computational process
--Thinking always seems to be about something.
What is computation?
--Computation is the process of taking symbolic structures, breaking them apart, comparing them, and
reassembling them according to a precise recipe called a procedure.
-The symbols at the start of the procedure are called the inputs.
-The symbols at the end of the procedure are called the outputs.
-The procedure is called on the inputs and returns the outputs
--Computation seems to be about nothing
= manipulating symbols in a mechanical way without taking into account what the symbols stand for.
What are symbols?
--In their simplest form, symbols are just characters from some alphabet, like the following:
digits: 3, 7, V (the last one is a Roman numeral) / letters: x, R, β (the last one is a Greek letter) / operators: +, ≤ , ∩
/ numerals: 5874, – 3.75 / words: John, don’t / mathematical expressions: 247 + 4(x – 1)3
/ the woman John loved / mathematical inequalities: 247 + 4(x – 1)3 ≤ n!
Informal definition to AI algorithms
--AI = problem solving using computational methods able to derive knowledge form available data
--This definition suggest:
-We need data (different formats – images, videos, audio, documents, survey answers)
-Need 1 or several computational procedures able to process input data and produce knowledge
-There is a strong link between AI and problem-solving tasks
Most AI problems can be expresses as search problems -- examples:
--Training deep neural network / Determining route to postman / Recommend suitable treatment
We can say that problem solving involves
--Optimizing a function f(x)
-X = candidate solution to be evaluated
-Each candidate solution = collection of variables describing the problem
-Variables can be – numeric (continuous = age) / symbolic (discrete = colors)
-Ex: blue = possible state for discrete var hair color / 400 = possible state for numerical var income
--The search space = collection of candidate solutions that might solve the problem
-Search space also contains solutions that might not be feasible solutions
When at least 1 variable of candidate solution takes non-feasible state
Ex: age of person is numerical variable → but 250 years old is not logical for a human being
So the domain of age variable is all real numbers
-Search space that contains feasible solutions = all positive integers till 164
Two building blocks of AI
--Symbolic knowledge representation
--Sub symbolic knowledge representation
Summary
Made by: A.Azzam
,Thinking as computation
Propositions vs. sentences
--Proposition can be expressed by a declarative sentence of English (or other language).
So think of the sentence as a symbolic representation of the proposition.
examples: My keys are in my coat pocket / Dinosaurs were warm-blooded.
Sentence → on the one hand (like the first one with seven words)
Proposition → on the other (like the idea that my keys are located somewhere).
--Propositions are considered to hold or to not hold.
A sentence is true if → proposition it expresses holds
A sentence is false if → that proposition does not hold.
Relationships between people and propositions = propositional attitudes.
-Uninterpreted sentences
--Understand thinking as computation = look sentence of EN as symbolic structure made up of sequence of words.
--Example: The snark was a boojum.
So → (What is this snark? What is a boojum?)
Observe that if one assumes that the sentence is true, even without knowing what
the words snark and boojum mean, one can answer certain questions:
What kind of thing was the snark? → (It was a boojum.)
Is it true that the snark was either a beejum or a boojum? → (Yes, because it was a boojum.)
If no boojum is ever a beejum, was the snark a beejum? → (No, it could not have been.)
What is an example of something that was a boojum? → (The snark, of course.)
The point is that one can provide appropriate answers to these questions without having to
know what the two symbols mean.
This is the first step toward linking thinking and computation.
-Logical entailment
--Determining if collection of sentences logically entails → not necessary to know what terms in sentences mean.
Example →The snark was a boojum ---> logically entails → Something was a boojum.
--The fact that these symbols can be used in uninterpreted way is what allows the connection with computation.
-Is thinking logic?
--Thinking seems to be so much richer than just dry logical entailments because thinking seems to depend on
what the words in a sentence mean.
Using what is known: The web of belief
--WOB to emphasize that → sentences don’t standalone but link to others by virtue of terms used
--Job of logical entailment = crawl over web looking for connections among nodes, sensitive to the
different types of links along the way
Knowledge bases
--To make plausible connection between thinking & computing, we have to imagine that we are considering →
Logical entailments of enormous collection of sentences (entire web of belief).
Such a collection is called a → knowledge base (KB).
So yes, there is a connection between thinking and logic but it is misleading to think of it as Logic
Summary
Made by: A.Azzam
,Symbolic knowledge representation
GOFAI (good old fashioned artificial intelligence) = AI paradigm born out of Dartmouth 1956
Symbolic AI
= term for the collection of all AI methods and algorithms that are based on high level symbolic
(human readable) representations of problems, logic and search
--According to Leibniz idea
-Every computational method can be understood as a symbolic one!
-This happens because even numerical structures can be encoded using symbols
--Assumes that many aspects of intelligence & reasoning can be achieved by manipulation of symbols
--Methods operating on symbolic structures that are not related to numerical quantities are symbolic.
