Which first order logic logic equivalences are not valid in intuitionistic logic?
0
I know that --A == A and -(A / B) == -A or -B don't hold in intuitionistic logic. Which are the relatives first order logic equivalence that don't hold in intuitionistic logic?
first-order-logic
asked Jan 4 at 11:11
MaicakeMaicake
615
add a comment |
0
I know that --A == A and -(A / B) == -A or -B don't hold in intuitionistic logic. Which are the relatives first order logic equivalence that don't hold in intuitionistic logic?
first-order-logic
asked Jan 4 at 11:11
MaicakeMaicake
615
See Intuitionistic logic.
– Mauro ALLEGRANZA
Jan 4 at 11:20
2
For example, it is not true that $lnot forall x lnot Px$ is equivalent to $exists x Px$.
– Mauro ALLEGRANZA
Jan 4 at 11:23
2
There are lots of examples. For examples, some kind of de Morgan's law $lnot (Aland B)to lnot Alor lnot B$ is not valid. $Ato B$ no longer implies $lnot Alor B$. You may find some examples by considering a statement under BHK interpretation.
– Hanul Jeon
Jan 4 at 11:30
add a comment |
0
0
0
I know that --A == A and -(A / B) == -A or -B don't hold in intuitionistic logic. Which are the relatives first order logic equivalence that don't hold in intuitionistic logic?
first-order-logic
asked Jan 4 at 11:11
MaicakeMaicake
615
I know that --A == A and -(A / B) == -A or -B don't hold in intuitionistic logic. Which are the relatives first order logic equivalence that don't hold in intuitionistic logic?
first-order-logic
first-order-logic
asked Jan 4 at 11:11
MaicakeMaicake
615
asked Jan 4 at 11:11
MaicakeMaicake
615
asked Jan 4 at 11:11
MaicakeMaicake
615
asked Jan 4 at 11:11
MaicakeMaicake
615
asked Jan 4 at 11:11
MaicakeMaicake
615
615
See Intuitionistic logic.
– Mauro ALLEGRANZA
Jan 4 at 11:20
2
For example, it is not true that $lnot forall x lnot Px$ is equivalent to $exists x Px$.
– Mauro ALLEGRANZA
Jan 4 at 11:23
2
There are lots of examples. For examples, some kind of de Morgan's law $lnot (Aland B)to lnot Alor lnot B$ is not valid. $Ato B$ no longer implies $lnot Alor B$. You may find some examples by considering a statement under BHK interpretation.
– Hanul Jeon
Jan 4 at 11:30
add a comment |
See Intuitionistic logic.
– Mauro ALLEGRANZA
Jan 4 at 11:20
2
For example, it is not true that $lnot forall x lnot Px$ is equivalent to $exists x Px$.
– Mauro ALLEGRANZA
Jan 4 at 11:23
2
There are lots of examples. For examples, some kind of de Morgan's law $lnot (Aland B)to lnot Alor lnot B$ is not valid. $Ato B$ no longer implies $lnot Alor B$. You may find some examples by considering a statement under BHK interpretation.
– Hanul Jeon
Jan 4 at 11:30
See Intuitionistic logic.
– Mauro ALLEGRANZA
Jan 4 at 11:20
See Intuitionistic logic.
– Mauro ALLEGRANZA
Jan 4 at 11:20
2
2
For example, it is not true that $lnot forall x lnot Px$ is equivalent to $exists x Px$.
– Mauro ALLEGRANZA
Jan 4 at 11:23
For example, it is not true that $lnot forall x lnot Px$ is equivalent to $exists x Px$.
– Mauro ALLEGRANZA
Jan 4 at 11:23
2
2
There are lots of examples. For examples, some kind of de Morgan's law $lnot (Aland B)to lnot Alor lnot B$ is not valid. $Ato B$ no longer implies $lnot Alor B$. You may find some examples by considering a statement under BHK interpretation.
– Hanul Jeon
Jan 4 at 11:30
There are lots of examples. For examples, some kind of de Morgan's law $lnot (Aland B)to lnot Alor lnot B$ is not valid. $Ato B$ no longer implies $lnot Alor B$. You may find some examples by considering a statement under BHK interpretation.
– Hanul Jeon
Jan 4 at 11:30
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061535%2fwhich-first-order-logic-logic-equivalences-are-not-valid-in-intuitionistic-logic%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061535%2fwhich-first-order-logic-logic-equivalences-are-not-valid-in-intuitionistic-logic%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
See Intuitionistic logic.
– Mauro ALLEGRANZA
Jan 4 at 11:20
2
For example, it is not true that $lnot forall x lnot Px$ is equivalent to $exists x Px$.
– Mauro ALLEGRANZA
Jan 4 at 11:23
2
There are lots of examples. For examples, some kind of de Morgan's law $lnot (Aland B)to lnot Alor lnot B$ is not valid. $Ato B$ no longer implies $lnot Alor B$. You may find some examples by considering a statement under BHK interpretation.
– Hanul Jeon
Jan 4 at 11:30