Lecture 1 week 1
(raw) Data are individual facts that are out of context, have no meaning, and are difficult to
understand.
Information is a set of data in context with relevance to one or more people at a point in time or for
a period of time.
Knowledge is the fact or condition of knowing something with familiarity gained through experience
or association.
Knowledge is information that has been retained with an understanding about the significance of
that information
What can be done with the information/data requires knowledge. Knowledge = information + rules.
Increases usefulness.
Data preparation accounts for about 80% of the work of a Data Scientists important to clean and
organize data.
Tacit knowledge (implicit knowledge): is the knowledge that a person retains in their mind
Explicit knowledge (formal knowledge): is the knowledge that has been formalized, codified and
stored. Once shared it belongs to everyone.
Normally from data to knowledge, but also possible to go from knowledge to data. Formal
knowledge can help us to interpret and reuse data and make it reusable for other purposes. Formal
knowledge necessary to efficiently interpret data.
Knowledge graphs are a useful way of representing data, information and knowledge…
- That are Heterogeneous (data from different sources)
- In such a way that others (system/people) can interpret piece of data correctly
- By making the semantics/meaning of a piece of information explicit
- Using graph (network)
- Explicitly on the Web
Knowledge graphs on the web.
Semantic Web of Data
- Web publish their information in a machine-readable format
- The data published by different sources is linked
- Enough domain knowledge is available to machines to make use of the information
- Machines can find and combine published information in appropriate ways to answer the
user’s information needs
4 proposals by Berners Lee:
1. Give all things (that you want to/can talk about) a name
2. The names are addresses on the Web: Uniform Resource Identifiers (URI). You can point
from any database to any database (different owners, different locations).
3. Relations form a graph between things. Relations are for example: “has_name” or
“starred_in”. a relates to c triplet: a b c
, 4. Make explicit the meaning of things: not just the data, but its underlying model as well:
a. Assign types to things
b. Assign types to relations
c. Organize types in a hierarchy
A (global) graph of Linked Data
Propositional Logic
A declarative sentence (or proposition) is a statement that is true or false. For example: grass is
green.
Conjunction is with a ^
Disjunction is the “or”
Syntax: the way you write something down. Semantics: the meaning of something. Sometimes it is
the case that different symbols are used for the operators. For example & in stead of ^ and | in stead
of “or”.
Prefix syntax is a syntax which starts with the operators and then the arguments. This will become a
list. For example: p1 & p2 becomes [&, p1, p2]. (p1 & p2) v p3 becomes [v,[&[p1],[p2]],[p3]]
Valuation. Given the valuations p = T, q = F, r = F. What is the truth value of the formula p v q r? F
Semantic equivalence. If a formula A is semantic equivalent to formula B then the truth tables of A
and B are the same.
A formula is a tautology if every column in the truth table is T.
A formula is a contraction if every column in the truth table is F.
, Semantic entailment. A formula X semantic entails the formula Y if every valuation of X that results
in the value True is also true for Y
Formal Systems
Formal systems for predictable inference. If something is known in a situation, the next time the
exact situation happens the “something” can be derived and be known again.
A logic of arithmetic: Syntax
- Unambiguous definitions of what sentences are well-formed
o 2 terms with a comparator between them
o A term is either a Natural Number, a Variable, or a complex term
o A complex term is an operator +,-,*,/ applied to two terms. In infix notation with
parenthesis: “(term1 operator term 2)”
Some examples:
- Well-formed
o X + 2 >= y
o (X+2) + 4 < 12
- Not correct
o X2+y
o 5+3=
o 5-=4
No ambiguity: 7+3+5=2x-3 is not well-formed, unless there is agreement (convention). This means
(7+3) + 5 = (2 * x) – 3
A logic of arithmetic: Semantics
Truth is defined in terms of assignment for variables. Let V be the set of variables then I V : V N is
an assignment, a function that assigns natural numbers to each variable.
- X + 2 >= Y is true w.r.t. an assignment IV where IV(X) = 7 and IV(Y) = 1, and many many more.
DEFINITION: We say that IV is a model of a formula F if IV(F) is true.
- X + 2 < X + 3 is true w.r.t all possible assignments, for all values.
- X + 2 >= y is false w.r.t an assignment IV where IV(x) = 0 and IV(y) = 6
- 3 > 5 is always false
Entailment: predictable inference!
- If we know that x + y < 6, can we conclude that x < 10?
- Formally: does x + y < 6 entails x < 10?
DEFINTION: A formula F entails another formula G (F |= G) if for all variables assignments I V(F) is true
implies that IV(G) is true
Example:
- If IV(x+y<6) is true, then IV(x) + IV(y) < 6 is true
- But then IV(x) < 6 – IV(y), which implies IV(x) < 6, as IV(y) >= 0, as it is a Natural number. But
then IV(x) is also smaller than 10.
