The document discusses Byrne's interpretation of suppression in conditional reasoning tasks using closed world reasoning. It defines key terms and outlines 4 versions of conditional arguments. The author claims CWR can explain participant responses and suppression by representing conditionals as statements about absence of abnormality. CWR allows modeling optional premises as additional conditionals and deriving logical forms involving disjunction. The author provides examples applying CWR to conditional premises using modus ponens, denial of the antecedent, affirmation of the consequent, and modus tollens.
Propositional Logic
CMSC 56 | Discrete Mathematical Structure for Computer Science
August 17, 2018
Instructor: Allyn Joy D. Calcaben
College of Arts & Sciences
University of the Philippines Visayas
The Foundations: Logic and Proofs: Propositional Logic, Applications of Propositional Logic, Propositional Equivalence, Predicates and Quantifiers, Nested Quantifiers, Rules of Inference, Introduction to Proofs, Proof Methods and Strategy.
Propositional Logic
CMSC 56 | Discrete Mathematical Structure for Computer Science
August 17, 2018
Instructor: Allyn Joy D. Calcaben
College of Arts & Sciences
University of the Philippines Visayas
The Foundations: Logic and Proofs: Propositional Logic, Applications of Propositional Logic, Propositional Equivalence, Predicates and Quantifiers, Nested Quantifiers, Rules of Inference, Introduction to Proofs, Proof Methods and Strategy.
Logicians sometimes talk about sentences being “true but unprovable." What does this mean? This presentation includes a fairly thorough introduction to mathematical logic.
Propositional Equivalences
CMSC 56 | Discrete Mathematical Structure for Computer Science
August 23, 2018
Instructor: Allyn Joy D. Calcaben
College of Arts & Sciences
University of the Philippines Visayas
With vocabulary
1. The Statements, Open Sentences, and Trurth Values
2. Negation
3. Compound Statement
4. Equivalence, Tautology, Contradiction, and Contingency
5. Converse, Invers, and Contraposition
6. Making Conclusion
Discrete Mathematics is a branch of mathematics involving discrete elements that uses algebra and arithmetic. It is increasingly being applied in the practical fields of mathematics and computer science. It is a very good tool for improving reasoning and problem-solving capabilities.
Выступление Сергея Кольцова (НИУ ВШЭ) на International Conference on Big Data and its Applications (ICBDA).
ICBDA — конференция для предпринимателей и разработчиков о том, как эффективно решать бизнес-задачи с помощью анализа больших данных.
http://icbda2015.org/
Brute force searching, the typical set and guessworkLisandro Mierez
Consider the problem of identifying the value of a discrete
random variable by only asking questions of the sort: is its
value X? That this is a time-consuming task is a cornerstone
of computationally secure ciphers
Logicians sometimes talk about sentences being “true but unprovable." What does this mean? This presentation includes a fairly thorough introduction to mathematical logic.
Propositional Equivalences
CMSC 56 | Discrete Mathematical Structure for Computer Science
August 23, 2018
Instructor: Allyn Joy D. Calcaben
College of Arts & Sciences
University of the Philippines Visayas
With vocabulary
1. The Statements, Open Sentences, and Trurth Values
2. Negation
3. Compound Statement
4. Equivalence, Tautology, Contradiction, and Contingency
5. Converse, Invers, and Contraposition
6. Making Conclusion
Discrete Mathematics is a branch of mathematics involving discrete elements that uses algebra and arithmetic. It is increasingly being applied in the practical fields of mathematics and computer science. It is a very good tool for improving reasoning and problem-solving capabilities.
Выступление Сергея Кольцова (НИУ ВШЭ) на International Conference on Big Data and its Applications (ICBDA).
ICBDA — конференция для предпринимателей и разработчиков о том, как эффективно решать бизнес-задачи с помощью анализа больших данных.
http://icbda2015.org/
Brute force searching, the typical set and guessworkLisandro Mierez
Consider the problem of identifying the value of a discrete
random variable by only asking questions of the sort: is its
value X? That this is a time-consuming task is a cornerstone
of computationally secure ciphers
This is the midterm paper. if some questions are favourable for you follow me.
Follow me on youtube: https://www.youtube.com/channel/UCP8iyUsyciJJc0o5sj0X3tA
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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
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.
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.