--Idea = relationships between those symbols to draw conclusions or symbolic reasoning
--Symbols themselves seem not to be relevant as can represent same phenomenon in different ways.
--Methods symbolic Ai rely on high level knowledge representations encoded through symbols
--Example:
Number 14 can represented as → Fourteen (English) / catorce (Spanish) / veertien (Dutch) / XIV / 1110
Meaning that numbers are symbolic representations!
--Symbolic reasoning is closely related to mathematical logic (first order logic)
--Logical inference rules → reasoning = deductive when conclusion is direct conclusion of premises
--Form symbolic AI = expert systems (Network production rules to connect symbols by IF - THEN statements
--There are 3 main arguments against symbolic AI
1. knowledge acquisition (& formalization) is time consuming & challenging process (create bottleneck)
2.symbolic representations are poor representations of real world
3.symbolic AI relayed on formal logic & deductive reasoning while ignoring other reasoning paradigms
Sub-symbolic knowledge representation
Strives to build computational systems operating with numerical representations
Numbers allow for richer knowledge representations
Sub-symbolic AI
--Don’t manipulate symbolic knowledge representations to find solution to a given problem
--Performs calculations according to effective problem-solving strategies without knowing solution
--Ex: Real coded heuristic search methods / Deep neural networks / Support vector machines / Random forest
--Attempt to mimic human brain & its complex network of interconnected neurons
--It is also known as connectionist AI and covers the connectionist approach
--Thinks using sub symbolic AI methods = Googles translations / Facebook face recognition / Self-driving cars
--The reason they are successful = They can automatically learn complex learning representations
What has motivated the AI fields recent news?
--Answer = the hardware
--Ex: foundations of most important deep learning models where known for many years
--The hardware was only not ready back then (long short-term memory and google translator)
--The introduction of powerful hardware has enabled deep learning models to solve problems with
larger search solution spaces (more brute force capabilities than real intelligence)
--DL Models involve important shortcomings → Consume massive amount of energy & Lack interpretability
--Sub symbolic reasoning models often perform as black boxes
They produce an output for a given input without explaining the inside mapping
Could lead to biased outcomes such as denying a loan to a person because it’s a women
Hybridizing both approaches
It is evidential that both symbolic and sub-symbolic AI have strengths and weaknesses
It is better to combine these approaches to create more accurate – robust - efficient – fair
reasoning algorithms supporting decision making processes
The synergy between symbolic and sub-symbolic AI can be implemented in several ways
ranging from human intervention during the knowledge acquisition and annotation to
developing hybrid machine intelligence algorithms able to reason together with human beings
The book suggests to combine the following building blocks
Block 1: connection to world of classical AI which does not conflict with deep learning progress
Benefit = from the abilities of symbolic AI to represent abstract knowledge
Block 2: need richer and large-scale knowledge sources
Summary
Made by: A.Azzam
, Knowledge acquisition and engineering are pivotal task in building block
Block 3: need able to reason using both symbolic and sub symbolic pieces of information
Convenient to involve human experts in the loop
Block 4: need cognitive models
Things inside our brain or inside of computers that tell us about the relations between entities that we see around us
in the world
Quiz lecture 1
1.Which of the following statements fits better the “reasoning” concept?
Reasoning is about explaining the decisions of intelligent algorithms.
Reasoning is equivalent to performing a search process in a large dataset.
Reasoning is a feature that only human beings have.
Reasoning is the formal manipulation of symbols to produce new knowledge.
2.Which of the following statements is true about symbolic reasoning?
Symbolic reasoning models are often less transparent than sub-symbolic reasoning ones.
Symbolic reasoning and sub-symbolic models cannot be compared.
Symbolic reasoning models are often more transparent than sub-symbolic reasoning ones.
Symbolic reasoning and sub-symbolic models are equally transparent.
3.Which of the following statements is true about sub-symbolic reasoning?
Sub-symbolic reasoning allows learning implicit knowledge representations from data.
Sub-symbolic reasoning allows understanding how the human brain works.
Sub-symbolic reasoning allows searching for the solution in symbolic search spaces.
Sub-symbolic reasoning allows solving easy problems while failing to solve complex ones.
4.Which of the following statements is true about knowledge-based systems?
Knowledge-based systems refer to sub-symbolic reasoning systems only.
Knowledge-based systems refer to symbolic reasoning systems only.
Knowledge-based systems refer to hybrid artificial intelligence systems.
Knowledge-based systems refer to reasoning systems using a knowledge base.
5.Which of the following statements is true about granularity?
Granularity is about dividing the knowledge into propositions and sentences
Granularity is about the level of detail to which we describe an environment.
Granularity is about producing internal knowledge representations from data.
Granularity is about producing new pieces of knowledge from existing ones.
Summary
Made by: A.Azzam
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