Logic | Keith Stenning | Byrne's Suppression Task explained with Closed World Reasoning

1. Submission by Sruzan Lolla (19128410)
Suppression Task
Byrne’s Interpretation
How closed world reasoning explains suppression
CGS 651A - Logic and Cognitive Science

2. Definitions
• Credulous: Accommodating the truth of all the speaker’s utterances
• Non-monotonicity: Addition of new information alters previously assigned conclusion
• Closed-World Reasoning(CWR): A formal logic system which allows non-monotonicity
Sample if-then statement: If I turn the switch on and nothing abnormal happens then, the light will turn on.
• Abnormality: All possible hinderances in the form of a proposition variable
E.g.: power cut, non functioning light, non functioning switch, dream, etc.
• Completion: In CWR, disjunction of known premisses will hold necessarily true due to an
assumption that no other premise is playing a role. We simply ignore whatever is unknown.
If A then B will convert to if and only if A then B

3. Definitions
p → q
p is given Modus Ponens (MP)
¬p is given Denial of the Antecedent(DA) | Fallacy
q is given Affirmation of the Consequent (AC) | Fallacy
¬q is given Modus Tollens (MT)
4 Versions of argument

4. Task Statements
Conditional 1: If she has an essay to write she will study late in the library.
Conditional 2: She has an essay to write.
Additional: If she has a textbook to read, she will study late in the library. (Optional 1)
Alternate: If the library is open, she will study late in the library. (Optional 2)
Conclusion: She will study late in the library.
Premisses and Conclusion - Modus Ponens

5. Task Results
Argument 2 Conditional Additional Alternative
MP 90 64 94
DA 49 49 22
AC 53 55 16
MT 69 44 69

6. Byrne’s Interpretation
Mental Models Theory
‘Mental models theory’ says that Human Reasoning doesn’t follow any sort of formal logic
system. Byrne further claims that the content of the optional premise is responsible for
interpretation by the participant based on their domain-specific knowledge. She doesn’t
offer any explanation for participant’s formulation out of discourse material.
• {p → q ; r → q}
• {p ∨ r → q} or {p ∧ r → q} (Connection is more or less given)
• Absence of Truth value of ‘r’ will suppress conjunction.

7. Criticism
The authors question the accuracy of Byrne’s explanation. They claim that logical forms are
the outcome of a rather laborious interpretive process and it thus becomes the task of the
process to explain the assignment of relation.
ResultMaterial
And Correction
Interpretive Process
(CWR)

8. CWR in Suppression Task
Conditional 1 : If she has an essay to write she will study late in the library.
Enriched Conditional ( p ∧ ¬ab → q )
Additional: If the library is open, she will study late in the library.
Enriched Conditional ( r ∧ ¬ab' → q )
Alternate: If she has a textbook to read, she will study late in the library.
Enriched Conditional ( r ∧ ¬ab' → q )
Absence of Abnormality: (ab ⊥) or ¬ab.
Logical formulation of statements

9. The Forward Inferences
MP and DA

10. MP & DA for 2 Conditional Premises
{ p , ( p ∧ ¬ab → q ), ⊥ → ab }
Upon completion,
{ p , (p ∧ ¬ab q) , ⊥ ab}
{ p , (p ∧ ⊤ q)}
{ p , (p q)}
{ p , (p q)} Given p, q is concluded. (MP)
{ ¬p , (p q)} Given ¬p, ¬q is concluded. (DA)

11. MP & DA for an Additional Premise
In real context, the library not being open is potential abnormality for visiting there. Similarly, the other
variant relation of not having a purpose to visit although it being open is another abnormality. Thus, we add
2 relational conditionals ¬p → ab’, ¬r → ab.
{ p , ( p ∧ ¬ab → q ), ( r ∧ ¬ab' → q ) , ⊥ → ab, ⊥ → ab', ¬p → ab’, ¬r → ab}
After grouping, { p , ( ( p ∧ ¬ab ) ∨ ( r ∧ ¬ab’) → q ) , ( ⊥ ∨ ¬r → ab ), ( ⊥ ∨ ¬p → ab’ ) }
Upon completion, { p , ( ( p ∧ ¬ab ) ∨ ( r ∧ ¬ab’) q ) , ( ⊥ ∨ ¬r ab ), ( ⊥ ∨ ¬p ab’ ) }
{ p , ( ( p ∧ ¬ab ) ∨ ( r ∧ ¬ab’) q ) , ( ¬r ab ), ( ¬p ab’ ) }
{ p , ( p ∧ r ) ∨ ( r ∧ p) q ) }
{ p , ( p ∧ r ) q ) }
Premise: If the library is open, she will study late in the library.

12. MP & DA for an Additional Premise
{ p , ( p ∧ r ) q ) } (MP)
From the reduced logical form, we can not conclude anything about q as the truth value of r is not available
to us. Thus, suppression of a valid argument (Modus Ponens) is expected.
{ ¬p , ( p ∧ r ) q ) } (DA)
Given¬p, ¬q can be concluded as either of the proposition’s False truth value is sufficient to conclude
about conjunction.
Premise: If the library is open, she will study late in the library.

13. MP & DA for an Alternate Premise
For alternate premise, we do not add relational conditionals. According to our context, not having a
textbook may not hinder the purpose of going to library for writing an essay. Also, not having a task of
writing an essay has nothing to do with the sole purpose of visiting a library for reading a textbook.
{ p , ( p ∧ ¬ab → q ), ( r ∧ ¬ab' → q ) , ⊥ → ab, ⊥ → ab’}
After grouping, { p , ( ( p ∧ ¬ab) ∨ ( r ∧ ¬ab’) → q ) , ⊥ → ab, ⊥ → ab’}
Upon completion,
{ p , ( ( p ∧ ¬ab) ∨ ( r ∧ ¬ab’) q ) , ⊥ ab, ⊥ ab’}
{ p , ( ( p ∧ ⊤) ∨ ( r ∧ ⊤) q )}
{ p , ( p ∨ r q )}
Premise: If she has a textbook to read, she will study late in the library.

14. MP & DA for an Alternate Premise
{ p , ( p ∨ r q )} (MP)
Given p, q can be concluded.
{ ¬p , ( p ∨ r ) q ) } (DA)
Truth value of q can not be concluded as r can alter the conclusion. Thus, suppression is expected.
Premise: If she has a textbook to read, she will study late in the library.

15. The Backward Inferences
AC and MT

16. AC & MT for 2 Conditional Premises
{ q , (p q)} Given q, p is concluded. (AC)
{ ¬q , (p q)} Given ¬q, ¬p is concluded. (MT)

17. AC & MT for an Additional Premise
Premise: If the library is open, she will study late in the library.
{ q , ( p ∨ r q )} (AC)
Given q, p is certain as p ∨ r holds true.
{ ¬q , ( p ∨ r ) q ) } (MT)
Given ¬q, truth value of p can not be concluded as either of p, r (or both) could be responsible for False
truth value of p ∨ r. Thus, Suppression is expected.

18. AC & MT for an Alternate Premise
{ q , ( p ∨ r q )} (AC)
Given q, the truth value of p can not be concluded as either of p, r (or both) could be responsible for p ∨ r
being true. Thus, Suppression is expected.
{ ¬q , ( p ∨ r ) q ) } (MT)
Given ¬q, not ¬(p ∨ r) follows which leads to ¬p and ¬r. Thus, ¬p can be concluded.
Premise: If she has a textbook to read, she will study late in the library.