Questions tagged [propositional-logic]
84 questions
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How does "if p, then q" compare to "p only if q"?
How do the statements if p then q and p only if q compare
Marsha
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What is wrong with these two conditionals?
Is it true that these two conditionals if A then B and if not-A then B cannot be both true?
Example :
"If I stay then I will eat fish"
"If I didn't stay then I will eat fish"
The reason I think it maybe the case, is because one can decide to eat…
SmootQ
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Justification of the material conditional truth function in Introduction to Formal Logic
Pages 150-151 of §18.3 of Introduction to Formal Logic by Peter Smith provide two justifications for the truth table of the material conditional.
In the first justification (paragraph (a) - (c) on pg. 150), Smith shows that the material conditional…
user51462
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Truth-functional vs non-truth functional conditionals
I'm struggling to understand truth functionality.
I know that a connective is truth-functional if the truth value of a compound statement formed with that connective is completely determined by the truth values of the input…
user51462
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Is the sentence "all apples are red" an atomic sentence?
In An Introduction to Logic by Patrick Suppes, an atomic sentence is defined as a sentence that contains no sentential connective. However, in a later chapter, a sentence is defined as a formula which contains no free variables.
Now if we take a…
somebody anybody
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Did William of Soissons prove the law of explosion in the 12th century?
In the 12th century, William of Soissons attempted to prove that any proposition can be inferred from a contradiction. I've adapted his proof into a logical system I'm more familiar with:
Let E represent any given proposition
P ^ ~P, Premise
P,…
N. Bar
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Why is it argued that an argument has one and only one conclusion?
Why can't an argument have more than just one conclusion? If we assume some premises and we assume them to be true, then by some inference rules we are sometimes able to deduce more than just one true conclusion, is that right? Why do they argue…
TKN
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What is the difference between a premise and an assumption in logic?
It seems to me that an assumption is an untold premise in my argument. Is it right?
TKN
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What are the conditions for RAA?
My textbook states that:
In this case, however, what about situations where we can get Q ^ ~Q (sorry, unfamiliar with this formatting) without depending on P? For instance, the proof of EFQ:
1 (1) P A
2 (2) ~P A
3 (3) ~Q A…
user538118
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What is the relationship between possible worlds and a valuations?
A propositional formula is something like this, A&~B, which uses letters to represent propositions. The letters are called propositional variables.
Compare the following two sets of terminologies related to propositional formulas:
A valuation is an…
David Gudeman
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How do you prove that a logic system is sound?
I am aware of the fact that a logic system must be sound, in order to be useful. However, I am not sure, about how, after setting up or coming up with the basic logic axioms that make up my system, I would prove that the logic system is sound.
In…
Joselin Jocklingson
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Why is any sentence a logical consequence of a set of inconsistent premises?
If a set of premises is inconsistent, there is no situation that makes all the premises true simultaneously.
Given a sentence S, there is no situation in which a conjunction of a set of inconsistent premises is true and S is false, simply because…
evianpring
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Classical propositional logic. Are all formulas sentences?
Let L the language of classical (two-valued) propositional logic consisting of a denumerable set of sentential variables as well as the usual operations of negation, disjunction, conjunction, implication, and equivalence.
Are all formulas of L…
Beginner
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Is b⊢C∧¬b⊢C∧b⇒C∧¬b⇒C possible?
Are there any cases where b and C are real world statements where b⊢C∧¬b⊢C∧b⇒C∧¬b⇒C where b and C are not tautologies? It may seem like a silly question, but after searching hard and deep, I couldn't find an answer! Please help me with this…
Math Bob
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Difference between Propositions and Statements
I have read the answers to many questions like mine I reached these two definitions of propositions (I don't know which one is correct)
A proposition is a statement that can be true or false.
If this is true then what characteristic should a…
Credence
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