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The propositional-logic tag has no summary.
144 questions
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Has a closed set of rules of inference, sans conditional/indirect proof, for a textbook system of natural deduction ever been crafted/discovered?
By "textbook system", I mean like the commonplace 18-or-so-rule kind of systems of natural deduction that prevalently appear in logic textbooks, such as those of, say, Patrick Hurley or Stan ...
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Is there a theory which is the true theory of logical reasoning?
Is there any theory of which any logician would be prepared to say that it is the true theory of logical reasoning?
If there is one, which is it, and who says that it is the true theory of logical ...
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Semantic Tableaux
I want to learn how to use semantic tableaux and understand, I cant seem to understand the branches and all the symbols. Could anyone recommend any resources to learn it from the beginning preferably ...
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When proving a conclusion of the form P v Q, we only have to prove a single disjunct. Is that a slight abuse of syntax and exactness required of proof
Take propositional logic and the simple proof archetypes in math that utilize propositional logic, such as in Velleman's How to Prove It (starting on page 376) and a plucked example such as: To prove ...
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name and validity of argument that observing (P & Q) implies there is evidence of (P implies Q)?
What is a name for the argument that observing (P & Q) implies there is evidence of (P implies Q)?
How do I show the argument is valid?
Below o(p) means "we have observed p" and e(p) ...
- 307
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1
answer
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Is there a simpler system of the statement calculus than Rosser's System?
In Irving M. Copi's book Symbolic Logic, he develops Rosser's System RS for the statement calculus ab ovo. It has two undefined logical operators 'not' and 'and', and three axioms and three ...
- 2,262
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Name for "P → (Q→P)"
"P → Q" is called "material conditional". "? P" is called "negation". What is the schema "P → (Q→P)" called? I know it is a tautology, but is there a ...
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Why are valid forms of hypothetical compound syllogisms not fallacies?
Let's say I have four arguments around the same subject matter:
A) Affirming the Antecedent (valid)
If it is raining then I will get wet
It is raining
Therefore I am wet
B) Denying the Consequent (...
- 143
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2
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What's the simplest way to prove if P is a theorem then P is a tautology?
An analytic deductive system is one such that
if ? P then P is a tautology.
? P if and only if P is a theorem.
Now ? P if and only if there is a demonstration of P.
Now in a system of natural ...
- 2,262
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Are the definitions of any deductive system necessarily theorems of it too?
I've been doing some work in proving my deductive system, which is a logistic system, is analytic and complete, I call it LP1. Right now I'm interested in showing that its definitions are theorems of ...
- 2,262
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Is there a short proof that the statement calculus is complete?
I know how to prove the statement calculus is complete, but the proof is long. The way I am familiar with, is to use Rosser's System RS. You have to prove 32 theorems, and 22 derived rules of ...
- 2,262
3
votes
1
answer
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meaning of semantic indexed truth-value assignments
The issue of the following reasoning is to learn completeness of propositional calculus.
I am learning the book "An introduction to Logic and its philosophy", Peter Schotch 2006. The aim of ...
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2
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3
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420
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Is 'A and not A' false in all many valued positivistic logics if 'not' and 'and' have their two valued meanings?
In order for many valued logics to make sense the following five parameters must be true.
The logic is positivistic.
One of the many truth values is 'true'.
One of the many truth values is 'false'.
'...
- 2,262
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Is the principle of explosion true in many valued logics?
To express this question clearly I have to define positivistic logic. In positivistic logic you don't have to say "Snow is white" is true, you can just say "snow is white". It's ...
- 2,262
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What's wrong with Implication? [duplicate]
As soon as I saw Implication, the Truth Table for it, I instinctively felt something is wrong. It took me quite some time to put that in words. I'll tell you what I feel later, but this question is to ...
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