Rule of inferenceIn philosophy of logic and logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics), in the sense that if the premises are true (under an interpretation), then so is the conclusion.
Axiomatic systemIn mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system. A formal theory is an axiomatic system (usually formulated within model theory) that describes a set of sentences that is closed under logical implication.
Surrogate keyA surrogate key (or synthetic key, pseudokey, entity identifier, factless key, or technical key) in a database is a unique identifier for either an entity in the modeled world or an object in the database. The surrogate key is not derived from application data, unlike a natural (or business) key. There are at least two definitions of a surrogate: Surrogate (1) – Hall, Owlett and Todd (1976) A surrogate represents an entity in the outside world. The surrogate is internally generated by the system but is nevertheless visible to the user or application.
Tautology (logic)In mathematical logic, a tautology (from ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". Similarly, "either the ball is green, or the ball is not green" is always true, regardless of the colour of the ball. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing from rhetoric, where a tautology is a repetitive statement.
ConsequentA consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if P implies Q, then P is called the antecedent and Q is called the consequent. In some contexts, the consequent is called the apodosis. Examples: If , then . is the consequent of this hypothetical proposition. If is a mammal, then is an animal. Here, " is an animal" is the consequent. If computers can think, then they are alive. "They are alive" is the consequent.
Interpretation (logic)An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of presenting an interpretation.
Natural keyA natural key (also known as business key or domain key) is a type of unique key in a database formed of attributes that exist and are used in the external world outside the database (i.e. in the business domain or domain of discourse). In the relational model of data, a natural key is a superkey and is therefore a functional determinant for all attributes in a relation.
Barred owlThe barred owl (Strix varia), also known as the northern barred owl, striped owl or, more informally, hoot owl or eight-hooter owl, is a North American large species of owl. A member of the true owl family, Strigidae, they belong to the genus Strix, which is also the origin of the family's name under Linnaean taxonomy. Barred owls are largely native to eastern North America, but have expanded their range to the west coast of North America where they are considered invasive.
Truth tableA truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid.
Affirming the consequentIn propositional logic, affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "if the lamp were broken, then the room would be dark"), and invalidly inferring its converse ("the room is dark, so the lamp must be broken"), even though that statement may not be true. This arises when the consequent ("the room would be dark") has other possible antecedents (for example, "the lamp is in working order, but is switched off" or "there is no lamp in the room").
