Talk:Modal logic

message: This article says these are equivalent, but the entry for Kripke semantics specifically says they are not in the very first sentence of its entry.  — Preceding unsigned comment added by 70.117.17.114 (talk) 19:40, 5 June 2016 (UTC)
thread_title:  Kripke semantics and possible world semantics 

message: The following is mostly a note to myself, but comments are welcome.  
To add
Wikipedia currently says nothing about the following items, which should go either here or in kripke semantics:
* The TRIV modality (where p <=> []p);
* Standard non-normal modal logics: S1-S3, E1-E5.
* S5 is a maximal modality;
* Bimodal logics, eg. S4*S4, S5*S5;
* Proof theory of modal logic: sequent systems, need for other systems, link to geometric theories
* Taxonomy of normal modal logics: Lemmon-Scott axioms.
* I think hybrid logic is well enough established to deserve a treatment
* Quantified modal logic, Barcan axiom, problem of quantifying-in
* Dynamic logic is important enough to deserve a short discussion on the main page
* Provability logic needs more discussion
To change
*Introduction of frame semantics very disjointed: should have normal modal logics introduced in this article, and frame semantics introduced the section following the idea of possible worlds interpretations.
*Temporal logic and tense logic are not the same thing
*The system most commonly used today is modal logic S5 -- how on earth can one tell?  S4 is pretty heavily used, and sees the most comp sci applications.
*Link to semantics of logic
Enough for now... ---- Charles Stewart 08:51, 16 Sep 2004 (UTC)
thread_title: To Dos

message: I removed the comment that "A new Introduction to Modal Logic" superseeds the other two Hughes and Cresswell works.
That was the original intension, but there is a lot in "An introduction to Modal Logic" that never made it into
the New Introduction.
Re: Publisher of Zeman's modal logic:
The copy of the book in front of me lists D. Reidel Publishing as the publisher.
Note that the web page Dr. Zeman maintains says the Original publisher was Oxford.
:Might this mean that there were different publishers in different countries, with OUP being who Zeeman gave his manuscript to? --- Charles Stewart 21:28, 25 October 2005 (UTC)
replies: text:  Possibly, that is not a subject we've cooresponded on.  But note that the book is copyright 1966, and the web pages have his copyright 1973-200, so I'm sure that there is an interesting story there.
The link to dynamic logic needed to be disambiguated. I haven't tested the other links to see if they go to the right place. Greg Woodhouse 22:46, 30 November 2006 (UTC)
thread_title:  Recent changes: 

message: There are some interesting statments of history there.  I think there is some confusion, and an odd bias here.
Lewis's 1918 work "A survey of Symbolic Logic" (University of California Press, Berkeley) was a followup on his articles in "Mind" and "Journal of Philosophy" (as his 1918 itself work points out). He even gave an axiom set in one earlier paper.  (So the 1918 paper shouldn't be cited as the start.)  Note that it is a survey of Symbolic Logic, not a survey of Modal Logics.  It introduces one recognisably modal system, the "Logic of Strict Implimentation, that was generally refered to as "Lewis' S system".
But even then, he wasn't the only one working on a calculus of strict implication...  Others were also working on the same problem in responce to Russell and Whitehead's "Principia Mathematica".   The journals of the time have many articles on the efforts to find a "real" implicational logic by people unhappy with Russell and Whiteheads "material implication".
[And of course, Lewis admited in his "Strict Implication, An Emendation</i>" in  the "Journal of Philosophy, and Scientific Method" (XVII [1920, p300])) that the axiom set in 1918 was flawed (in Responce to E.L. Post's proof that it had the generated theorem "possibly p is equivalent to p".
(And Lewis provided a fix for the problem.)
On page 292 of the 1918 work credited the basic ideas to MacColl's "Symbolic Logic and its Applications."
Note that as late as 1920 paper it was just "Lewis's system S".  The series S1 through S5 were introduced in Lewis and Langfords 1932 "Symbolic Logic".  At that point the "System of Strict Implication" of the 1918 paper was renamed to be S3.  [Still the most interesting of the set to my mind.]
In 1918 his system was based on an indivisible "impossiblity" operator.
By 1932 he was using possibility as an operator, with impossibility being the negation of that operator, and he had the basic Lewis Systems.
Kurt Gödels papers were key in changing the view from Lewis' "impossiblilty" based axioms
to the current "Necessity" based axioms.  [Edit:  And Gödel introduced using a basis of PC + modal axioms, instead of modal axioms from which PC could also be proved.]
Note that the main history from 1936 on is on line at the various Journal's web pages.
Some history of the 1918 system is covered on my page http://www.cc.utah.edu/~nahaj/logic/structures/systems/s.html which I'm currently working on.
If I hear no objections, I'll make a major edit adding the historical context that Lewis' work grew out of.  [The goal was, after all, a legitimate calculus of strict entailment, not a modal logic... those just grew out of the effort. Nahaj 03:24, 28 October 2005 (UTC)
replies: text: If you are calling it a calculus of strict *entailment*, then I already object with any changes you might make. Nortexoid 05:16, 28 October 2005 (UTC)
replies: text: I agree, strict implication is the normal term. --- Charles Stewart 14:25, 28 October 2005 (UTC)

