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In logic and mathematics, inclusion is the concept that all the contents of one object are also contained within a second object. [ 1 ] For example, if m and n are two logical matrices , then
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics .
In logic, disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated as and read aloud as "or".
Inclusion–exclusion illustrated by a Venn diagram for three sets. Generalizing the results of these examples gives the principle of inclusion–exclusion. To find the cardinality of the union of n sets: Include the cardinalities of the sets. Exclude the cardinalities of the pairwise intersections.
The inclusion relation has a natural interpretation in various Boolean algebras: in the subset algebra, the subset relation; in arithmetic Boolean algebra, divisibility; in the algebra of propositions, material implication; in the two-element algebra, the set { (0,0), (0,1), (1,1) }. Some useful properties of the inclusion relation are:
A model with this condition is called a full model, and these are the same as models in which the range of the second-order quantifiers is the powerset of the model's first-order part. [3] Thus once the domain of the first-order variables is established, the meaning of the remaining quantifiers is fixed.
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If an atom A belongs to a stable model of a logic program P then A is the head of one of the rules of P. Minimality Any stable model of a logic program P is minimal among the models of P relative to set inclusion. The antichain property If I and J are stable models of the same logic program then I is not a proper subset of J.