Computational Logic both as a descriptive theory of human thinking and as a normative theory of how humans can think and communicate more effectively - PowerPoint PPT Presentation

Loading...

PPT – Computational Logic both as a descriptive theory of human thinking and as a normative theory of how humans can think and communicate more effectively PowerPoint presentation | free to download - id: 7650ae-MGFiO



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Computational Logic both as a descriptive theory of human thinking and as a normative theory of how humans can think and communicate more effectively

Description:

Title: The Louse and the Mars Explorer Author: Bob Last modified by: Robert Kowalski Created Date: 10/13/2003 8:34:03 AM Document presentation format – PowerPoint PPT presentation

Number of Views:1
Avg rating:3.0/5.0

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Computational Logic both as a descriptive theory of human thinking and as a normative theory of how humans can think and communicate more effectively


1
Computational Logic both as a descriptive theory
of human thinking and as a normative theory of
how humans can think and communicate more
effectively
  • The selection task
  • Switching and truncation of conditionals
  • The relationship between natural language and
    the
  • language of thought
  • The University of Michigan Lease termination
    clause
  • The British Nationality Act

2
Dual process theory human thinking involves two
cognitive systems (from Daniel Kahneman, Nobel
Prize in Economics 2002) Intuitive
thinking Reflective thinking Automatic
Controlled Effortless Effortful Associativ
e Deductive Rapid, parallel Slow,
serial Process opaque Self-aware Skilled
action Rule application Intuitive thinking
quickly proposes intuitive answers to judgement
problems as they arise, Reflective thinking
monitors the quality of these proposals, which
it may endorse, correct, or override
3
Computational logic can help to explain intuitive
thinking in the selection task
  • Determine whether given data/observations
  • satisfy the following rule
  • If D is on one side,
  • then 3 is on the other side.
  • Interpretation descriptively as a
    clause/belief inhibits
  • the contrapositive
  • If 3 is not on one side,
  • then D is not on the other side.
  • Interpretation of if as if-and-only-if justifies
  • the converse
  • If 3 is on one side,
  • then D is on the other side.
  • Abduction also justifies the converse.

4
Computational logic can help to explain intuitive
thinking in the selection task
  • Determine whether given data/observations
  • satisfy the following rule
  • If a person is drinking beer in a bar,
  • then the person should be over eighteen.
  • Here it is natural to interpret the conditional
    deontically
  • as a goal or integrity constraint
  • It is not the case that
  • a person is drinking beer in a bar and
  • the person is not over eighteen (i.e. the person
    is eighteen or under)
  • The classical logic interpretation of the rules
    is compatible with the consistency semantics of
    integrity satisfaction.

5
An abstract formulation of the selection task
  • Given some incomplete information/observations,
  • what conclusions can be derived using the
    conditional if P then Q?
  • Suppose the conditional is interpreted
    descriptively as a belief (LP clause).
  • Given an observation P
  • forward reasoning can be used to derive Q
  • Given an observation Q
  • Backward reasoning can be used to derive P as an
    explanation of Q.
  • These are the classic responses to Wasons
    original selection task.
  • The modus tollens derivation of not P from not Q
    is also possible, but more difficult.

6
The modus tollens derivation of not P from not
Q, assuming the conditional is interpreted
descriptively.
  • Because observations are atomic sentences, not Q
    needs to be derived by means of an integrity
    constraint
  • if Q and Q then false i.e.
  • not(Q and Q)
  • where Q is the positive observation or some
    generalization of the observation (such as the
    card has a consonant on the face).
  • In the ALP agent model, given an observation O
    that leads by forward reasoning to the conclusion
    Q, a further step of forward reasoning is needed
    to derive not Q. Backward reasoning with the
    conditional Q if P (inside not Q) derives not P.
  • As Sperber, Cara, and Girotto (1995) argue, the
    longer the derivation of not Q, and the greater
    the number of irrelevant, alternative
    derivations, the less likely the subject will be
    able to perform the derivation of not P.

