This preview shows pages 1–5. Sign up to view the full content.
Review of Semantic Concepts
•
Truthfunctional truth: Statement true on every truthvalue
assignment
•
Truthfunctional falsity: Statement false on every truthvalue
assignment
•
Truthfunctional indeterminacy: Neither truthfunctionally true
nor truthfunctionally false
•
Consistency: A truthvalue assignment where all the members
of the set are true
•
Equivalence: No truthvalue assignment where one is true and
the other false (i.e. They have identical truthvalues)
•
Entailment: Every truthvalue assignment that makes the
members of the set true makes the further sentence true
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Set Terminology
2200
Γ
= Represents a set of sentences of SL
•
{
P
}: Set whose only member is
P
. Sometimes
referred to as the “unit set of
P
” or “singleton
P
”
2200
∪
= Used to represent the joining together of
the members of two sets
2200
∅
= Represents the “empty set” (the set
which has no members)
Consistency and Truth
functional Truth
•
Prove: If {~
P}
is inconsistent,
P
is truth
functionally true
•
Strategy: Assume inconsistency of {~
P
},
show that the truthfunctional truth of
P
follows
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
functional Truth
•
Explanation:
Assume that {~
P
}
is
inconsistent.
A set is inconsistent just in case
there is no truthvalue assignment on which
all the members of that set are true. Since ~
P
is the only member of this set, the
inconsistency of the set shows that ~
P
must
be truthfunctionally false (as it would be false
on every truthvalue assignment). Since ~
This is the end of the preview. Sign up
to
access the rest of the document.
This document was uploaded on 11/03/2009.
 Spring '09

Click to edit the document details