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The graph shown here appears as a subgraph of an undirected graph if and only if models the sentence ,,,... In the first-order logic of graphs, a graph property is expressed as a quantified logical sentence whose variables represent graph vertices, with predicates for equality and adjacency testing.
The simplest constituents are atomic sentences. A contemporary semantic definition of truth would define truth for the atomic sentences as follows: An atomic sentence F(x 1,...,x n) is true (relative to an assignment of values to the variables x 1, ..., x n)) if the corresponding values of variables bear the relation expressed by the predicate F.
However, in first-order logic, these two sentences may be framed as statements that a certain individual or non-logical object has a property. In this example, both sentences happen to have the common form () for some individual , in the first sentence the value of the variable x is "Socrates", and in the second sentence it is "Plato". Due to ...
David Lewis offered a list of criteria that should condense the distinction between intrinsic and extrinsic properties (numbers and italics added): [1]. A sentence or statement or proposition that ascribes intrinsic properties to something is entirely about that thing; whereas an ascription of extrinsic properties to something is not entirely about that thing, though it may well be about some ...
An intensive property does not depend on the size or extent of the system, nor on the amount of matter in the object, while an extensive property shows an additive relationship. These classifications are in general only valid in cases when smaller subdivisions of the sample do not interact in some physical or chemical process when combined.
A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values : as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.
A specific property is the intensive property obtained by dividing an extensive property of a system by its mass. For example, heat capacity is an extensive property of a system. Dividing heat capacity, , by the mass of the system gives the specific heat capacity, , which is an intensive property. When the extensive property is represented by ...
Physical property, any property that is measurable whose value describes a state of a physical system; Thermodynamic properties, in thermodynamics and materials science, intensive and extensive physical properties of substances; Mathematical property, a property is any characteristic that applies to a given set; Semantic property