Many-Valued Logics Flashcards
What is validity for MV Logics?
Iff it is impossible to have designated P’s and an undesignated Conc
What is designated in K3?
{1}
What are the values for K3 negation?
1 if ν(A) = 0
n if ν(A) = n
0 if ν(A) = 1
What is the conditional in K3?
A –> B := ~AvB
Translate this before doing tableaux!
What is important to remember about translations (eg conditional)?
Do it before you start the Tableaux
What is the difference between the semantics of L3 and K3?
L3 has primitive conditional (–> filled in)
Give the TT for L3 –>
Write it down and that
What are designated values in LP?
{1,b}
Give values of negation for LP
1 if ν(A) = 0
b if ν(A) = b
0 if ν(A) = 1
What is the difference between the semantics of LP and RM3?
RM3 has primitive conditional (–>)
Do TT for RM3 conditional
Aye
What Tableaux we be using?
K3 and LP
Conjunction for Tab
+∧rule A∧B,+✓
______ A,+
______ B,+
−∧rule A∧B,−✓
_____/ __ \
____A,− __B,−
Disjunction for Tab
+∨rule A∨B,+✓
_____/ __ \
____A,+ __B,+
−∨rule A∨B,−✓
______ A,−
______ B,−
Negated Conjunction for Tab
+¬∧rule ¬(A∧B),+✓
_________ |
_______¬A∨¬B,+
−¬∧rule ¬(A∧B),−✓
_________ |
_______¬A∨¬B,−
Negated Disjunction for Tab
+¬∨rule ¬(A∨B),+✓
_________ |
_______¬A∧¬B,+
−¬∨rule ¬(A∨B),−✓
_________ |
_______¬A∧¬B,−
What are the DN rules for Tableaux?
+¬¬rule ¬¬A,+✓
________ |
________A,+
−¬¬rule ¬¬A,−✓
________ |
________A,−
When does a branch close in K3?
- If a branch contains both A,+ and A,− for some sentence A
- If a branch contains both A,+ and ¬A,+ for some sentence A
What are the countermodel values for K3?
- For every atomic or negated atomic such that A,+ is on the branch, assign ν(A) = 1
- If A,− and ¬A,− are on the branch, set ν(A) = n
- If A,− is on the branch but its negative force negation is not on the branch, set ν(A) = 0
How does a branch close in LP?
- If a branch contains contains both A,+ and A,− for some sentence A
- If a branch contains both A,− and ¬A,− for some sentence A
What are the countermodel values for LP?
- Where A,+ is on the branch but its positive-force negation is not on the branch, set ν(A) = 1
- Where A ,+ and ¬A,+ are on the branch, set ν(A) = b
- For every atomic or negated atomic such that A,− is on the branch, assign ν(A) = 0
