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Questions and Answers
Which of the following models demonstrates the invalidity of the formula K 2φ Ñ 3φ?
Which of the following models demonstrates the invalidity of the formula K 2φ Ñ 3φ?
- A model where 2φ is true but 3φ is false. (correct)
- A model where both 2φ and 3φ are true.
- A model where both 2φ and 3φ are false.
- A model where 2φ is false while 3φ is true.
In classical propositional logic, which statement is true regarding the premises and conclusion relationship?
In classical propositional logic, which statement is true regarding the premises and conclusion relationship?
- The conclusion is always a semantic consequence of its premises. (correct)
- No false premises can lead to a true conclusion.
- Some premises can be false under certain interpretations.
- All interpretations lead to the same set of false premises.
Which of these is a characteristic of Kleene's three-valued logic?
Which of these is a characteristic of Kleene's three-valued logic?
- It exclusively uses true and false values.
- It concludes that every argument is valid.
- It incorporates an additional value representing indeterminacy. (correct)
- It is not useful for semantic arguments.
What does the abbreviation Cφ represent?
What does the abbreviation Cφ represent?
In Priorean tense logic, what is the conclusion of the formula φ Ñ HFφ?
In Priorean tense logic, what is the conclusion of the formula φ Ñ HFφ?
Which of the following is a valid formula in the logic of paradox (LP)?
Which of the following is a valid formula in the logic of paradox (LP)?
What is the primary concern when establishing validities in modal logics?
What is the primary concern when establishing validities in modal logics?
What does the formula D 2φ Ñ 3φ imply about the relationship between necessity and possibility?
What does the formula D 2φ Ñ 3φ imply about the relationship between necessity and possibility?
What condition must be satisfied for $VI(pCφ, wq)$ to equal 1 in terms of $VI(pφ, uq)$?
What condition must be satisfied for $VI(pCφ, wq)$ to equal 1 in terms of $VI(pφ, uq)$?
What should students who have not studied Elements of Deductive Logic do regarding the ‹’ questions?
What should students who have not studied Elements of Deductive Logic do regarding the ‹’ questions?
Which statement fails when replacing S5 with S4?
Which statement fails when replacing S5 with S4?
If $O1$ expresses the same modality as $O2$ in S, what can be concluded about their concatenated strings $OO1$ and $OO2$?
If $O1$ expresses the same modality as $O2$ in S, what can be concluded about their concatenated strings $OO1$ and $OO2$?
Which of the following expressions does VI pφ Ñ ψq equal to when it is true?
Which of the following expressions does VI pφ Ñ ψq equal to when it is true?
In propositional logic, what does the expression VI p„φq = 1 indicate?
In propositional logic, what does the expression VI p„φq = 1 indicate?
How many modalities are expressed by strings in S5?
How many modalities are expressed by strings in S5?
What implication does the interpretation I ` have on any sentence φ with no negation?
What implication does the interpretation I ` have on any sentence φ with no negation?
What is the truth condition for the ‘Peirce arrow’ Ó in propositional logic?
What is the truth condition for the ‘Peirce arrow’ Ó in propositional logic?
Which of the following represents a semantic consequence in propositional logic?
Which of the following represents a semantic consequence in propositional logic?
What can be said about the occurrence of parentheses in an MPL-sentence?
What can be said about the occurrence of parentheses in an MPL-sentence?
When using Sider’s presentation of the semantics of propositional logic, which condition holds for conjunction?
When using Sider’s presentation of the semantics of propositional logic, which condition holds for conjunction?
Which of the following is a true statement about the axiomatic proofs required for PL?
Which of the following is a true statement about the axiomatic proofs required for PL?
Which statement represents an interpretation that includes negation?
Which statement represents an interpretation that includes negation?
If φ contains at most one occurrence of any sentence letter, what does PL φ represent?
If φ contains at most one occurrence of any sentence letter, what does PL φ represent?
What is the relationship between the truth conditions provided and Halbach’s presentation in The Logic Manual?
What is the relationship between the truth conditions provided and Halbach’s presentation in The Logic Manual?
Which of the following binary generalized quantifiers can be symbolized in L“?
