1.2 Application of Propositional Logic
Section Summary
 Translating English sentences
 Systems Specifications
 Consistence System Specifications
 Boolean Search
Translating English Sentences
 Steps to convert an English sentence to a statement in
propositional logic
 Identify atomic propositions and represent using
propositional variables.
 Determine appropriate logical connectives
 “If I go to Harry’s or to the country, I will not go
shopping.”
 p: I go to Harry’s
 q: I go to the country.
 r: I will go shopping.
If p or q then not r.
Example
Problem: Translate the following sentence into
propositional logic:
 “You can access the internet from campus only if you are a





computer science major or you are not a freshman”
a: “You can access the internet from campus”
b: “you are a computer science major”
c: “you are a freshman”
Where a,b,c are propositional variables
a  (b  c)
System Specifications
 Express the specification ”The automated reply
cannot be sent when the file system is full“ using
logical connectives.
P: “The automated reply can be sent”
q: “The file system is full”
q  p
System specifications should be consistent
They should not contain conflicting requirements that
could be used to drive a contradiction
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Consistent System Specifications
Definition: A list of propositions is consistent if it is
possible to assign truth values to the proposition
variables so that each proposition is true.
 Translating sentences in natural language into logical
expressions is an essential part of specifying both hardware and
software systems.
 System and software engineers take requirements in natural
language and produce precise and unambiguous specifications
that can be used as the basis for system development.
Consistent System Specifications
determine whether these system specifications are consistent :
a. “The diagnostic message is stored in the buffer or it is
retransmitted”
b. “The diagnostic message is not stored in the buffer”
c. “if the diagnostic message is stored in the buffer, then it is
retransmitted”
P: “The diagnostic message is stored in the buffer”
q: “The diagnostic message is retransmitted”
a.
pq
b. p
c. pq
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Consistent System Specifications
p  q
p pq
p q p
F F T
F T T
T F F
T T F
p q
p  q
F
T
T
T
T
T
F
T
system specifications are consistent
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Consistent System Specifications
determine whether these system specification are consistent :
a. “The diagnostic message is stored in the buffer or it is
retransmitted”
b. “The diagnostic message is not stored in the buffer”
c. “if the diagnostic message is stored in the buffer, then it is
retransmitted”
d. “The diagnostic message is not retransmitted”
P: “The diagnostic message is stored in the buffer”
q: “The diagnostic message is retransmitted”
a. p  q
b. p
c. pq
d. q
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Consistent System Specifications
p  q
p pq q
p q p
F F T
F T T
T F F
T T F
p q
p  q
F
T
T
T
T
T
F
T
q
T
F
T
F
system specifications are inconsistent
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Boolean Searches
Logical connectives are used extensively in searches of large collections of
information:
Indexes of Web pages, these searches employ techniques from
propositional logic.
The connective
AND is used to match records that contain both of the two search items.
OR is used to match one or both of two search items.
NOT is used to exclude a particular search item (- is used in Google).