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Encyclopedia: List of topics in logic In logical calculus of mathematics, the logical conditional (also known as the material implication, sometimes material conditional) is a binary logical operator connecting two statements, if p then q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). Provability logic, or the logic of provability, is a modal logic where the necessity operator is interpreted as provability in a reasonably rich formal theory such as Peano arithmetic. Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century. www.nationmaster.com /encyclopedia/List-of-topics-in-logic   (5150 words)

Logical equivalence - Wikipedia, the free encyclopedia In logic, statements p and q are logically equivalent if they have the same logical content. Logical equivalence is often confused with material equivalence. Logical equivalence is sometimes denoted p ≡ q or p ⇔ q. en.wikipedia.org /wiki/Logically_equivalent   (180 words)

First-order logic - Wikipedia, the free encyclopedia First-order logic is mathematical logic that is distinguished from higher-order logic in that it does not allow quantification over properties. Nevertheless, first-order logic is strong enough to formalize all of set theory and thereby virtually all of mathematics. The predicate calculus is an extension of the propositional calculus. www.wikipedia.com /wiki/First-order_predicate_calculus   (884 words)

Logical biconditional - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-08-08) In logical calculus of mathematics, logical biconditional is a logical operator connecting two statements to assert, p if and only if q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). The only difference from logical conditional is the case when the hypothesis is false but the conclusion is true. When we shall have to demonstrate a biconditional we shall usually analyze it into two converse conditionals and demonstrate them separately. wikipedia.lotsofinformation.com /wiki/index.php/Logical_biconditional   (417 words)

Logical operator - Wikipedia Note that the logical equivalence of certain compound statements entails that not all of these operators are necessary for a full-blooded logical calculus. For example, ¬ A ∨ B is logically equivalent to A → B; since logical equivalence means that equivalent terms may be subsituted for each other in an expression, it's not necessary to have a conditional operator. A common exercise in introductory classes in symbolic logic is to define a single operator, from which all five operators can be derived through equivalence (the most common means of defining an operator is by describing its truth table). nostalgia.wikipedia.org /wiki/Logical_operator   (260 words)

Logic terms and concepts : Thomas Alspaugh : UCI Examples: “A ∧ B” and “¬ (¬ A ∨ ¬ B)” are logical statements; “ ‘A ∧ B is logically equivalent to ‘¬ (¬ A ∨ ¬ B)’ ” is a meta-logical statement. In first-order logic, variables are bound by quantifiers; any variable that is not bound by a quantifier is a free variable whose relation to the objects of the domain is unknown. Logical equivalence is a meta-logical relationship, not to be confused with the logical operation material biconditional. www.ics.uci.edu /~alspaugh/logic/logicConcepts.html   (3603 words)

Encyclopedia: Iff The corresponding logical symbols are "↔" and "⇔" and "≡". However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those formulas (e.g., in metalogic). In philosophy and logic, "iff" is used to indicate definitions, since definitions are supposed to be universally quantified biconditionals. www.nationmaster.com /encyclopedia/Iff   (1652 words)

Logical biconditional - Wikipedia, the free encyclopedia When a theorem and its reciprocal are true we say that its hypothesis is the necessary and sufficient condition of the thesis; that is to say, that it is at the same time both cause and consequence. For example, "I'll buy you an ice cream if you pass the exam" is meant as a biconditional, since the speaker doesn't intend a valid outcome to be buying the ice cream whether or not you pass the exam (as in a conditional). However, "it is cloudy if it is raining" is not meant as a biconditional, since it can obviously be cloudy while not raining. en.wikipedia.org /wiki/Biconditional   (553 words)

truth table   (Site not responding. Last check: 2007-08-08) Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. The logical operators are not, and, or, conditional, and biconditional. Truth tables are usually limited to boolean logic systems where only two truth values are possible, true or false, usually denoted simply T and F in the tables. www.yourencyclopedia.net /truth_table.html   (459 words)