(raw) Data are individual facts that are out of context, have no meaning, and are difficult to
understand.
Information is a set of data in context with relevance to one or more people at a point in time or for
a period of time.
Knowledge is the fact or condition of knowing something with familiarity gained through experience
or association.
Knowledge is information that has been retained with an understanding about the significance of
that information
What can be done with the information/data requires knowledge. Knowledge = information + rules.
Increases usefulness.
Data preparation accounts for about 80% of the work of a Data Scientists important to clean and
organize data.
Tacit knowledge (implicit knowledge): is the knowledge that a person retains in their mind
Explicit knowledge (formal knowledge): is the knowledge that has been formalized, codified and
stored. Once shared it belongs to everyone.
Normally from data to knowledge, but also possible to go from knowledge to data. Formal
knowledge can help us to interpret and reuse data and make it reusable for other purposes. Formal
knowledge necessary to efficiently interpret data.
Knowledge graphs are a useful way of representing data, information and knowledge…
- That are Heterogeneous (data from different sources)
- In such a way that others (system/people) can interpret piece of data correctly
- By making the semantics/meaning of a piece of information explicit
- Using graph (network)
- Explicitly on the Web
Knowledge graphs on the web.
Semantic Web of Data
- Web publish their information in a machine-readable format
- The data published by different sources is linked
- Enough domain knowledge is available to machines to make use of the information
- Machines can find and combine published information in appropriate ways to answer the
user’s information needs
4 proposals by Berners Lee:
1. Give all things (that you want to/can talk about) a name
2. The names are addresses on the Web: Uniform Resource Identifiers (URI). You can point
from any database to any database (different owners, different locations).
3. Relations form a graph between things. Relations are for example: “has_name” or
“starred_in”. a relates to c triplet: a b c
, 4. Make explicit the meaning of things: not just the data, but its underlying model as well:
a. Assign types to things
b. Assign types to relations
c. Organize types in a hierarchy
A (global) graph of Linked Data
Propositional Logic
A declarative sentence (or proposition) is a statement that is true or false. For example: grass is
green.
Conjunction is with a ^
Disjunction is the “or”
Syntax: the way you write something down. Semantics: the meaning of something. Sometimes it is
the case that different symbols are used for the operators. For example & in stead of ^ and | in stead
of “or”.
Prefix syntax is a syntax which starts with the operators and then the arguments. This will become a
list. For example: p1 & p2 becomes [&, p1, p2]. (p1 & p2) v p3 becomes [v,[&[p1],[p2]],[p3]]
Valuation. Given the valuations p = T, q = F, r = F. What is the truth value of the formula p v q r? F
Semantic equivalence. If a formula A is semantic equivalent to formula B then the truth tables of A
and B are the same.
A formula is a tautology if every column in the truth table is T.
A formula is a contraction if every column in the truth table is F.
, Semantic entailment. A formula X semantic entails the formula Y if every valuation of X that results
in the value True is also true for Y
Formal Systems
Formal systems for predictable inference. If something is known in a situation, the next time the
exact situation happens the “something” can be derived and be known again.
A logic of arithmetic: Syntax
- Unambiguous definitions of what sentences are well-formed
o 2 terms with a comparator between them
o A term is either a Natural Number, a Variable, or a complex term
o A complex term is an operator +,-,*,/ applied to two terms. In infix notation with
parenthesis: “(term1 operator term 2)”
Some examples:
- Well-formed
o X + 2 >= y
o (X+2) + 4 < 12
- Not correct
o X2+y
o 5+3=
o 5-=4
No ambiguity: 7+3+5=2x-3 is not well-formed, unless there is agreement (convention). This means
(7+3) + 5 = (2 * x) – 3
A logic of arithmetic: Semantics
Truth is defined in terms of assignment for variables. Let V be the set of variables then I V : V N is
an assignment, a function that assigns natural numbers to each variable.
- X + 2 >= Y is true w.r.t. an assignment IV where IV(X) = 7 and IV(Y) = 1, and many many more.
DEFINITION: We say that IV is a model of a formula F if IV(F) is true.
- X + 2 < X + 3 is true w.r.t all possible assignments, for all values.
- X + 2 >= y is false w.r.t an assignment IV where IV(x) = 0 and IV(y) = 6
- 3 > 5 is always false
Entailment: predictable inference!
- If we know that x + y < 6, can we conclude that x < 10?
- Formally: does x + y < 6 entails x < 10?
DEFINTION: A formula F entails another formula G (F |= G) if for all variables assignments I V(F) is true
implies that IV(G) is true
Example:
- If IV(x+y<6) is true, then IV(x) + IV(y) < 6 is true
- But then IV(x) < 6 – IV(y), which implies IV(x) < 6, as IV(y) >= 0, as it is a Natural number. But
then IV(x) is also smaller than 10.