7
Suppose the conditional is interpreted
deontically as a goal (integrity constraint)
  • The integrity constraint if P then Q is used to
    reason forwards, to derive Q from P. It is not
    used backwards to derive P from Q.
  • Negative premises such as not Q and not P need
    to be derived by forward reasoning from positive
    atomic observations, using integrity constraint
    such as
  • if Q and Q then false
  • if P and P then false
  • Given positive observations that imply Q and P
    , it is possible to derive
  • if Q then false, i.e. not Q
  • if P then false, i.e. not P.
  • The only further inference that is possible is
  • From if P then Q
  • and if Q then false
  • derive if P then false, i.e. not P.
  • This inference step is needed for the consistency
    view of integrity constraint satisfaction.

8
Determining the logical meaning of natural
language conditionals
  • Given the two sentences
  • If an object looks red, then it is red.
  • This object looks red.
  • it is natural to draw the conclusion
  • This object is red.
  • However, given the additional sentence
  • If an object is illuminated by a red light, then
    it looks red.
  • it is natural to withdraw the conclusion.
  • This can be explained by interpreting the two
    natural language conditionals as having the
    underlying logical meaning
  • An object looks red if it is red.
  • An object looks red if it is illuminated by a
    red light.
  • Here the first natural language conditional is
    the switched form of the logical meaning.

9
Switching and truncation of conditionals
  • Consider the two clauses
  • A if B.
  • A if C.
  • whose completion is
  • A if and only if B or C.
  • It is possible to write the two clauses in the
    switched form
  • B or C if A.
  • The disjunction in the conclusion of the switched
    form can be eliminated by using negative
    conditions, yielding the switched clauses
  • B if A and not C.
  • C if A and not B.
  • It is also common to truncate certain conditions,
    obtaining
  • B if A
  • C if A
  • In AI applications such as fault diagnosis, the
    standard representation models causality in the
    form effect if cause. But this requires the use
    of abduction to explain observations. The
    switched representation, cause if effect and not
    other-causes, is also common because it requires
    only the use of deduction.

10
Computational Logic can help to improve
reflective thinking
  • Thinking and human communication
  • can be made
  • clearer
  • simpler
  • more coherent
  • more effective

11
The relationship between language, thought and
the world. Two kinds of meaning Natural
language sentences (surface structure) Meanin
g Meaning as as logical form
reference in a language of thought to the
real world (deep structure)
12
(No Transcript)
13
Computational logic for human language
  • Clarity Minimise the distance between the
  • surface structure of natural language and
  • deep structure of the meaning in logical form.
  • Simplicity Use logically simple forms of
    sentences.
  • Coherence Use logical relationships to link
    sentences (e.g. in particular, in
    general. therefore. in order to,
    old-new.)
  • Effectiveness Make relations between goals and
    subgoals explicit.

