Talk:Atomic formula
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| Mathematics rating: | Stub Class | Low Priority | Field: Foundations, logic, and set theory | ||||||||||||||||||||
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[edit] merge?
I'm not sure this shouldn't be merged into formula (mathematical logic). Is there enough to say to justify a separate article? --Trovatore 04:49, 23 March 2006 (UTC)
- Probably merge. I can't see any reason not to merge them. Unless somebody else comes up with one, I'd say that it makes sense to do so. Jon Awbrey 05:54, 23 March 2006 (UTC)
- Don't merge: The idea of an atom is important whenever you formally describe a logical system. This article could be expanded with more examples than the current example, with some statements about how atoms are usually chosen, with a category-theoretic description of atoms (aren't they terminal or initial objects in the category of statements in that logic, or something like that?). This term is used in a lot of definitions, and the article has several good inlinks. CiteSeer and Google Scholar indicate that this term is used by an awful lot of journal articles. So, I think that it would be helpful to have a separate article. -- Creidieki 20:10, 2 April 2006 (UTC)
- Yes, you're right, there is not nearly enough to say about atomic formulas to make an article about it. Even this stub spends most of its space on well-formed formulas of propositional logic rather than atomic formulas. It is worth merging Well-formed formula at the same time, and its redirect WFF. CMummert · talk 02:48, 30 March 2007 (UTC)
- Hmm, I'm less sure about the latter. I don't really know how "well-formed formula" is standardly used, but if it's really as represented in the article, then it seems to be a much more general concept than "formula of the predicate calculus". It looks like any string accepted by a (given) formal grammar, which is surely too general to merge into formula (mathematical logic). --Trovatore 03:07, 31 March 2007 (UTC)
[edit] definition
I think the opening definition can be improved upon. It says "In mathematical logic, an atomic formula (also known simply as an atom) is a formula with no deeper propositional structure. Atoms are thus the simplest propositions of the logic. The well-formed formulas of the logic are formed by combining the atomic formulas using the connectives of the logic."
The expression "with no deeper propositional structure" is rather loose - at least it does not explain what is meant by "deeper propositional structure."
It says "The well-formed formulas of the logic are formed by combining the atomic formulas": this is confusing thing to say because atomic formulas are themselves well-formed formulas. It would be more accurate to say "Compound formulas are formed by combining atomic formulas .."
I have suggested:
- "In Logic (propositional logic and predicate logic), an atomic formula is an expression consisting of either a sentential letter or an n-place predicate letter followed by n individual symbols or functions. If it contains no free variables it is an Atomic sentence."
An alternative would be "it is a Well-formed formula that includes no logical connectives or quantifiers."
This article should link to formula (mathematical logic),atomic sentence and Well-formed formula Kaustuv Chaudhuri does not care for my suggestions. Any alernative suggestions?
--Philogo 21:54, 25 September 2007 (UTC)
- I have incorporated what I consider to be the reasonable parts of your suggestion. The article already links to formulas and wffs in the text; see-also sections are for other articles not directly linked. Atomic sentence as a Wikipedia article is a disgrace; ideally these two articles should be merged, but the turf wars that will result with that attempt are entirely too predictable. You might consider reading more than a single textbook on logic. I have taken the liberty of replacing your <br>s with paragraph breaks. — Kaustuv Chaudhuri 13:14, 26 September 2007 (UTC)
Thank you for incorporating what you consider to be the reasonable parts of my suggestion. Your suggestion that I "might consider reading more than a single textbook on logic." may have been meant constructiovely but it appears to me to be an unnecessarily combative remark, not in the spirit of Wikapedia, would appear to be in the nature of a personal attack. (It is of course petitio principii and perhaps meant as a joke to see if I would notice that!) It is better to discuss matters calmly and rationally. I hope you agree, and meant no offence, and in that hope I would comment as follow. The current definition is:
In mathematical logic, an atomic formula (also known simply as an atom) is a formula with no deeper propositional structure, that is, a formula with no logical connectives or strict sub-formulas. Atoms are thus the simplest well-formed formulas of the logic. Compound formulas are formed by combining the atomic formulas using the logical connectives.