text:   I had trouble figuring out what the "it" in your sentence refered to.  I'm guessing you mean it to mean Modal Logic.   I don't call modal logic such a calculus.  But modal logic *DID* come out of attempts to develop such a calculus.  The original Lewis systems *WERE* by his direct statement such calculi. Nahaj 13:27, 28 October 2005 (UTC)
replies: text: It was supposed to formally capture a notion of *implication*, not entailment. Nortexoid 14:20, 28 October 2005 (UTC)

text: Please go ahead.  This material sounds interesting. --- Charles Stewart 04:04, 28 October 2005 (UTC)
replies: text:  I'm still researching MacColl's work. If Lewis thinks the main ideas of his work trace there (as he says he does), then at least a mention is needed. Nahaj 13:27, 28 October 2005 (UTC)
replies: text: I'm researching MacColl at the moment for an Algebraic Logic account, and MacColl's influence on Lewis is something that might go into the story there.  Maybe we should exchange notes.  Most of the sources I am using are in the algebraic logic point at User:Chalst/tasks. --- Charles Stewart 14:25, 28 October 2005 (UTC)

text:  I'm reading his series on "Symbolic Reasoning" in "Mind" (A series that appeared from the 1890's to 1900's). I'm availiable through email if you want to discuss the topic in a non-public forum. Nahaj 15:57, 28 October 2005 (UTC)
thread_title:  History. 

message: Is there a difference between LTL and PLTL? -- Neatlittleeraser 13:17, 6 July 2006 (UTC)
replies: text: LTL usually means the propositional variant, although there is a quantified version, QLTL. — Charles Stewart (talk) 10:18, 17 March 2009 (UTC)
thread_title:  PLTL and LTL 

