What the definition of validity of a formule in a possible Kripke-world in Modal Logic?
up vote
3
down vote
favorite
Basic question here but I cannot find the definition:
Given a modal logic and a set of propositions $P$, a model $M=(W,R,V)$ where $W$ are possible worlds, $R$ an accesibility relation and $V$ a valuation for every $pin P$
What is de definition of $(M,w)models varphi$?
And whats the name of it? Validity?
Thanks
logic modal-logic
asked Aug 22 '15 at 20:07
Applied mathematician
1,00342041
add a comment |
up vote
3
down vote
favorite
Basic question here but I cannot find the definition:
Given a modal logic and a set of propositions $P$, a model $M=(W,R,V)$ where $W$ are possible worlds, $R$ an accesibility relation and $V$ a valuation for every $pin P$
What is de definition of $(M,w)models varphi$?
And whats the name of it? Validity?
Thanks
logic modal-logic
asked Aug 22 '15 at 20:07
Applied mathematician
1,00342041
Have you looked at en.wikipedia.org/wiki/Modal_logic#Semantics ?
– mrp
Aug 22 '15 at 20:15
2
We say that $varphi$ is true at world $w$ in model $M$ (in symbols: $(M,w) vDash varphi$); we say that $varphi$ is true in model $M$ (in symbols: $M vDash varphi$) when $(M,w) vDash varphi$ for all $w in W$. We say that $varphi$ is valid ($vDash varphi$) when $M vDash varphi$ for every model $M$. See e.g : Edward Zalta, Basic Concepts in Modal Logic.
– Mauro ALLEGRANZA
Aug 22 '15 at 20:27
mauro thanks a lot
– Applied mathematician
Aug 23 '15 at 14:41
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
Basic question here but I cannot find the definition:
Given a modal logic and a set of propositions $P$, a model $M=(W,R,V)$ where $W$ are possible worlds, $R$ an accesibility relation and $V$ a valuation for every $pin P$
What is de definition of $(M,w)models varphi$?
And whats the name of it? Validity?
Thanks
logic modal-logic
asked Aug 22 '15 at 20:07
Applied mathematician
1,00342041
Basic question here but I cannot find the definition:
Given a modal logic and a set of propositions $P$, a model $M=(W,R,V)$ where $W$ are possible worlds, $R$ an accesibility relation and $V$ a valuation for every $pin P$
What is de definition of $(M,w)models varphi$?
And whats the name of it? Validity?
Thanks
logic modal-logic
logic modal-logic
asked Aug 22 '15 at 20:07
Applied mathematician
1,00342041
asked Aug 22 '15 at 20:07
Applied mathematician
1,00342041
asked Aug 22 '15 at 20:07
Applied mathematician
1,00342041
asked Aug 22 '15 at 20:07
Applied mathematician
1,00342041
asked Aug 22 '15 at 20:07
Applied mathematician
1,00342041
1,00342041
Have you looked at en.wikipedia.org/wiki/Modal_logic#Semantics ?
– mrp
Aug 22 '15 at 20:15
2
We say that $varphi$ is true at world $w$ in model $M$ (in symbols: $(M,w) vDash varphi$); we say that $varphi$ is true in model $M$ (in symbols: $M vDash varphi$) when $(M,w) vDash varphi$ for all $w in W$. We say that $varphi$ is valid ($vDash varphi$) when $M vDash varphi$ for every model $M$. See e.g : Edward Zalta, Basic Concepts in Modal Logic.
– Mauro ALLEGRANZA
Aug 22 '15 at 20:27
mauro thanks a lot
– Applied mathematician
Aug 23 '15 at 14:41
add a comment |
Have you looked at en.wikipedia.org/wiki/Modal_logic#Semantics ?
– mrp
Aug 22 '15 at 20:15
2
We say that $varphi$ is true at world $w$ in model $M$ (in symbols: $(M,w) vDash varphi$); we say that $varphi$ is true in model $M$ (in symbols: $M vDash varphi$) when $(M,w) vDash varphi$ for all $w in W$. We say that $varphi$ is valid ($vDash varphi$) when $M vDash varphi$ for every model $M$. See e.g : Edward Zalta, Basic Concepts in Modal Logic.
– Mauro ALLEGRANZA
Aug 22 '15 at 20:27
mauro thanks a lot
– Applied mathematician
Aug 23 '15 at 14:41
Have you looked at en.wikipedia.org/wiki/Modal_logic#Semantics ?
– mrp
Aug 22 '15 at 20:15
Have you looked at en.wikipedia.org/wiki/Modal_logic#Semantics ?
– mrp
Aug 22 '15 at 20:15
2
2
We say that $varphi$ is true at world $w$ in model $M$ (in symbols: $(M,w) vDash varphi$); we say that $varphi$ is true in model $M$ (in symbols: $M vDash varphi$) when $(M,w) vDash varphi$ for all $w in W$. We say that $varphi$ is valid ($vDash varphi$) when $M vDash varphi$ for every model $M$. See e.g : Edward Zalta, Basic Concepts in Modal Logic.
– Mauro ALLEGRANZA
Aug 22 '15 at 20:27
We say that $varphi$ is true at world $w$ in model $M$ (in symbols: $(M,w) vDash varphi$); we say that $varphi$ is true in model $M$ (in symbols: $M vDash varphi$) when $(M,w) vDash varphi$ for all $w in W$. We say that $varphi$ is valid ($vDash varphi$) when $M vDash varphi$ for every model $M$. See e.g : Edward Zalta, Basic Concepts in Modal Logic.