14
Coherence Place old, familiar ideas at the
beginning of a sentence. Place new ideas at the
end of the sentence. e.g.    A. If A then B.
If B then C. Therefore C. C? C if B.
B if A. A. Therefore C.  
15
Coherence Rules and exceptions   Birds fly.
But penguins don't fly. Not Penguins don't
fly. But (most other) birds do.  
16
Coherence Object-orientation     The prime
minister stepped off the plane. She was
immediately surrounded by journalists.  
Not The prime minister stepped of the plane.
Journalists immediately surrounded her.
17
University of Michigan Lease Termination
Clause The University may terminate this lease
when the Lessee, having made application and
executed this lease in advance of enrolment, is
not eligible to enrol or fails to enrol in the
University or leaves the University at any time
prior to the expiration of this lease, or for
violation of any provisions of this lease, or for
violation of any University regulations relative
to residence or for health reasons, by providing
the student with written notice of termination 30
days prior to the effective time of
termination, unless life, limb or property would
be jeopardised, the Lessee engages in the sale or
purchase of controlled substances in violation of
Federal, state, or local law, or the Lessee is no
longer enrolled as a student, or the Lessee
engages in the use of firearms, explosives,
inflammable liquids, fireworks or other dangerous
weapons within the building or turns in a false
alarm in which case a maximum of 24 hours notice
would be sufficient.
18
The Lease Termination Clause has the ambiguous
form A if B and B, C or D or E or F or G or
H unless I or J or K or L or M in which case
A. Intended meaning A if B and B and
C or D or E or F or G or H and not
A A if H or I or J or K or L or M.
19
The University may terminate this lease by
providing the student with written notice of
termination 30 days prior to the effective time
of termination if the Lessee has
made application and
executed this lease in
advance of enrolment and
the Lessee is not eligible to enrol or
the Lessee
fails to enrol in the University or the
Lessee leaves the University at any time
prior to the
expiration of this lease or the Lessee
violates any provisions of this lease or the
Lessee violates University regulations regarding
residence or there are health reasons and it
is not the case that
the
University may terminate this lease with a
maximum of 24 hours notice
of termination.
20
The University may terminate this lease by ?
with maximum 24 hours notice if life, limb or
property would be jeopardised or the
Lessee engages in the sale or purchase of
controlled substances in violation
of Federal, state, or local law or the
Lessee is no longer enrolled as a student or
the Lessee engages in the use of firearms,
explosives, inflammable liquids,
fireworks or other dangerous weapons
within the building or the Lessee turns in
a false alarm.
21
In general
  • An agent does X if the agent may do X by doing Y
    and
  • the agent does Y
  • i.e.
  • The University terminates a lease
  • if The University may terminate the lease by
    providing the student with written notice of
    termination 30 days prior to the effective time
    of termination
  • and the University provides the student with
    written notice of termination 30 days prior to
    the effective time of termination

22
(No Transcript)
23
Subsection 1.-(1) 1.-(1) A person born in the
United Kingdom after commencement shall be a
British citizen if at the time of the birth his
father or mother is (a) a British citizen
or (b) settled in the United Kingdom.
24
The logic of subsection 1.-(1) A person shall be
a British citizen by 1.-(1) if the person was
born in the United Kingdom and the person was
born after commencement and a parent of the
person was a British citizen at the time of the
persons birth or a parent of the person was
settled in the United Kingdom at the time of the
persons birth.
25
Subsection 1.-(2) (2) A new-born infant who,
after commencement, is found abandoned in the
United Kingdom shall, unless the contrary is
shown, be deemed for the purposes of subsection
(1) (a) to have been born in the United
Kingdom after commencement and (b) to have
been born to a parent who at the time of the
birth was a British citizen or settled in the
United Kingdom.
26
The logic of subsection 1.-(2) The conditions of
1.-(1) hold for a person if the person was
found new-born abandoned in the United
Kingdom after commencement and it can not be
shown that it is not the case that the
conditions of 1.-(1) hold for the person.
Or in more conventional English (2) A person who
is found abandoned in the United Kingdom after
commencement shall be deemed to satisfy the
conditions of subsection (1), unless the contrary
is shown.
27
Rules and exceptions 40.-(1) Subject to the
provisions of this section, the Secretary of
State may by order deprive any British citizen to
whom this subsection applies of his British
citizenship if the Secretary of State is
satisfied that the registration or certificate of
naturalisation by virtue of which he is such a
citizen was obtained by means of fraud, false
representation or the concealment of any material
fact. 40.-(5) The Secretary of State - (a)
shall not deprive a person of British citizenship
under this section unless he is satisfied that it
is not conducive to the public good that that
person should continue to be a British citizen
...
28
Rules and exceptions simplified 40.-(1) The
Secretary of State may deprive any British
citizen to whom this subsection applies of his
British citizenship if the Secretary of State is
satisfied that the registration or certificate of
naturalisation by virtue of which he is such a
citizen was obtained by means of fraud, false
representation or the concealment of any material
fact and it is not the case that section 40.-(5)
applies. Section 40.-(5) applies If the
Secretary of State is satisfied that it is not
conducive to the public good that that person
should continue to be a British citizen ...
29
Conclusions
The Language of Thought versus Natural Language.
Computational logic is a candidate for the
language of thought. Natural language is an
imperfect expression of the language of thought.
Even seemingly logical use of natural language
needs to be interpreted into its intended
logical form.
About PowerShow.com