message: Is this a correct example? 
Let me explain why I am in doubt: it's very well possible that 2 + 2 = 0. We can either define a number system in which the same symbols as we're used to represent different quantities and the identity might hold. Or we could work in the numbers modulo 4. Or we could work in some group where "2 + 2" is the group operation, which happens to be denoted by the symbol +, applied to some element, which happens to be denoted by the symbol 2. My point is: the statement is only necessarily true given the proper axioms and definitions (or: given the appropriate context) in which case it is necessarily true because if follows from those axioms and definitions (which is exactly against the point the original author is trying to make, if I understand correctly). Without such context, one could argue both "2 + 2 = 4" and "2 + 2 = 6" to be logically necessary. --CompuChip 14:44, 15 November 2006 (UTC)
replies: text: Recent developments in modal logic attempt to address these concerns (e.g., 2-dimensionalism) and should be included in this article. Your right, we have to say, "given our semantics for 2, +, = and 4, "2 + 2 = 4" could never be false, in any possible world. But there could conceivably be a possible world (even a possible language in this world) where these symbols have different meanings, and where "2 + 2 = 4" comes out false. Thus, there are multiple propositions expressed by any given sentence (esp. when you consider possible worlds), but when we assume one of these propositions as expressed, we can talk meaningfully about necessity (see Chalmers, David. The Conscious Mind pp. 56-69).--Heyitspeter (talk) 19:51, 16 March 2009 (UTC)
replies: text: I agree about the indeterminacy regarding the relation of expressions to propositions, but (i) when one says P is necessarily true, one talks about the proposition that we understand the expression to be, not whatever proposition one might counterfactually conceive to be be understood. And (ii) there is of necessity some "charity of interpretation" going on here, where symbols should be interpreted by us in the usual way; one is not a constructive participant in the conversation if one says "But when I was using those alethic modalities, I was talking of the degenerate interpretation of possibility, where the only possibility is actuality".  If one wishes to use symbols in a nonstandard way without being a nuisance, one must advertise the fact.  One is violating more than one of Grice's maxims if one does not. — Charles Stewart (talk) 10:32, 17 March 2009 (UTC)
replies: text: Eh, the charity of interpretation goes both ways. CompuChip is talking about, for example, a vector space where "1+1=1." You don't advertise that this is a vector space where the symbols are used in a non-standard way. You just deduce it. "1+1=1" is a true proposition in some mathematical environment (so "1+1≠1" is false in some mathematical environment). The 1s can be interpreted (really deduced) to be 0-vectors. But "1+1≠1" sure seems necessarily true when we take the symbols to have their usual contents. That is to say, given one usage of the terms, "1+1=1" is a statement that expresses a necessarily true proposition. However, given another usage, "1+1=1" expresses a false proposition. That's 2-dimensionalism in a nutshell (clumsily). There are two levels of necessity: deep and superficial. "1+1≠1" is deeply necessary when we fix its meaning. But "1+1≠1" is superficially contingent, because it can be false under some possible interpretation. --Heyitspeter (talk) 11:02, 17 March 2009 (UTC)

text: Sure, but outside of a context where we don't draw attention to the possibilities for rival interpretations, there is a strong convention that we are talking about the proposition determined by the meaning conventionally used by the relevant language community.  Sure one can say "look what happens when I vary the interpretation", however to say "that's nonsense!" because of the possibility of rival interpretations is problematic. — Charles Stewart (talk) 11:18, 17 March 2009 (UTC)
replies: text: Ahh, yeah. I see what you mean. So the two-dimensionalist (usually) would agree with you, that the cognitive content of a proposition is its primary content (the fixed meaning, not the possible one). But he or she would also claim that the secondary content is important, and not trivial. It's supposed to explain how "2+2=4" is necessary, but appears contingent, because of the possible propositions it can be taken to express. It sounds like you would agree with this. I'm sorry if I've been really muddled in my explications, it's late here...--Heyitspeter (talk) 11:35, 17 March 2009 (UTC)

text: Right.  I guess the 2d semantics is more relevant to the rigid designator article than here, though this article should have something about that, since it is so crucial to the interpretation of mode in natural language by modal logic. — Charles Stewart (talk) 14:51, 17 March 2009 (UTC)
replies: text: Haha yeah I think you're right. It is kind of secondary to this article. I think I just saw this guy's question and was like, "wow, that is something important to discuss (in general), we should talk about that!" without really thinking about relevancy. --Heyitspeter (talk) 19:13, 17 March 2009 (UTC)

text: And they would not be necessary if we chose to use 'necessary' in some way other than it is usually used, even if all of the numerals and the entire symbolism of arithmetic is given its intended interpretation. But that does not make '2+2=4' not necessary; it's called changing the subject. The sentence is necessary under the standard interpretation of the symbolism of arithmetic. That's what we mean when we say it's necessary. We don't mean under every interpretation of the symbolism, as that is obviously false, and not very interesting. Nortexoid 20:57, 15 December 2006 (UTC)
replies: text:  It really isn't trivial, though. e.g., suppose "water = watery stuff"; that this is just what water is. That's an a priori truth. We don't have to look at the world to know it. But now suppose there is another world where the watery stuff isn't the same as the watery stuff in our world (where mercury has watery qualities, and our water [H20] doesn't). This world is possible, which means that "water = watery stuff" isn't necessarily true, because the stuff we call water isn't necessarily watery stuff. There is some possible world where our fixed meaning of water isn't watery. So "water = watery stuff" is an example of an a priori contingent truth, and it is so because different interpretations can be had for the same symbols. --Heyitspeter (talk) 20:09, 16 March 2009 (UTC)

