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*From*: Apostolis Xekoukoulotakis <apostolis.xe...@xxxxxxxxx>*Date*: Sun, 11 Nov 2018 06:37:44 +0200*References*: <a9da40e6-492d-4ca7-89a5-1ca10bc44796@googlegroups.com> <C9866991-C155-4FAB-A462-6E381AC29208@gmail.com> <c2c27b65-0fb1-407d-948d-6194dbd1b335@googlegroups.com> <CAFEV_-gVYQbSZ6vzaZy6z5zcxF6DGKmvk7ZSC2eVb7_d2fMXMQ@mail.gmail.com> <18199B06-496C-4AC6-861E-B1CB95412185@gmail.com>

Ok, let me try to learn something.

According to Jim Pryor(1) ,

"The **extension** of a term is the set of things which it picks out in the world, as the world actually is."

The terms "Leslie Lamport" and "the inventor of TLA" have the same extension , because both of them refer to the same person.

"A sentence fragment "___ is such-and-such" counts as **extensional**
just in case filling in the blank with different terms having the same
extension will always result in sentences with the same truth-value."

In our case, the sentence " __ is the winner of the 2013 Turing award." is extensional. Both "Leslie Lamport" and "the inventor of TLA" have the same truth value.

On the other hand, the sentence "It is necessary that __ is a man." is intensional becuase the inventor of TLA could have been a woman.

Now, to do the same for TLA, I would say that the extension of a tla _expression_ is the one we get by replacing all defined operators by their definitions.

Since the truth value of an _expression_ is determined by the truth value of the primitive operators and variables , constants , two expressions with the same extension have the same truth value.

On Fri, Nov 9, 2018 at 10:09 AM Stephan Merz <stepha...@xxxxxxxxx> wrote:

I was referring to "intensional logics" [1]. Just as standard mathematical logic and as pointed out by Leslie, TLA+ is extensional, i.e. the meaning of TLA+ formulas is defined by the interpretations ("designations") of symbols.--Stephan[1] https://plato.stanford.edu/entries/logic-intensional/On 8 Nov 2018, at 21:06, Apostolis Xekoukoulotakis <apostolis.xe...@xxxxxxxxx> wrote:Functional extensionality is the property of being able to prove that two functions f , g are equal if for every x in their "domain" , f x = g x .In current dependent type languages, this is not possible to prove. There might be other more general uses of the term "extensional" and "intensional".By "Inheritance" I meant that a property P is true for A if and only if P is true for B.I was a bit lazy.On Thu, Nov 8, 2018 at 9:15 PM Leslie Lamport <tlapl...@xxxxxxxxx> wrote:I'm not a logician, so I don't know what Stephan means by

"extensionally" and "intensional" here. Also, I don't know what you

mean by your statement that "fairness properties on action A will also

be inherited by action B".The meaning of any _expression_ exp in a TLA+ module is the _expression_

obtained by (recursively) replacing all defined operators in exp by

their definitions. This implies that the meaning of exp is a formula

containing only the constants and variables declared in the module and

the primitive TLA+ operators. If you defineA == defA

B == defBwhere defA and defB are equivalent expressions, then replacing "A" by "B"

in any _expression_ does not change the meaning of that _expression_."Leslie Lamport" and "the inventor of TLA" are two different names for

me. Would you say that properties of Leslie Lamport areinheritedby

the inventor of TLA? It's not how I would use the term "inherited",

but I don't claim to be an expert on the meaning of English words.The Inventor of TLA

On Thursday, November 8, 2018 at 9:50:20 AM UTC-8, Stephan Merz wrote:TLA+ actions are defined "extensionally" by formulas evaluated over pairs of states. If two action formulas A and B are equivalent, then so are WF_v(A) and WF_v(B), and any execution satisfying one of these formulas also satisfies the other one. There is no "intensional" notion of actions that would differentiate between two equivalent action formulas.

If the distinction is important, for example for identifying the server executing the action, you will have to make the distinction explicit in your specification, for example by including the server identity as a parameter of the action.

Regards,

Stephan

> On 8 Nov 2018, at 15:30, apostolis.xekoukoulotakis wrote:

>

> Consider the case that we have two actions which are identical, they have the same conditions for triggering them and the same restrictions on the "next" step in case we don't have stuttering.

>

> From what I understand, any fairness properties on action A will also be inherited by action B. In other words, either both actions are triggered or none.

>

> Which means that from a meta-theoretic point of view, you can not attach a specific action to a specific entity, like a program, or a specific server etc.

>

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**Follow-Ups**:**Re: [tlaplus] How to determine an Action execution.***From:*Jorge Adriano Branco Aires

**References**:**How to determine an Action execution.***From:*apostolis . xe . . .

**Re: [tlaplus] How to determine an Action execution.***From:*Stephan Merz

**Re: [tlaplus] How to determine an Action execution.***From:*Leslie Lamport

**Re: [tlaplus] How to determine an Action execution.***From:*Apostolis Xekoukoulotakis

**Re: [tlaplus] How to determine an Action execution.***From:*Stephan Merz

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