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The word "relationship" is often used as a synonym. [6] The entities related to each other are called the relata. [7] The term "relation" comes from the Latin terms relatio and referre, which mean reference or towardness. [8] In mathematics and logic, relations are defined as set-theoretic structures.
In database theory, a relation, as originally defined by E. F. Codd, [1] is a set of tuples (d 1,d 2,...,d n), where each element d j is a member of D j, a data domain. Codd's original definition notwithstanding, and contrary to the usual definition in mathematics, there is no ordering to the elements of the tuples of a relation.
Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...
These two definitions of formal logic are not identical, but they are closely related. For example, if the inference from p to q is deductively valid then the claim "if p then q" is a logical truth. [16] Formal logic needs to translate natural language arguments into a formal language, like first-order logic, to assess whether they are valid.
In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...
An ontology is a description (like a formal specification of a program) of the concepts and relationships that can formally exist for an agent or a community of agents. This definition is consistent with the usage of ontology as set of concept definitions, but more general. And it is a different sense of the word than its use in philosophy. [18]
The Year Without a Santa Claus, a Christmas special from Jules Bass and Arthur Rankin, Jr., turns 50 this December. The beloved special was adapted from the book of the same name by Phyllis ...
For instance, in a standard semantics for first-order logic, the formula (,) would be true on an interpretation if the entities denoted by and stand in the relation denoted by . Since predicates are non-logical symbols , they can denote different relations depending on the interpretation given to them.