text: That's a typical ascii representation, yes, but many texts and articles actually use a square rotated 45% and not a thin rhombus. Simões (talk/contribs) 17:51, 30 March 2007 (UTC)
thread_title:  ''Logically necessary'' example 

message: I'd like to see a section or page for Doxastic logic. Gregbard 00:06, 29 June 2007 (UTC)
replies: text: Be bold, add one. :) If you need them, I can probably dig up a non-web print reference two I could point you at.  Send email, I have frequently gone months without signing on here.] And for web references, have you checked out Professor Peter Suber's site? He (among other things) collects information of many many different types of logics. Nahaj 21:10, 20 September 2007 (UTC)
thread_title: Doxastic logic

message: I have changed the system name T in the article to upper case.   No modal logic book in my collection lists it as lower case.  (For example, Hughes and Cresswell's "Introduction to Modal Logic", Brian Challas' Introduction, Fey's Introduction... [fuller list upon request])  In addition the articles in "The Journal of Symbolic Logic" and in the "Notra Dame Journal of Formal Logic" also have it upper case. [Specific examples upon request].   In the two years since I challenged the lower case claim above, nobody has yet given a single reference that supports the claim that it is usually lowercased.   So, I think it is fair to say that the lower case usage is NOT standard, and the upper case usage is. Nahaj 23:38, 18 September 2007 (UTC)
thread_title:  Lower case T 

message: From the article:  
Metaphysical possibility is generally thought to be stronger than bare logical possibility (i.e., fewer things are metaphysically possible than are logically possible). Its exact relation to physical possibility is a matter of some dispute. Philosophers also disagree over whether metaphysical truths are necessary merely "by definition", or whether they reflect some underlying deep facts about the world, or something else entirely.
If philosophers disagree about whether or not metaphysically true is the same as true by definition, it seems unlikely that they have come to a consensus about whether metaphysical possibility differs from logical possibility.  Phrenophobia 07:15, 7 November 2007 (UTC)
thread_title:  A contradiction? 

message: I've uploaded an english version of a schema used on the french article. You may want to use it, or not. There are Kripke models schemata in the Kripke semantics article as well, tell me (here, because I don't watch pages on the english WP) if you want SVG versions in english. --Eusebius en (talk) 10:07, 21 September 2008 (UTC)
thread_title:  Schemata 

message: The article included the claim that all contingent propositions are actually true, but this does not accord with current usage. I have therefore changed the wording to this:
:
Among the copious evidence for this usage are these sources: , , , , , and .
I have also changed a piped wikilink to read "physical laws", since physical possibility is defined in terms of physical laws and not natural laws. A minority of philosophers, such as David Chalmers, hold that there is a difference. While we may not agree (I don't!), the notional distinction ought to be maintained. After all, we maintain other distinctions, between metaphysical and logical necessity for example – which Chalmers himself claims amount to the same.
Elsewhere I have changed wording for strict propriety, so that the term possible is not itself used in examples to show the difference between alethic possibility and epistemic possibility. That is bound to confuse people needlessly.
–⊥¡ɐɔıʇǝoNoetica!T– 10:24, 4 February 2009 (UTC)
thread_title:  A change concerning contingent propositions, etc. 

message: *(v.1) It seems reasonable to say that possibly it will rain tomorrow, and possibly it won't; on the other hand, seeing as how we can't change the past, if it rained yesterday, it cannot be quite correct to say "It may not have rained yesterday." 
*(v.2) It seems reasonable to say that possibly it will rain tomorrow, and possibly it won't; on the other hand, if we know that it rained yesterday, then it cannot be quite correct to say "It may not have rained yesterday."
So I changed v.2 to v.1, and it was reverted because it was asserted that v.1 was problematic, as it does not explicitly state that we know something about the past. Just want to point out that this is a conditional (if it rained yesterday, it cannot be quite correct to say "It may not have rained yesterday"), so it doesn't matter whether we know that the antecedent is true or not. For example, "if P and not-P, then every proposition is true." We know this conditional to be true, even though we can never know that the antecedent is true, because the antecedent is never true. So it doesn't matter whether we know anything about the past. The point is, if x happened (note the past tense), then x necessarily happened. We don't need to know anything about the past to see that this statement is true (of course, it may not be true, but our knowledge of the past has nothing to do with it). Possible problems crop up because the statement is ambiguous as to whether or not the consequent involves a subjective statement or a proposition. I'll change it a bit to avoid this. I figure: 
*(v.3) It seems reasonable to say that possibly it will rain tomorrow, and possibly it won't; on the other hand, seeing as how we can't change the past, if it rained yesterday, it probably isn't true that it may not have rained yesterday. 
Happy editing :) ---Heyitspeter (talk) 21:54, 14 March 2009 (UTC)
thread_title: Little conflict resolution