– Mauro ALLEGRANZA
Aug 22 '15 at 20:27
mauro thanks a lot
– Applied mathematician
Aug 23 '15 at 14:41
mauro thanks a lot
– Applied mathematician
Aug 23 '15 at 14:41
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
We write $(M,w) vDash varphi$ if $varphi$ is true at world $w$ in model $M$.
We say that $varphi$ is true in model $M$ (in symbols: $M vDash varphi$) when $(M,w) vDash varphi$ for all $w in W$.*
We say that $varphi$ is valid ($vDash varphi$) when $M vDash varphi$ for every model $M$.
(*) This terminology is a bit unfortunate since it means that most of the time, neither $varphi$ nor $negvarphi$ will be true in $M$.
Chellas, Brian F., Modal logic. An introduction, Cambridge etc.: Cambridge University Press. XII, 295 p. hbk: £ 17.50; pbk: £ 6.50 (1980). ZBL0431.03009.
answered Nov 18 at 5:56
Bjørn Kjos-Hanssen
1,876818
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
We write $(M,w) vDash varphi$ if $varphi$ is true at world $w$ in model $M$.
We say that $varphi$ is true in model $M$ (in symbols: $M vDash varphi$) when $(M,w) vDash varphi$ for all $w in W$.*
We say that $varphi$ is valid ($vDash varphi$) when $M vDash varphi$ for every model $M$.
(*) This terminology is a bit unfortunate since it means that most of the time, neither $varphi$ nor $negvarphi$ will be true in $M$.
Chellas, Brian F., Modal logic. An introduction, Cambridge etc.: Cambridge University Press. XII, 295 p. hbk: £ 17.50; pbk: £ 6.50 (1980). ZBL0431.03009.
answered Nov 18 at 5:56
Bjørn Kjos-Hanssen
1,876818
add a comment |
up vote
0
down vote
We write $(M,w) vDash varphi$ if $varphi$ is true at world $w$ in model $M$.
We say that $varphi$ is true in model $M$ (in symbols: $M vDash varphi$) when $(M,w) vDash varphi$ for all $w in W$.*
We say that $varphi$ is valid ($vDash varphi$) when $M vDash varphi$ for every model $M$.
(*) This terminology is a bit unfortunate since it means that most of the time, neither $varphi$ nor $negvarphi$ will be true in $M$.
Chellas, Brian F., Modal logic. An introduction, Cambridge etc.: Cambridge University Press. XII, 295 p. hbk: £ 17.50; pbk: £ 6.50 (1980). ZBL0431.03009.
answered Nov 18 at 5:56
Bjørn Kjos-Hanssen
1,876818
add a comment |
up vote
0
down vote
up vote
0
down vote
We write $(M,w) vDash varphi$ if $varphi$ is true at world $w$ in model $M$.
We say that $varphi$ is true in model $M$ (in symbols: $M vDash varphi$) when $(M,w) vDash varphi$ for all $w in W$.*
We say that $varphi$ is valid ($vDash varphi$) when $M vDash varphi$ for every model $M$.
(*) This terminology is a bit unfortunate since it means that most of the time, neither $varphi$ nor $negvarphi$ will be true in $M$.
Chellas, Brian F., Modal logic. An introduction, Cambridge etc.: Cambridge University Press. XII, 295 p. hbk: £ 17.50; pbk: £ 6.50 (1980). ZBL0431.03009.
answered Nov 18 at 5:56
Bjørn Kjos-Hanssen
1,876818
We write $(M,w) vDash varphi$ if $varphi$ is true at world $w$ in model $M$.
We say that $varphi$ is true in model $M$ (in symbols: $M vDash varphi$) when $(M,w) vDash varphi$ for all $w in W$.*
We say that $varphi$ is valid ($vDash varphi$) when $M vDash varphi$ for every model $M$.
(*) This terminology is a bit unfortunate since it means that most of the time, neither $varphi$ nor $negvarphi$ will be true in $M$.
Chellas, Brian F., Modal logic. An introduction, Cambridge etc.: Cambridge University Press. XII, 295 p. hbk: £ 17.50; pbk: £ 6.50 (1980). ZBL0431.03009.
answered Nov 18 at 5:56
Bjørn Kjos-Hanssen
1,876818
answered Nov 18 at 5:56
Bjørn Kjos-Hanssen
1,876818
answered Nov 18 at 5:56
Bjørn Kjos-Hanssen
1,876818
answered Nov 18 at 5:56
Bjørn Kjos-Hanssen
1,876818
1,876818
add a comment |
add a comment |
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.
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%2f1406251%2fwhat-the-definition-of-validity-of-a-formule-in-a-possible-kripke-world-in-modal%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
Have you looked at en.wikipedia.org/wiki/Modal_logic#Semantics ?
– mrp
Aug 22 '15 at 20:15
2
We say that $varphi$ is true at world $w$ in model $M$ (in symbols: $(M,w) vDash varphi$); we say that $varphi$ is true in model $M$ (in symbols: $M vDash varphi$) when $(M,w) vDash varphi$ for all $w in W$. We say that $varphi$ is valid ($vDash varphi$) when $M vDash varphi$ for every model $M$. See e.g : Edward Zalta, Basic Concepts in Modal Logic.
– Mauro ALLEGRANZA
Aug 22 '15 at 20:27
mauro thanks a lot
– Applied mathematician
Aug 23 '15 at 14:41