Circumscriptively

Definitions

  • Webster's Revised Unabridged Dictionary
    • adv Circumscriptively In a limited manner.
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Century Dictionary and Cyclopedia
    • circumscriptively In a circumscriptive or limited manner or sense.
    • circumscriptively In such a manner as to occupy space and prevent other bodies from occupying it: as, a body is situated where it is circumscriptively.
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Usage

In literature:

A figure is the exterior appearance, the circumscription, and the boundary of a body.
"Essays and Miscellanies" by Plutarch
It is better that such places should be merged in a larger circumscription.
"Considerations on Representative Government" by John Stuart Mill
And yet here again see the swift circumscription!
"Essays" by Ralph Waldo Emerson
Thus in measure as the Referendum comes into play does the circumscription practicing it become a complete community.
"Direct Legislation by the Citizenship through the Initiative and Referendum" by James W. Sullivan
Cicero gives many names to the period, calling it a winding about, a circuit, a comprehension, continuation, and circumscription.
"The Training of a Public Speaker" by Grenville Kleiser
One short distribution and circumscription of historical ages will soon place matters in a more hopeful aspect.
"The Posthumous Works of Thomas De Quincey, Vol. II (2 vols)" by Thomas De Quincey
In Hainault (Valenciennes and Tournai forming special circumscriptions), Mons remained alone to represent their interests.
"Belgium" by Emile Cammaerts
The Marquesan, it will be observed, adheres to the old idea of the local circumscription of beliefs and duties.
"The Works of Robert Louis Stevenson - Swanston Edition Vol. 18 (of 25)" by Robert Louis Stevenson
In 1868 he was made a major-general, and in the following year became chief of the staff in the Kiev military circumscription.
"Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 6" by Various
The department forms part of the ecclesiastical province of Reims and of the circumscriptions of the appeal-court of Nancy and the VI.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5" by Various
The department falls within the circumscription of the appeal-court of Agen, and the region of the XVII.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 8" by Various
We spend a dreamy hour in the Tribune, whose very circumscription is a relief.
"From the Oak to the Olive" by Julia Ward Howe
He was meditating rather sadly upon the circumscription of human fame.
"The Passionate Elopement" by Compton Mackenzie
Their prerogative is more extensive than with us, but at the same time it has its points of circumscription.
"Checkmate" by Joseph Sheridan Le Fanu
In educational matters it falls within the circumscription of the academie of Toulouse.
"Encyclopaedia Britannica, 11th Edition, Volume 13, Slice 1" by Various
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In science:

It is not hard to see that circumscription coincides with reasoning under the extended closed world assumption, in which all formulae involving only propositions from P that cannot be derived from Γ are assumed to be false [GPP89].
Complexity of Non-Monotonic Logics
These results reveal that, alike default logic and autoepistemic logic, circumscription exhibits an increase in the complexity of model checking and reasoning as compared to traditional propositional logic.
Complexity of Non-Monotonic Logics
Define the circumscriptive model checking problem for sets of relations from S as the problem to decide, given a a set Γ of applications of relations from S , an assignment σ : Vars(Γ) → {0, 1} and a partition (P, Q, Z ) of Vars(Γ), whether σ is a minimal model of Γ with respect to ≤(P,Z ) .
Complexity of Non-Monotonic Logics
In this case, the circumscriptive model checking problem Turing reduces to the satisfiability problem, which in this case is tractable by [Sch78].
Complexity of Non-Monotonic Logics
Define the circumscriptive model checking problem for sets of B-formulae as the problem to decide, given a set Γ ⊆ L(B), an assignment σ : Vars(Γ) → {0, 1} and a partition (P, Q, Z ) of Vars(Γ), whether σ is a minimal model of Γ with respect to ≤(P,Z ) .
Complexity of Non-Monotonic Logics
Then the circumscriptive model checking problem for sets of B-formulae is 1. coNP-complete if S02 ⊆ [B] or S12 ⊆ [B] or D1 ⊆ [B], and 2. in P in all other cases (that is, if [B] ⊆ M).
Complexity of Non-Monotonic Logics
Key to the classification is that if the set B of all available Boolean functions is monotone, then the circumscriptive model checking problem Turing-reduces to the the model checking problem for monotone Boolean formulae.
Complexity of Non-Monotonic Logics
Thus circumscriptive model checking problem for sets of B-formulae is tractable if [B] ⊆ M.
Complexity of Non-Monotonic Logics
As for the inference problem, the computational complexity of circumscriptive inference was first studied in 1990 by Cadoli and Lenzerini [CL94], who analyzed the complexity of reasoning under various closed world assumptions.
Complexity of Non-Monotonic Logics
This problem, henceforth referred to as the circumscriptive model counting problem, has recently gained a lot of interest.
Complexity of Non-Monotonic Logics
Theorem 5.8 ([DHK05]) The minimal model counting problem and the circumscriptive model counting problem are #·coNP-complete via subtractive reductions.
Complexity of Non-Monotonic Logics
The complexity of model checking for circumscriptive formulae.
Complexity of Non-Monotonic Logics
On the counting complexity of propositional circumscription.
Complexity of Non-Monotonic Logics
Propositional circumscription and extended closed world reasoning are Π p 2 -complete.
Complexity of Non-Monotonic Logics
On the relationship between circumscription and negation as failure.
Complexity of Non-Monotonic Logics
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