WHAT IS PRECISIATION

1
WHAT IS PRECISIATION?
L lexical entity (lexene)
p proposition c command i instruction q
question
L
LAZ 09-12-00
2
WHAT IS PRECISIATION?

• p proposition
• Michelle is slim
• usually Robert returns from work at about 6 pm
• c command
• move closer
• park the car

LAZ 09-12-00
3
WHAT IS PRECISIATION?

• i instruction
• drive slowly
• use with adequate ventilation
• q question
• how old is Marie?
• where does Carol live?

LAZ 09-12-00
4
PRECISIATION

• key assumption
• I know the meaning of L
• what I need is the meaning of L expressed
  precisely and in a form that lends itself to
  computation and automated reasoning
• key assumption
• precisiation of c, i, and q can be reduced to
  precisation of p
• key assumption
• a proposition, p, is an answer to a question, q
• in general, q is not unique

LAZ 09-12-00
5
PRECISIATION

• precisiation calibration composition
• calibration usually Robert returns from work
  at about 6 pm.

about 6 pm
usually
?
?
1
1
1
0
6 pm
time
0
proportion
LAZ 09-12-00
6
PRECISIATION

• composition procedure which combines
  calibrations of constituents of p
• in PNL, calibration and composition are
  procedures in CSNL (Constraint-Centered Semantics
  of Natural Languages)

LAZ 09-12-00
7
PRECISIATION
example rule set R if X is small
then Y is small if X is medium then
Y is large if X is large then Y
is small
?
large
small
medium
1
0
v
LAZ 09-12-00
8
PRECISIATION
composition
if X is small then Y is small
(X, Y) is small x small if X is medium
then Y is large (X, Y) is medium x large
if X is large then Y is small (X,
Y) is large x small R (X, Y) is
small x small medium x large large x small
composition
composition
LAZ 09-12-00
9
PRECISIATION
composition
if X is small then Y is small
Y/X is R1 if X is medium then Y
is large Y/X is R2
? R1 (u, v) 1 ? (1- ? small (u) ? small (v) )
composition
? R2 (u, v) 1 ? (1- ? medium (u) ? large (v) )
LAZ 09-12-00
10
PRECISIATION
if X is large then Y is small Y/X
is R3
composition
? R3 (u, v) 1 ? (1- ? large (u) ? small (v) )
R R1 ? R2 ? R3
LAZ 09-12-00
11
PRECISIATION
NL
GCL
PNL
precisiation translation
p
p
precisiation language
natural language
p

• translate of p
• generalized constraint
• propositions in NL which are precisiable through
  translation into GCL
• CSNL constraint- centered semantics of natural
  languages

GCL is a mathematical language
PNL
LAZ 09-12-00
12
A FUNDAMENTAL LIMITATION OF EXISTING
SCIENTIFIC THEORIES

• inability to process perception-based
  information expressed in a natural language
• PNL adds to existing scientific theories the
  capability to compute and reason with
  perception-based information expressed in a
  natural language

LAZ 09-15-00
13
NEW DIRECTIONS IN EVOLUTION OF FUZZY LOGIC

• Granular Computing GrC
• Computing with Words CW
• Computational Theory of Perception CTP
• Precisiated Natural Language PNL
• Perception-Based Theory of Probabilistic
  Reasoning PTp

LAZ 09-22-00
14
NEW DIRECTIONS IN EVOLUTION OF FUZZY LOGIC

• Perception-Based Decision Analysis DAp
• Information Orthogonality
• Generalized Definability
• Pseudo-X

LAZ 09-22-00
15
OPTIMAL SOLUTION MAXIMIZING SOLUTION?
Gain
0
u
Maximizing Solution

• Single-Criterion Optimality requires, in
  reality, multi-criterion optimization expressed
  in PNL

LAZ 09-22-00