The reader may not know what "strict sub-formulas" and there is no definition in Wikipwedia. It should say I believe with no logical connectives or quantifiers The phrase "with no deeper propositional structure" is perhaps redundant. A more standard way of proceeding is to define wffs in terms of atomic wffs rather than the other way around., eg. we might say :
In (the) sentential calculus/logic an atomic formula consists of a sentential letter. In first-order predicate calculus/logic it consist of a predicate letter followed by the appropriate number of individual contstants as arguments [or terms if it function letters are alowed].
If the circumstances for higher order logic atomic formula is different then that would be interesting to add.
I grant this is not too far off from my original suggestion to which you objected: "In Logic (propositional logic and predicate logic), an atomic formula is an expression consisting of either a sentential letter or an n-place predicate letter followed by n individual symbols or functions. If it contains no free variables it is an Atomic sentence."
I suggest we might allow others to make their comments now since they may have better suggestions than either of us.
--Philogo 12:39, 27 September 2007 (UTC)
—Preceding unsigned comment added by Philogo (talk • contribs) 12:12, 27 September 2007 (UTC)
I propose we reinstate the definition:
- "In Logic (propositional logic and predicate logic), an atomic formula is an expression consisting of either a sentential letter or an n-place predicate letter followed by n individual symbols or functions. If it contains no free variables it is an Atomic sentence."
Any objections? —Preceding unsigned comment added by 82.27.226.211 (talk) 21:55, 20 February 2008 (UTC)
[edit] edit
Added new first paragrah with more precise definition--Philogo 20:41, 3 September 2007 (UTC)
- Sorry, I disagree entirely with your draft. Firstly, terms such as sentential letter, individual symbol, function, etc., which you (rather inappropriately) bolded, were nowhere defined as technical terms. Even were they to be so defined, this is a confusing definition of an otherwise trivial concept. Certain of these terms, such as sentential letter, are often idiosyncratically used by various authors of logical texts, and are possibly only relevant to Hilbert systems in any case. — Kaustuv Chaudhuri 08:28, 7 September 2007 (UTC)
If you disagree with my proposed definition it would be better, more constructive and polite to cite an authority for an alternative or better definition rather than just deleting it.
I said: In Logic (propositional logic and predicate logic), an atomic formula is an expression consisting of either a sentential letter or an n-place predicate letter followed by n individual symbols or functions. If it contains no free variables it is an Atomic sentence.
I would consider this a standard definition in (propositional logic and predicate logic), as are the terms used in its definition. An alternative would be it is a Well-formed formula that includes no logical connectives or quantifiers.
I do not now what you mean by desribing the concept as "trivial" is this not POV? I think it is basic. --Philogo 13:14, 25 September 2007 (UTC)
- Just to be clear, I meant that defining a trivial concept as atomic formula using scary sounding terminology is unnecessary. Wikipedia is not trying to be a logic textbook. Furthermore, your particular definition as "sentential letter or n-place predicate letter" commits to an unnecessarily narrow view of logic; for example, it doesn't generalize to higher-order logic, though the concept of atom would certainly apply even at higher kinds. The thing you call an alternative above is what the article presently states, with the minor (but crucial!) difference that it doesn't assume that well-formedness is already understood, and it additionally hints at the modern view of atoms as sites for substitution. The fervor for citation is well and good, but there is really no "authority" on logical syntax or terminology. Every author rolls his or her own. — Kaustuv Chaudhuri 14:36, 25 September 2007 (UTC)
Kaustav: have you visited Wikipedia:WikiProject Logic? This WikiProject is a community of Wikipedians who share an interest in logic and who wish to improve the general quality of Wikipedia logic articles, and how they are accessed. It is an effort to coordinate the work of Wikipedians who are knowledgeable about logic.
[edit] She just growed.
I've been trying to make some sense out of a confusing maze of articles, such as statement (logic), sentence (mathematical logic), proposition (logic), atomic formula, atomic sentence, and more others than you can shake a stick at.
It seems to me that there should be three threads, internally consistant and at least not mutually contradictory. The first thread is philosophy, the second elementary mathematics, and the third technical mathematics.
To that end, unless someone objects, I'm going to start moving some articles around, starting on May 29, 2008.
Rick Norwood (talk) 12:54, 28 May 2008 (UTC)