Which of the following binary generalized quantifiers can be symbolized in L“?
What condition must be met for the quantifier 'Finitely many α: φψ' to be true?
What condition must be met for the quantifier 'Finitely many α: φψ' to be true?
Which of the following identifies a valid schema in SQML?
Which of the following identifies a valid schema in SQML?
In the context of semantic equivalence, what is required for two sentences?
In the context of semantic equivalence, what is required for two sentences?
Which of the following statements about second-order logic is true?
Which of the following statements about second-order logic is true?
What does the symbol '2' typically represent in the schemas listed in SQML?
What does the symbol '2' typically represent in the schemas listed in SQML?
Which of the following helps justify whether a generalized quantifier can be symbolized in L“?
Which of the following helps justify whether a generalized quantifier can be symbolized in L“?
What is a condition for a quantifier to be considered as capturing a certain meaning in logic?
What is a condition for a quantifier to be considered as capturing a certain meaning in logic?
What does the selection function f ensure in relation to the validity of the expression VM pφ € ψ, wq?
What does the selection function f ensure in relation to the validity of the expression VM pφ € ψ, wq?
Which of the following represents a semantic consequence for the material conditional?
Which of the following represents a semantic consequence for the material conditional?
What is a non-consequence for Stalnaker’s conditional?
What is a non-consequence for Stalnaker’s conditional?
In the formalization of the argument regarding the coin flip, what condition is applied to conclude the argument?
In the formalization of the argument regarding the coin flip, what condition is applied to conclude the argument?
Which logical system is argued as the correct logic for metaphysical necessity according to Salmon?
Which logical system is argued as the correct logic for metaphysical necessity according to Salmon?
What does the countermodel in part (b) intends to demonstrate regarding the formal argument?
What does the countermodel in part (b) intends to demonstrate regarding the formal argument?
Which of the following conditions fails to preserve truth in the English counterfactual conditional?
Which of the following conditions fails to preserve truth in the English counterfactual conditional?
What does the expression pφ ∧ ψq denote in the context of semantic non-consequences for Stalnaker’s conditional?
What does the expression pφ ∧ ψq denote in the context of semantic non-consequences for Stalnaker’s conditional?
Study Notes
Recommended Readings
- Students who have not read Elements of Deductive Logic (EDL) should skip the questions marked ‹'
- Students who have read EDL should attempt the questions marked ‹', but may skip the questions marked :
- The : and ‹ markings will become less common as the term progresses, as the material will bridge the gap between EDL and the current material.
Propositional Logic
- Students should read the provided chapters from "Vagueness" by Tim Williamson and "Sorites Paradoxes and the Semantics of Vagueness" by Michael Tye to prepare for later questions in the course.
Variations of PL
- The "Peirce arrow" (Ó) is a connective where VI pφ Ó ψq “ 1 iff VI pφq “ 0 and VI pψq “ 0
- The "Peirce arrow" (Ó) is also known as "nor"
Semantics for MPL
- K, D, T, B, S4, and S5 are modal logic systems
- The semantics for these systems should be explored through informal semantic arguments
Tense Logic
- "Cφ" is an abbreviation for 3φ ^ 3„φ
- "Cφ" is called "C"
- The semantics of "C" are determined by the value of VI pφ, uq ### Induction on Complexity
- The number of occurrences of parentheses in an MPL-sentence is twice the number of occurrences of Ñ
Axiomatic Proofs in PL
- PL P Ñ pP Ñ P q is a valid axiomatic proof
- PL P Ñ P is a valid axiomatic proof
- PL p„P Ñ P q Ñ P is a valid axiomatic proof
The Logic of Metaphysical Necessity - Task A
- Students should read the chapters from "The Logic of What Might Have Been" by Nathan Salmon and sections 3.1–3.3 from "Modal Logic as Metaphysics" by Tim Williamson
Task B
- Students should consider if second-order logic can be seen as "logic"
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Description
This quiz covers key concepts from Propositional Logic and Semantics, including the Peirce arrow and various modal logic systems. Students are encouraged to reference 'Elements of Deductive Logic' and provided readings for a comprehensive understanding. Prepare for questions related to tense logic and the nuances of vagueness.