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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)
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:
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)
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:
Any objections? —Preceding unsigned comment added by 82.27.226.211 ( talk) 21:55, 20 February 2008 (UTC)
Added new first paragrah with more precise definition-- Philogo 20:41, 3 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)
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.
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)
Article states: for propositional logic, for example, the atomic formulas are the propositional variables.
I think that since logical constants, are atomic formulas as well, this definition should be expanded to include both variables and constants . -- Obradović Goran (talk 15:29, 6 September 2008 (UTC)
This
level-5 vital article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
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)
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:
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)
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:
Any objections? —Preceding unsigned comment added by 82.27.226.211 ( talk) 21:55, 20 February 2008 (UTC)
Added new first paragrah with more precise definition-- Philogo 20:41, 3 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)
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.
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)
Article states: for propositional logic, for example, the atomic formulas are the propositional variables.
I think that since logical constants, are atomic formulas as well, this definition should be expanded to include both variables and constants . -- Obradović Goran (talk 15:29, 6 September 2008 (UTC)