message: I don't feel strongly about this and in fact I have barely looked at the article. It's just that I think talking about facts in the past that we may not know about introduces unnecessary complications that distract from the main point. It's quite possible that I don't know whether it rained yesterday, so in natural language "It may not have rained yesterday." is a perfectly valid sentence. --Hans Adler (talk) 22:01, 14 March 2009 (UTC)
replies: text: Ahh I see what you're saying. You're trying to include sentential operators (For all x knows that: ). "For all I know, it didn't rain yesterday" can be true even if it actually did rain yesterday, so you would need actual knowledge of the antecedent to force the consequent (i.e., I know it didn't rain yesterday, so it actually didn't rain yesterday). But when you drop these epistemic modal operators you get a different story. If it rained yesterday, it is not possible that it did not rain yesterday (whether we know it rained or not). Your analysis is correct if you assume that these statements are epistemic, but it isn't if we don't assume that they're epistemic. And we don't want to, because we want to talk about the world, and not about our conception of it. That's kind of cheating, and one could argue that there are no non-epistemic propositions, but that's kind of not in question here. What do you think? EDIT: I think we posted responses to each other at the same time, so they ended up as two different sections (see above). --Heyitspeter (talk) 22:12, 14 March 2009 (UTC)
replies: text: I stopped thinking. I am not at all familiar with modal logic, and it seems it's too late for me (hourwise) to learn what "epistemic" means so I have a chance to respond in a meaningful way. Sorry for having bothered you. I will simply trust that you know what you are doing. --Hans Adler (talk) 23:03, 14 March 2009 (UTC)
replies: text: Hey it's not a bother or anything, in any way. The point you made was right, even. For now, get some sleep, haha, but please read this over tomorrow and see if you still think I've made a bad move. I'd be happy to hear about it.--Heyitspeter (talk) 23:19, 14 March 2009 (UTC)

text: p.s. the section on 'epistemic logic' in this article clarifies a lot of these issues.--Heyitspeter (talk) 23:27, 14 March 2009 (UTC)
thread_title:  yesterday's rain 

message: The article currently has sections Brief history and Development of modal logic.  In view of the latter, the former seems redundant.  Is there any reason not to delete it? — Charles Stewart (talk) 12:38, 3 May 2009 (UTC)
replies: text: Done.--Heyitspeter (talk) 05:35, 26 July 2009 (UTC)
thread_title:  Redundant section 

message: It might be of some value if the article could mention the role that modal logic has played in the development of Catholic theology. For example, Gödel's ontological proof mentions the extent to which modal logic was used in Saint Anselm's ontological argument for the existence of God. ADM (talk) 14:36, 6 November 2009 (UTC)
replies: text: Want to add a section? Worst comes to worst someone will delete it. I believe Alvin Plantinga has made a modal argument for the necessary existence of God as well...--Heyitspeter (talk) 23:38, 6 November 2009 (UTC)
thread_title: Catholic theology

message: In what deontic universe is killing a victim a moral obligation? Aren't there better examples that better avoid the emotional distress of reading the example overshadowing the underlying logic? Rursus dixit. (mbork3!) 20:58, 6 March 2010 (UTC)
replies: text: Hmm. I mean, it's supposed to be the case that there isn't such a deontic universe, for the sake of the reductio. But I see what you mean about the example being graphic to some extent. I figured it would be good to use an instance of an action deemed more or less universally evil, and it is matched in the citation, but I see what you mean. Care to propose an alternative reprehensible act that isn't so emotionally distressful?--Heyitspeter (talk) 00:03, 8 March 2010 (UTC)
thread_title: Deontic killing

