The subsumption of the condition of another possible judgement under the condition of the rule is the minor.
"The Critique of Pure Reason" by Immanuel Kant
There was associative apperception, subsumptive apperception, assimilative apperception, and others up to sixteen.
"Talks To Teachers On Psychology; And To Students On Some Of Life's Ideals" by William James
Thirdly, the subsumption of several laws under one more general expression.
"Logic" by Carveth Read
There would be no difficulty with this subsumption if the objects and the conceptions of the understanding were the same in kind.
"A History of Philosophy in Epitome" by Albert Schwegler
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In section , we studied the di(cid:11)erence between (cid:18) -subsumption and implication on clauses.
Generalization of Clauses under Implication
We presented our approach to (cid:12)nd all generalizations under implication, by reducing implication to (cid:18) -subsumption.
Generalization of Clauses under Implication
We also described expansion of clauses, which summarizes our idea of reduction of implication to (cid:18) -subsumption.
Generalization of Clauses under Implication
For every generalization under implication of a clause there exists an expansion of the clause, logically equivalent to the clause, such that the generalization under implication is reduced to a generalization under (cid:18) -subsumption. .
Generalization of Clauses under Implication
For each non-tautological clause there exists a T-complete expansion, which means that every generalization under T-implication of the clause is reduced to a generalization under (cid:18) -subsumption of the expansion.
Generalization of Clauses under Implication
This is not surprising since our framework for generalization under implication is based on and extends Plotkin's framework for generalization under (cid:18) -subsumption, which already su(cid:11)ers from complexity problems.
Generalization of Clauses under Implication
Even an LGG reduced under (cid:18) -subsumption, which means that all literals that are redundant under (cid:18) -subsumption are removed, may grow exponentially in the number of clauses (Kietz, ).
Generalization of Clauses under Implication
However, although Plotkin's framework for generalization under (cid:18) -subsumption is computationally expensive, it has been widely used as a theoretical framework.
Generalization of Clauses under Implication
Third, we have further developed previous work of the author (Idestam-Almquist, c) on extending Plotkin's framework for generalization under (cid:18) -subsumption to generalization under implication.
Generalization of Clauses under Implication
Of these three orders, subsumption is the most tractable.
Least Generalizations and Greatest Specializations of Sets of Clauses
It was implemented for example by Shapiro ( ) in the subsumption order in the form of re(cid:12)nement operators.
Least Generalizations and Greatest Specializations of Sets of Clauses
He proved that any (cid:12)nite set S of clauses has a least generalization under subsumption (LGS).
Least Generalizations and Greatest Specializations of Sets of Clauses
For this second approach, subsumption is again not fully satisfactory.
Least Generalizations and Greatest Specializations of Sets of Clauses
As this example also shows, the subsumption order is particularly unsatisfactory when we consider recursive clauses: clauses which can be resolved with themselves. .
Least Generalizations and Greatest Specializations of Sets of Clauses
There is also relative subsumption (Plotkin, b), which will be brie(cid:13)y touched in Section . .
Least Generalizations and Greatest Specializations of Sets of Clauses
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