Questions tagged [propositional-logic]
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Worksheets for Logic
Wanted to ask, could you point me to a resource that gives problems to use logic to detect arguments, fallacies, etc. (problems like those in Copi's Intro to Logic) with an answer key?
Thanksl
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What is a definition, written in symbolic logic, for a person living nearby?
Students often need some axioms and/or definitions to play with in order to learn formal logic.
What is a definition of a neighbor written in the style of symbolic logic?
By neighbor, we mean a person ...
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If a proposition is necessarily true, does it follow that it's a tautology?
If □P, does it follow that P is a tautology?
I know in K modal logic, the law of NEC states
⊢ P; therefore □P.
The corresponding conditional of the previous argument is
If ⊢ P then □P.
Now ⊢P iff P is ...
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Is there only one viable definition of the logical connectives? [closed]
Is there a way to prove there's only one viable definition of the connectives, which is their truth functional definitions?
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What is the proper form of universal instantiation?
Definitions
C is a specific constant iff ∃! x [x=C]
C is a general constant iff ∀x [x=C]
C is an arbitrary constant iff ∀x [x=C] ∨ ∃! x [x=C]
Consider the commonly accepted form of the rule of ...
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Can the entirety of first order logic be reduced to the propositional calculus?
I've been wondering, whether or not first order logic can be reduced to the propositional calculus.
Rosser's system RS_1, described by Irving M. Copi in 'Symbolic Logic', has 5 axioms or postulates:
...
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Which is better, an empirical basis for the meanings of the logical connectives or a relevance logic definition of them, and why?
em·pir·i·cal / emˈpirikəl/ (also em·pir·ic) • adj. based on, concerned with, or verifiable by observation or experience rather than theory or pure logic: they provided considerable empirical evidence ...
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Do the paradoxes of material implication in relevance logic, invalidate reductio ad absurdum?
One of the paradoxes of material implication in relevance logic is
P → (Q → P)
A proof of this statement in classical propositional logic is:
P [OSC1]
P ∨ ¬Q [1; addition]
¬Q ∨ P [2; commutativity of ...
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What is the reason behind the fourth axiom in Gödel's ontological proof?
In Gödel's ontological proof, axiom 4 goes like this:
And I'm not sure about what it means. If that P(φ) is true, then isn't it necessarily true as well? There's some basic concept about modal logic ...
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How can you derive Conjunction if your only underived rule of inference is modus ponens? [closed]
Suppose you are working with a logistic system for the propositional calculus that only has one underived rule of inference, namely Modus Ponens. How can you derive Conjunction in it?
Rule 1: A, if A ...
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Can assumption in Hilbert style proof system be contradictory?
⊢（¬A→A）→A
I don't know how to solve this proof with the Axiom, Theorem and Inference rule in Hilbert-style proof system so I ask my classmate and he show me his answer. After viewing his proof, I was ...
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Is this a valid Disjunctive Syllogism
According to the website it is not, the alternative is to use a double negative, but double negation elimination, is only valid as an atomic expression, for context this is the full question.
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Why not just give up on the idea of truth-functionality?
I understand that today only a minority of academics who are specialised in formal logic accept the horseshoe (aka "Classical Logic" or "First-Order Logic") as an accurate, or even ...
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How can “a implies not a” be true?
Why does the capacity of the formula a -> ~a to be true seem so counterintuitive?
Can you give me some ordinary language examples of this case?
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Do statements have an intrinsic, unchanging truth value, even when currently unknown, or can they have different truth values at different times?
Example:
I state that a coin will come up heads, then flip it. While the coin is flipping, does the statement 'the coin I just flipped will come up heads' have a truth value?
Based on my ...
