http://biblioteca.universia.net/vernivel.do?nivel=1103 Mostrando recursos 1 - 20 de 133 es http://biblioteca.universia.net/img/logotipo.jpg http://biblioteca.universia.net/ http://biblioteca.universia.net/ficha.do?id=76440 A term in logic meaning pertaining to truth and falsehood. See also: False, Predicate, True Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=76692 Inference of the truth of an unknown result obtained by noting its similarity to a result already known to be true. In the hands of a skilled mathematician, analogy can be a very powerful tool for suggesting new and extending old results. However, subtleties can render results obtained by analogy incorrect, so rigorous proof is still needed. See also: Gauss's Formulas, Induction, Napier's Analogies Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=77352 In logic, a statement which cannot be broken down into smaller statements, also simply called an "atom." Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=77477 Propositional calculus, first-order logic, and other theories in mathematical logic are defined by their axioms (or axiom schemata, plural: axiom schemata) and inference rules. An axiom schema is a sentential formula representing infinitely many axioms. These axioms are obtained by replacing variables in the schema by any formula. For example, the axiom schema F \Rightarrow F \lor G in propositional calculus represents the axioms A \Rightarrow A \lor B, A \Rightarrow A \lor A, \lnot A... Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=78317 Capable of taking on one out of two possible values. See also: Law of the Excluded Middle, Univalent Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=78398 One of the logic operators AND \land, OR \lor, and NOT \lnot. See also: Quantifier Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=78514 An occurrence of a variable in a logic which is not free. Bound variables are also called dummy variables. See also: Dummy Variable, Sentence Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=78929 A puzzle in logic in which one or more facts must be inferred from a set of given facts. Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=79765 A reduction system is said to posses the Church-Rosser property if, for all x and y such that x \leftrightarrow_* y, there exists a z such that x\to_* z and y\to_* z. A reduction system is Church-Rosser iff it is confluent. See also: Church-Rosser Theorem, Confluent, Critical Pair, Finitely Terminating, Knuth-Bendix Completion Algorithm, Reduction Order Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=79766 The Church-Rosser theorem states that lambda calculus as a reduction system with lambda conversion rules satisfies the Church-Rosser property. See also: Church-Rosser Property, Lambda Calculus Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=80005 A clause is a disjunction of literals. See also: Empty Clause, Horn Clause, Literal, Top Clause Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=80084 A closed sentential formula is a sentential formula in which none of the variables are free (i.e., all variables are bound). Examples of closed sentential formulas are given by \forall x\forall y(x+y \equiv y+x), which expresses the commutativity of addition, and \forall x \exists y(\forall u \forall v (x + y \not= (u+2)(v+2))), which expresses the infinitude of the primes. A closed sentential formula is called a sentence (Carnap 1958, pp. 24-25 and 85). However, in some language system... Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=80247 In December 1920, M. Schönfinkel presented a report to the Mathematical Society in Göttingen a new type of formal logic based on the concept of a generalized function whose argument is also a function (Schönfinkel 1924). This mathematical discipline was subsequently termed combinatory logic by Curry and "\lambda-conversion" or "\lambda-calculus" by Church. Combinators can be used in the study of algebra, topology, and category theory, and have found... Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=80274 A fundamental system of logic based on the concept of a generalized function whose argument is also a function (Schönfinkel 1924). This mathematical discipline was subsequently termed combinatory logic by Curry and "\lambda-conversion" or "lambda calculus" by Church. The system of combinatory logic is extremely fundamental, in that there are a relatively small finite numbers of atoms, axioms, and elementary rules. Despite the fact that the system contains no formal... Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=80675 A conclusion is a statement arrived at by applying a set of logical rules known as syllogisms to a set of premises. The process of drawing conclusions from premises and syllogisms is called deduction. See also: Deduction, Logic, Premise, Propositional Calculus, Syllogism Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=80877 A statement is in conjunctive normal form if it is a conjunction (sequence of ANDs) consisting of one or more conjuncts, each of which is a disjunction (OR) of one or more literals (i.e., statement letters and negations of statement letters; Mendelson 1997, p. 30). Examples of conjunctive normal forms include A (1) (A\lor B)\land({!A}\lor C) (2) (A\lor B\lor {!A})\land(C\lor {!B})\land(A\lor {!C}) (3) A\lor B (4) A\land(B\lor C), (5) where \lor denotes OR, \land denotes AND, and !... Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=80921 The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency. See also: Axiomatic Set Theory, Axiomatic System, Complete Axiomatic Theory, Consistency Strength, Gödel's Incompleteness Theorem Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=80922 If the consistency of one of two propositions implies the consistency of the other, the first is said to have greater consistency strength. Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=80953 A formal argument in logic in which it is stated that (1) P\Rightarrow Q and R\Rightarrow S (where \Rightarrow means "implies"), and (2) either P or R is true, from which two statements it follows that either Q or S is true. See also: Destructive Dilemma, Dilemma Weisstein, Eric W. http://biblioteca.universia.net/ficha.do?id=80960 A sentence is called a contingency if its truth table contains at least one 'T' and at least one 'F.' See also: Contradiction, Tautology, Truth Table Weisstein, Eric W.