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Knowledge Representation
Created @September 3, 2020 11:19 AM
Class S1
Type S1
Materials
Lecture 1 (1 Sept 2020):
Knowledge Representation and AI
GOAL of course: Looking at slow thinking elements and how they contribute to AI
What is knowledge representation
A field of AI dedicated to representing information about the world in a form that a computer system can
utilize to solve complex tasks
What is a Knowledge Representation? (so when do we call an object KR)
According to AAAI Magazine 1993:
fundamentally a surrogate, a substitute for the thing itself, that is used to enable an entity to determine
consequences by thinking rather than acting, that is, by reasoning about the world rather than taking
action in it [we dont talk about the objects itself but about some explicit representations]
a set of ontological commitments
a relation between a language and certain objects postulated to be extant by that language, in this
world we assign a table some properties. So giving the surrogate some properties
a fragmentary theory of intelligent reasoning expressed in terms of three components:
1. the representation’s fundamental conception of intelligent reasoning,
2. the set of inferences that the representation sanctions, and
3. the set of inferences that it recommends.
a medium for pragmatically efficient computation, that is, the computational environment in which
thinking is accomplished.
a medium of human expression, that is, a language in which we say things about the world. So
basically about human knowledge and how to communicate this
When does sth have intelligence?
when it can carry out complex reasoning [prove theorem, solve physics problems]
draw plausible inferences (=gevolgtrekkingen) [solve a murder mystery]
use natural language [read stories and answer questions about them, carry out extended conversation]
Knowledge Representation 1
, solving novel complex problems [generating plans, designing artifacts]
social activities that require a theory of mind
Two main lines (different types of application) of development in AI
Symbolic representation
machine learning part
fast thinking,
perception [= waarneming]
pattern recognition
motor skills (robots)
speech generation (sound)
search engines
Statistical representation
more with reasoning
slow thinking
you need explicit applications, as surrogates for objects
planning (autonomous space missions)
reasoning (diagnosis, design, decision support)
language generation (conversations)
search engines
AI is not a stairway where we started from symbolic to statisctic but an pendulum, constant switch between
them. And in the future most likely to be combinations of both
-connectionist; ML algorithm
-explainable by connectionist, you know or may not know why it happened and it is not possible to explain
to humans
-Scalable: symbolic is worse with more data, connectionist is the opposite
-perf cliff of symbolic, radical drop after a certain point the quality drastically decreases, however the cliff
of connectionists is diagonal
Knowledge Representation 2
, cliff can also be as symbolic when its a domain whit whom the algorithm isnt trained with
-Scalable means that you can deal with huge amounts of data or knowledge etc.
-Explainability means that a system can explain humans why it takes some decisions or why not. The
system that recognizes the shower cap on the Queen cannot tell you why it though it was not a crown.
Symbolic systems can usually do this better.
Nowadays research on: how can we use little data with reasoning by learning fast. So how can we combine both
into one
Propositional logic
Logic for KR, what is the goal of logic in a knowledge base
To state statements which are known to be true (the “knowledge base”)
Some statements that describe the current state of the world ("premises")
To state statements for which we want to check if they are true (the “conclusions”)
To see if the conclusions can be derived from the knowledge base + the premises through logical
reasoning
S1 |= S2 : something follows logically (semantically) [= should be the same]
S1 |- S2 : something can be calculated [= is the same]
Syntax: concerned with structure of a sentence
Semantics: concerned with the meaning, it is determined by its interpretation
Logics: (formal) languages (syntax) with semantics
Automatising logics: Automated reasoning develops logic-based representation mechanisms with formal
semantics and algorithms for reasoning
Model: for a KB is a "possible world" (assignment of truth values to propostional symbols) in which each
sentence in the KB is True
P entails Q (P|=Q): means that whenever P is True, so is Q. In other words, all models of P are also models of
Q.
Knowledge Representation 3
, Theory about KRs
Properties of logic:
Soundness: |- str_1= str_2 implies |= str_1 = str_2 [= if it can be calculated that str_1=str_2 than it
follows logically that str_1=str_2]
Completeness: |= str_1 = str_2 implies |- str_1= str_2 [= if str_1=str_2 follows logically than that can
be calculated]
sound but incomplete ? than it is just not sound
Decision problem, and decidability:
A termination, sound and complete calculus decides a decision problem of the logic (whether S1|=S2)
undecidable: I know that two things should be the same but I can proof that there will be no algorithm
which directly can proof this. —> decidable when algo exists else undecidable
We are interested in the complexity of the logic, i.e. how difficult it is to solve the satisfiability problem
The knowledge base
knowledge bases that consists of statements in a very simple logic: propositional logic
Its a weak language
The letters only desribe complete "states" of the world, we cannot talk about individuals
Can’t directly talk about properties of individuals or relations between individuals (e.g., “Bill is tall”)
Generalizations, patterns, regularities can’t easily be represented (e.g., “all triangles have 3 sides”)
First-Order Logic (abbreviated FOL or FOPC) is expressive enough to concisely represent this kind of
information
in propostional logic, a knowledge base can have (those are the syntax):
simple statements
states one fact about the world (- it is hot, or just a letter)
complex statements
made by combining other statements
hierbij komen de conjunction (and,^), disjuntion (or, V), negation en implication (→)
hoe werkt "→"?
als P waar is, Q ook waar is. Deze bewering is alleen onwaar als het antecedent P waar is en het
consequent Q onwaar is.
