Intuitionistic logic refer constructive logic, a logical system avoiding deduction rules like Reductio ad absurdum.
Intuitionistic logic refers to constructive logic, a logical system avoiding deduction rules like Reductio ad absurdum.
Questions tagged [intuitionistic-logic]
415 questions
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Proof of contradiction vs refutation by contradiction and what is/isn't allowed in constructive logic?
Here it is stated that constructive logic allows refutation by contradiction:
The proposition to be proved is ¬P.
Assume P.
Derive falsehood.
Conclude ¬P.
But not indirect proof:
The proposition to be proved is P.
Assume ¬P.
Derive…
user590921
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Filter on Heyting algebra
Consider the first order intuitionistic logic.
Let $H$ be an Heyting algebra, let $F$ be a filter on $H$ and let $V:\text{Frm} \rightarrow H$ be an evaluation function.
Suppose that $b \rightarrow V^{[x:=d]}(A(x)) \in F$ for every $d \in D$ ($D$ is…
effezeta
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Gentzen Style Intuitionistic Sequent Proofs
I am trying to provide intuitionistic sequent proofs (Gentzen Style) for a few statements.
The rules that I have are the rule of assumption, conjunction introduction and elimination, disjunction introduction and elimination, conditional introduction…
user837496
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Watered down axiom of choice
I'm wondering what the following statement is equivalent to in an intuitionistic framework.
For a union of sets $C = \bigcup\limits_{i \in I} X_i,$ if $S \in C,$ there
exists $s \in I$ such that $S \in X_s.$
In classical logic, the proof just…
Display name
- 5,144
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Can we prove using intuitionist logic that $\neg \exists r: \forall x: [P(x,r) \iff \neg P(x,x)]$
Can we prove using intuitionist logic that $\neg \exists r: \forall x: [P(x,r) \iff \neg P(x,x)]$ where $P$ is a binary logical predicate?
Dan Christensen
- 14,529
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Intuitionistic Logic. Interpretation proof.
Proof interpretation for:
The citation comes from: http://aleteya.cs.buap.mx/~jlavalle/papers/van%20Dalen/Intuitionistic%20Logic.pdf
$$ A \implies (B \implies A) $$ We want an operation $p$ that turns a
proof $a : A$ into a proof of $B \implies…
user376326
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Simple sentence in intuitionstic logic.
Let's consider the following sentence:
$$ A \implies B $$
If $A$ has no a construction / proof, does it mean that sentence is true?
user376326