message: Will someone create a lead that will alow me to understand what the hell this article is talking about. Thanks 198.85.219.5 (talk) 23:13, 22 July 2010 (UTC)
thread_title: SOS

message: Chellas's "Modal Logic an Introduction", CUP, 1980, mentions classical systems of modal logic and minimal models for them.  The article could well discuss these matters (with references to Montague and Scott), and so much else besides: it seems to me to be a mere sketch.  —Preceding unsigned comment added by 213.122.58.155 (talk) 14:10, 11 August 2010 (UTC)
replies: text: WP:BOLD --Heyitspeter (talk) 04:09, 13 August 2010 (UTC)
thread_title:  Classical Systems and Minimal Models 

message: Not all modal operators are intensional, for example, Łukasiewicz and Tarksi worked on extensional modal logics, most notably Łukasiewicz's many-valued logics.   Gödel's many-valued (and the fuzzy variant also known as Dummett logic) also has an extensional modal operator.
The section on Other Modal Logics confuses this, and is wrong.  —Preceding unsigned comment added by 94.173.19.247 (talk) 17:04, 3 November 2010 (UTC)
thread_title:  Not all model logics are Intensional 

message: I feel it is worth mentioning the soundness and completeness results for axiomatic systems, at least for K. The approach of canonical models is also very important.
Going forward, finite and bounded model properties, decidability and complexity are worth a mention.
j.t. (talk) 19:52, 29 May 2011 (UTC)
thread_title:  Soundness and completeness of axiomatic systems 

message: Consider ROBDD used for satisfiability tests, or formal verification on software, while these typically use combinational / sequential logic, their prime intention is modal, i.e. does something meet a specification? it should meet the specification, it may not violate specific requirements,...
Now to phrase my question in theoretical computer science terms: can modal logics be translated into each other? like skolemnization: can quantifiers as letters in words be treated as propositions? Im pretty new to modal logics... can reasonings in modal logic be described as predicate logic? to what extents are modal logic syntactic sugar and to what extent impossible to rephrase in another logic?  — Preceding unsigned comment added by 83.134.181.100 (talk) 18:29, 22 January 2012 (UTC)
thread_title:  Modal translation? 

message: :I had the same confusion, transitive means if one have aRb and bRc, then aRc also exists, while Euclidean says if one have aRb and aRc, then bRc. A subtle difference, but here it is important to know which is the implied segment.
: I am some reluctant to understand this subtle difference, what makes me accept this differentiation, is the relation between the form of the formula (axiom) and the accessibility relation.  — Preceding unsigned comment added by 189.178.233.172 (talk) 11:13, 4 November 2012 (UTC)
replies: text: Yes, of course, Euclidean is not the same thing as transitive. but transitive plus symmetric relation is, and in the intervening decade, the article has been altered to say "its all the same thing". From what I can tell, the urge to define "euclidean" is a historical artifact. 67.198.37.16 (talk) 21:59, 31 May 2024 (UTC)
replies: text: Transitive and symmetric is the same as Euclidean and symmetric (Prop.3 at Euclidean relation). However, transitive and symmetric is not the same as Euclidean alone (see 2nd picture for a relation that is Euclidean, but not symmetric). - Jochen Burghardt (talk) 17:39, 2 June 2024 (UTC)
thread_title:  Euclidean =/= Transitive 

message: Section 2.2, on axiomatic systems, states outright that possibility and necessity are interderivable through negation. This isn't true of all modal logics, only classical ones; intuitionistic logic, as usual, excludes some de Morgan duals, and this is true of intuitionistic modal logic.
I might not quibble, but the distinction is made in the introduction (where the duality is qualified as existing in classical modal logic) and in section 3 on alethic logic (where intuitionistic logic is mentioned), so there is an issue of consistency. Luke Maurer (talk) 18:47, 16 July 2012 (UTC)
thread_title:  Interderivation of necessity and possibility 