P→Q is zelfde als -PVQ
Knowledge Representation 4
Knowledge Representation
Created @September 3, 2020 11:19 AM
Class S1
Type S1
Materials
Lecture 1 (1 Sept 2020):
Knowledge Representation and AI
GOAL of course: Looking at slow thinking elements and how they contribute to AI
What is knowledge representation
A field of AI dedicated to representing information about the world in a form that a computer system can
utilize to solve complex tasks
What is a Knowledge Representation? (so when do we call an object KR)
According to AAAI Magazine 1993:
fundamentally a surrogate, a substitute for the thing itself, that is used to enable an entity to determine
consequences by thinking rather than acting, that is, by reasoning about the world rather than taking
action in it [we dont talk about the objects itself but about some explicit representations]
a set of ontological commitments
a relation between a language and certain objects postulated to be extant by that language, in this
world we assign a table some properties. So giving the surrogate some properties
a fragmentary theory of intelligent reasoning expressed in terms of three components:
1. the representation’s fundamental conception of intelligent reasoning,
2. the set of inferences that the representation sanctions, and
3. the set of inferences that it recommends.
a medium for pragmatically efficient computation, that is, the computational environment in which
thinking is accomplished.
a medium of human expression, that is, a language in which we say things about the world. So
basically about human knowledge and how to communicate this
When does sth have intelligence?
when it can carry out complex reasoning [prove theorem, solve physics problems]
draw plausible inferences (=gevolgtrekkingen) [solve a murder mystery]
use natural language [read stories and answer questions about them, carry out extended conversation]
Knowledge Representation 1
, solving novel complex problems [generating plans, designing artifacts]
social activities that require a theory of mind
Two main lines (different types of application) of development in AI
Symbolic representation
machine learning part
fast thinking,
perception [= waarneming]
pattern recognition
motor skills (robots)
speech generation (sound)
search engines
Statistical representation
more with reasoning
slow thinking
you need explicit applications, as surrogates for objects
planning (autonomous space missions)
reasoning (diagnosis, design, decision support)
language generation (conversations)
search engines
AI is not a stairway where we started from symbolic to statisctic but an pendulum, constant switch between
them. And in the future most likely to be combinations of both
-connectionist; ML algorithm
-explainable by connectionist, you know or may not know why it happened and it is not possible to explain
to humans
-Scalable: symbolic is worse with more data, connectionist is the opposite
-perf cliff of symbolic, radical drop after a certain point the quality drastically decreases, however the cliff
of connectionists is diagonal
Knowledge Representation 2
, cliff can also be as symbolic when its a domain whit whom the algorithm isnt trained with
-Scalable means that you can deal with huge amounts of data or knowledge etc.
-Explainability means that a system can explain humans why it takes some decisions or why not. The
system that recognizes the shower cap on the Queen cannot tell you why it though it was not a crown.
Symbolic systems can usually do this better.
Nowadays research on: how can we use little data with reasoning by learning fast. So how can we combine both
into one
Propositional logic
Logic for KR, what is the goal of logic in a knowledge base
To state statements which are known to be true (the “knowledge base”)
Some statements that describe the current state of the world ("premises")
To state statements for which we want to check if they are true (the “conclusions”)
To see if the conclusions can be derived from the knowledge base + the premises through logical
reasoning
S1 |= S2 : something follows logically (semantically) [= should be the same]
S1 |- S2 : something can be calculated [= is the same]
Syntax: concerned with structure of a sentence
Semantics: concerned with the meaning, it is determined by its interpretation
Logics: (formal) languages (syntax) with semantics
Automatising logics: Automated reasoning develops logic-based representation mechanisms with formal
semantics and algorithms for reasoning
Model: for a KB is a "possible world" (assignment of truth values to propostional symbols) in which each
sentence in the KB is True
P entails Q (P|=Q): means that whenever P is True, so is Q. In other words, all models of P are also models of
Q.
Knowledge Representation 3
, Theory about KRs
Properties of logic:
Soundness: |- str_1= str_2 implies |= str_1 = str_2 [= if it can be calculated that str_1=str_2 than it
follows logically that str_1=str_2]
Completeness: |= str_1 = str_2 implies |- str_1= str_2 [= if str_1=str_2 follows logically than that can
be calculated]
sound but incomplete ? than it is just not sound
Decision problem, and decidability:
A termination, sound and complete calculus decides a decision problem of the logic (whether S1|=S2)
undecidable: I know that two things should be the same but I can proof that there will be no algorithm
which directly can proof this. —> decidable when algo exists else undecidable
We are interested in the complexity of the logic, i.e. how difficult it is to solve the satisfiability problem
The knowledge base
knowledge bases that consists of statements in a very simple logic: propositional logic
Its a weak language
The letters only desribe complete "states" of the world, we cannot talk about individuals
Can’t directly talk about properties of individuals or relations between individuals (e.g., “Bill is tall”)
Generalizations, patterns, regularities can’t easily be represented (e.g., “all triangles have 3 sides”)
First-Order Logic (abbreviated FOL or FOPC) is expressive enough to concisely represent this kind of
information
in propostional logic, a knowledge base can have (those are the syntax):
simple statements
states one fact about the world (- it is hot, or just a letter)
complex statements
made by combining other statements
hierbij komen de conjunction (and,^), disjuntion (or, V), negation en implication (→)
hoe werkt "→"?
als P waar is, Q ook waar is. Deze bewering is alleen onwaar als het antecedent P waar is en het
consequent Q onwaar is.
P→Q is zelfde als -PVQ
Knowledge Representation 4
