Talk:Accessibility relation

5 and E

The five axiom is also known as the E axiom im many texts. Especailly over here in Italy. But it's no big deal--Lacatosias 16:23, 20 February 2006 (UTC).

Paragraph missing?

Is there a paragraph (the most important one) missing? First paragraph is "Basic review of (propositional) modal logic", second is "Importance of AR in formal semantics".

The article explains the importance and applications of AR, but does not say what it actually is, which I would find very interesting, especially in an article about AR :P

132.231.54.1 12:22, 30 March 2007 (UTC)

Reflexivity basic or not?

Question: I was taught that the following two forms are equivalent expressions of the reflexivity axiom, given standard dual definitions of box and diamond:

if p then diamond-p

and

if box-p then p

So I don't see why the first, diamond form is given in the list of the "six basic" axioms that are treated as uncontroversial, whereas the second, box form, is put in the list of optional, controversial axioms, as the axiom equivalent to reflexivity of access-relations.

Probably I'm missing something, but proof-theoretically, isn't it trivial to deduce either from either, given the inter-definition of box and diamond? And model-theoretically, isn't the diamond form that is listed among the basic axioms already characteristic of all and only reflexive models? (I mean, unless I'm missing something, I don't see how it can be an axiom unless we're restricting ourselves to reflexive models.)

Nice article in general, but this caught my eye as a potential glitch. —Preceding unsigned comment added by 71.127.179.179 (talk) 16:10, 28 January 2008

I see that this was changed in March. Good! But I don't agree with the use of the word "controversial". Surely all the axioms are widely used in different systems? --Spug (talk) 20:02, 10 May 2010 (UTC)

Something's missing

I cannot see that "accessible" is defined or informally described anywhere, it is just assumed, and then "accessibility" between two worlds w and w' is defined. ... said: Rursus (bork²) 10:32, 15 January 2009 (UTC)

Heh! Yes, unfortunately this article is almost useless. The Stanford encyclopedia article on modal logic is much better (though it does not explain accessibility relations either). Part of the problem is that the language of modal logic was specifically designed to be as general as possible. This means, in practice, that the terms are as empty as possible. An accessibility relation R, is some arbitrary relationship between two possible worlds, w and w'. That relationship is binary, either true or false. If the relationship is true, then w' is accessible from w. Otherwise, w' is not accessible from w. You might decide that R(w,w') is true if both w and w' are members of the set of possible worlds. In the normal case, every single world is possible, so R(w,w') is always true. In temporal logic, you might decide that R(w,w') is true if w is a time that comes before w' (this only makes sense if the worlds w and w' represent points in time), so that only future times are accessible from a given time. — Preceding unsigned comment added by 107.3.37.113 (talk) 10:28, 27 May 2013 (UTC)

and and or

In the second paragraph, the "a" and "o" in "and" and "or" are accented as you would accent a letter in Spanish, rather than having both words in scare quotes. If an editor could fix that, it would read better. I really liked the article. A great job editing. :-) — Preceding unsigned comment added by 70.72.44.213 (talk) 04:52, 22 May 2012 (UTC)

Can this Article be Write Protected?

I remember making several changes to the article a while back, and others have changed these with bad editing, like not capitalizing letters or removing scare quotes. Could this article be write protected (I believe that's the term) so that only some people may make changes to it?

70.72.44.213 (talk) 02:23, 23 May 2012 (UTC)

Comment

I originally wrote the comment about the accessibility relation but it was edited by someone else. Now it reads awkwardly and I don't like it. I think the article is write protected, so if the person who edited the article is out there listening, it is worthing revising that section. I'd like to re-write it myself.

70.72.45.98 (talk) 04:08, 8 November 2012 (UTC)

Errors

The article is riddled with errors, some at a sub-undergraduate level. For example, the Earth is not a possible world, but the universe. the Earth is one planet within the world. Again, a possible world is not a situation; a possible situation is a set of possible worlds. This is one more reason that I have to order undergraduates not to use Wikipedia; it's not just that it gets things wrong (that can be said to be true of any book or paper), but that it gets things wrong so badly. --146.90.84.86 (talk) 12:52, 16 November 2012 (UTC)

Almost unreadable, full of OR, and seems to be wrong wherever I can understand it.

Only a small section of the article, "The Four Types of the 'Accessibility Relation' in Formal Semantics", is actually about accessibility relations. And it's almost entirely wrong.

Even before we get to that, the whole thing is a mess. For example, in reviewing modal logic, the article says:

There are at least six basic axioms or principles of almost all modal logics or steps in thinking/reasoning. The first two hold in all regular modal logics, and the last holds in all normal modal logics.

It then goes on to list 5 axioms (describing 2 in detail, and just throwing the other 3 out in symbolic form), plus another 4 "controversial" axioms. Where does the "six" come from? Did you forget one? Add three extras? At any rate, it's the fifth that holds in all normal logics, not the last.

Getting to the actual relevant part of the article, let's look at a few of the explanations.

For reflexive:

This says that if every world is accessible to itself, then any world in which A is true will be a world from which there is an accessible world in which A is true.

Nope. The reflexive axiom says that every world is accessible to itself. And, if you put that axiom together with this statement, you get A->MA, not the LA->A of axiom (T).

For transitive:

This says that R is transitive, LA is true at a world w only when A is true at every world w' accessible from w.

No, that's the definition of necessity, not transitivity. Continuing:

Hence, LLA is true at a world w only when A is true at every world accessible from every world w' accessible from w.

So you've argued for LLA->LA, rather than for LA->LLA, getting axiom (4) backward.

Also, the first three definitions ends with "Notice that this is a variation, more detailed description of the 'necessity' definition above." I have no idea what that means, but again, I can't think of a reading that makes it true.

The "Comment about the 'Accessibility Relation'" is almost entirely OR. First it briefly describes Lewis's "key innovation", then there's a massive barely-coherent paragraph that seems to be arguing that Lewis has no idea what he's talking about. Then there's a brief discussion of what Kripke might say to counter this OR, followed by another long paragraph saying that straw-man Kripke is an idiot.

I read this article as a brief refresher, but I think the net effect was instead to confuse or even erase large swaths of my knowledge. --70.36.140.230 (talk) 09:55, 20 November 2012 (UTC)

Discussion of possible worlds

The definition 'possible worlds' has some problems.

e.g. "Earth one minute from now is a 'possible world.'" Possible worlds are not (on any philosopher's account) planets, and the actual world≠Earth. Rather, planets are particular objects that exist at a world (just like any other particular objects). Also, possible worlds are not limited to particular temporal instants, so "one minute from now" doesn't make any sense here either.

I'm not sure off the top of my head what the best way to concisely and intuitively explain possible worlds would be, since there are various ways that philosophers understand them. But the way they are discussed at present is somewhat confused and misleading in important ways.

138.16.123.51 (talk) 22:02, 14 September 2016 (UTC) Rachel

This complaint, and the litany of 2012 complaints, appear to have been fixed in a sequence of July 2020 edits. 67.198.37.16 (talk) 16:24, 28 August 2021 (UTC)

References