message: I asked to delete the page axiom S5 but a supervisor removed the petition, suggesting me to change that to merge. 
I see that the part about S5, here, seems to be more complete than the Axiom S5 page, which must be removed. I have not read the S5 (modal logic) page, but I think it may be merged with this one if it contains something not included here, if not just need to be deleted.
In synthesis, the other pages should be deleted, for the reasons written in the discussion page of axiom S5, starting with the wrong title.  — Preceding unsigned comment added by 189.178.233.172 (talk) 11:03, 4 November 2012 (UTC)
thread_title:  the page [[Axiom S5]] should be merged or erased the reasons in that discussion page 

message: This article has been revised as part of a large-scale clean-up project of multiple article copyright infringement. (See the investigation subpage) Earlier text must not be restored, unless it can be verified to be free of infringement. For legal reasons, Wikipedia cannot accept copyrighted text or images borrowed from other web sites or printed material; such additions must be deleted. Contributors may use sources as a source of information, but not as a source of sentences or phrases. Accordingly, the material may be rewritten, but only if it does not infringe on the copyright of the original or plagiarize from that source. Please see our guideline on non-free text for how to properly implement limited quotations of copyrighted text. Wikipedia takes copyright violations very seriously. Moonriddengirl (talk) 00:10, 17 November 2013 (UTC)
thread_title:  Possible copyright problem 

message: Was Ruth Barcan Arthur Norman Prior's protégé?  Maybe so, but why does the author think so?  — Preceding unsigned comment added by 86.185.217.237 (talk) 12:25, 8 September 2014 (UTC)
thread_title:  Prior and Barcan 

message: Check it out: <BR>
WP:SLANG  http://en.wikipedia.org/wiki/Argot
 "Wikipedia articles, and other encyclopedic content, should be written in a formal tone. ... Formal tone means that the article should not be written using unintelligible argot, slang, colloquialisms, doublespeak, legalese, or jargon; it means that the English language should be used in a businesslike manner."
Even worse, this crap is in the intro paragraph, quote: <BR>
"("Possibly, p", "It is possible that p"), necessity ("Necessarily, p", "It is necessary that p"), and impossibility ("Impossibly, p", "It is impossible that p")." 
Yer shittin me,right? And I've studied logic. Looks promising and keystone, try it in English. Also see: MOS:LEAD: 
 "The lead should contain no more than four paragraphs, must be carefully sourced as appropriate, and should be written in a clear, accessible style with a neutral point of view to invite a reading of the full article....." 
and MOS:INTRO:
 "...In general, specialized terminology and symbols should be avoided in an introduction. ....Where uncommon terms are essential to describing the subject, they should be placed in context, briefly defined, and linked.  The subject should be placed in a context with which many readers could be expected to be familiar."
First sentence Wikipedia:MOSINTRO#First_sentence  
 "The article should begin with a declarative sentence telling the nonspecialist reader what (or who) is the subject.  <BR> ...If its subject is amenable to definition, then the first sentence should give a concise definition: where possible, one that puts the article in context for the nonspecialist. Similarly, if the title is a specialised term, provide the context as early as possible...."
Inappropriate jargon is always bad writing. Guess what? Good writing ain't easy, takes work. Wiki's about Communication, it's no longer about impressing people that you really read the book...that is assumed. —Cheers! <BR> --2602:306:CFCE:1EE0:3044:A2C3:2683:987B (talk) 16:02, 21 November 2018 (UTC)
thread_title:  Does not meet Wiki standards.  

message: Am I right in thinking that the necessitation rule is logically equivalent to the axiom: 
\neg \Diamond \bot
In which case, it would be useful to include it as an axiom. Dezaxa (talk) 02:15, 15 August 2022 (UTC)
thread_title:  Necessitation 

message: ◊(x²=1 ∧ 0=y) is NOT logically equivalent to (◊(x²=1)) ∧ ◊(0=y).  The first formula says that x²=1 ∧ 0=y is true at some accessible possible world, whereas the second formula says that x²=1 is true at some accessible possible world and 0=y is true at some accessible possible world.  In the first formula, the worlds for the subformulas x²=1 and 0=y are the same, whereas in the second formula, they may differ.
:Thanks. I went to address the problem and somehow ended up rewriting the section. Botterweg14 (talk) 01:43, 10 November 2022 (UTC)
thread_title:  Isn't the example in “Syntax for modal operators” wrong?