PDL without converse operator -
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I found this exercise (5.14) in the book "Dynamic Logic" by Harel, Kozen and Tiuryn. I have no clue how to construct the mentioned model in the exercise body.
Construct the Kripke model, such that the operator $<alpha>$ is not continous.
In PDL with - (converse operator), the map $phi rightarrow <alpha>phi$ is continuous with respect to the order of logical implication. That is, if $K$ is a Kripke frame, $A$ a (finite or infinite) set of formulas, and $phi$ a formula such that $m_K(phi) = sup_psi in Am_K(psi)$ then $sup_psi in Am_K(<alpha>psi)$ exists and is equal to $m_K(<alpha>phi)$.
We define $m_K(psi)$ as a set of states in $K$ satisfying formula $psi$.
If program $alpha$ maps state $s_1$ to state $s_2$ then program $alpha-$ ($alpha$ with converse operator) maps $s_2$ to $s_1$.
logic graph-theory modal-logic
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I found this exercise (5.14) in the book "Dynamic Logic" by Harel, Kozen and Tiuryn. I have no clue how to construct the mentioned model in the exercise body.
Construct the Kripke model, such that the operator $<alpha>$ is not continous.
In PDL with - (converse operator), the map $phi rightarrow <alpha>phi$ is continuous with respect to the order of logical implication. That is, if $K$ is a Kripke frame, $A$ a (finite or infinite) set of formulas, and $phi$ a formula such that $m_K(phi) = sup_psi in Am_K(psi)$ then $sup_psi in Am_K(<alpha>psi)$ exists and is equal to $m_K(<alpha>phi)$.
We define $m_K(psi)$ as a set of states in $K$ satisfying formula $psi$.
If program $alpha$ maps state $s_1$ to state $s_2$ then program $alpha-$ ($alpha$ with converse operator) maps $s_2$ to $s_1$.
logic graph-theory modal-logic
1
what is the converse operator?
â Apostolos
Aug 26 at 16:08
I have added the definition of converse operator.
â Adam Mata
Aug 26 at 17:24
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I found this exercise (5.14) in the book "Dynamic Logic" by Harel, Kozen and Tiuryn. I have no clue how to construct the mentioned model in the exercise body.
Construct the Kripke model, such that the operator $<alpha>$ is not continous.
In PDL with - (converse operator), the map $phi rightarrow <alpha>phi$ is continuous with respect to the order of logical implication. That is, if $K$ is a Kripke frame, $A$ a (finite or infinite) set of formulas, and $phi$ a formula such that $m_K(phi) = sup_psi in Am_K(psi)$ then $sup_psi in Am_K(<alpha>psi)$ exists and is equal to $m_K(<alpha>phi)$.
We define $m_K(psi)$ as a set of states in $K$ satisfying formula $psi$.
If program $alpha$ maps state $s_1$ to state $s_2$ then program $alpha-$ ($alpha$ with converse operator) maps $s_2$ to $s_1$.
logic graph-theory modal-logic
I found this exercise (5.14) in the book "Dynamic Logic" by Harel, Kozen and Tiuryn. I have no clue how to construct the mentioned model in the exercise body.
Construct the Kripke model, such that the operator $<alpha>$ is not continous.
In PDL with - (converse operator), the map $phi rightarrow <alpha>phi$ is continuous with respect to the order of logical implication. That is, if $K$ is a Kripke frame, $A$ a (finite or infinite) set of formulas, and $phi$ a formula such that $m_K(phi) = sup_psi in Am_K(psi)$ then $sup_psi in Am_K(<alpha>psi)$ exists and is equal to $m_K(<alpha>phi)$.
We define $m_K(psi)$ as a set of states in $K$ satisfying formula $psi$.
If program $alpha$ maps state $s_1$ to state $s_2$ then program $alpha-$ ($alpha$ with converse operator) maps $s_2$ to $s_1$.
logic graph-theory modal-logic
edited Aug 26 at 17:24
asked Aug 26 at 14:03
Adam Mata
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386
1
what is the converse operator?
â Apostolos
Aug 26 at 16:08
I have added the definition of converse operator.
â Adam Mata
Aug 26 at 17:24
add a comment |Â
1
what is the converse operator?
â Apostolos
Aug 26 at 16:08
I have added the definition of converse operator.
â Adam Mata
Aug 26 at 17:24
1
1
what is the converse operator?
â Apostolos
Aug 26 at 16:08
what is the converse operator?
â Apostolos
Aug 26 at 16:08
I have added the definition of converse operator.
â Adam Mata
Aug 26 at 17:24
I have added the definition of converse operator.
â Adam Mata
Aug 26 at 17:24
add a comment |Â
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1
what is the converse operator?
â Apostolos
Aug 26 at 16:08
I have added the definition of converse operator.
â Adam Mata
Aug 26 at 17:24