Metamath Proof Explorer - mmtheorems2 Infer a converse implication from a logical equivalence. Deduce a converse implication from a logical equivalence. Deduce a converse commuted implication from a logical equivalence. us.metamath.org /mpegif/mmtheorems2.html   (619 words)

Encyclopedia: Syllogism A premise (sometimes spelled premiss in philosophy) is a statement presumed true within the context of a discourse, especially of a logical argument. A metaphor, in contrast, resembles a form of syllogism called affirming the consequent, which is a logical fallacy: In language, a metaphor is a rhetorical trope defined as a direct comparison between two seemingly unrelated subjects. The fallacy of the undistributed middle is a logical fallacy that is committed when the middle term in a categorical syllogism isnt distributed. www.nationmaster.com /encyclopedia/Syllogism   (903 words)

First-order logic - Encyclopedia, History, Geography and Biography   (Site not responding. Last check: 2007-08-08) First-order predicate calculus or first-order logic (FOL) permits the formulation of quantified statements such as "there exists an x such that..." ($\backslash exists\; x$) or "for any x, it is the case that..." ($\backslash forall\; x$), where x is a member of the domain of discourse. Symbols denoting logical operators: ¬ (logical not), $\backslash wedge$ (logical and), $\backslash vee$ (logical or), → (logical conditional), ↔ (logical biconditional). Article on classical logic (http://plato.stanford.edu/entries/logic-classical/) by Stewart Shapiro at the Stanford Encyclopedia of Philosophy, which covers the definition, model theory and soundness and completeness results for first-order logic characterised in a natural deduction style. www.arikah.com /encyclopedia/Predicate_logic   (940 words)

Logical biconditional   (Site not responding. Last check: 2007-08-08) In logical calculus of mathematics, logical biconditional is a logical operator connecting two statements to assert, p if and only if q wherep is a hypothesis (or antecedent) and q isa conclusion (or consequent). The only difference from logical conditional is the casewhen the hypothesis is false but the conclusion is true. When both members of the biconditional are propositions, it can be separated into two conditionals, of which one is called atheorem and the other its reciprocal. www.therfcc.org /logical-biconditional-88688.html   (454 words)

If And Only If articles and news from Start Learning Now   (Site not responding. Last check: 2007-08-08) In mathematics, philosophy, logic and technical fields that depend on them, "if and only if" is a connective between statements which means that the truth of either one of the statements requires the truth of the other. The corresponding logical symbols are "↔" and "⇔" and "≡", and sometimes "iff". In philosophy and logic, "iff" is used to indicate definitions, since definitions are supposed to be universal quantificationuniversally quantified biconditionals. www.startlearningnow.com /iff.htm   (989 words)

Symbolic Logic: lessons on negation, conjunction, disjunction, conditional, compound, biconditional, equivalence, ... The goal of this unit is to teach concepts in symbolic logic including sentences and statements, logical connectors, conditional and biconditional statements, and equivalence and tautologies. To identify the hypothesis and the conclusion of a biconditional. To recognize that the biconditional of two equivalent statements is a tautology. www.mathgoodies.com /lessons/toc_vol9.html   (469 words)

logical - definition of logical by the Free Online Dictionary, Thesaurus and Encyclopedia.   (Site not responding. Last check: 2007-08-08) These adjectives mean capable of or reflecting the capability for correct and valid reasoning: a logical mind; an analytic thinker; the ratiocinative process; a rational being. logical - capable of thinking and expressing yourself in a clear and consistent manner; "a lucid thinker"; "she was more coherent than she had been just after the accident" The greatest of all logical truths, and the one of which writers on philosophy are most apt to lose sight, the difference between words and things, has been most strenuously insisted on by him, although he has not always avoided the confusion of them in his own writings. dict.thefreelibrary.com /Logical   (507 words)

Truth table Truth tables are used in logic to determine whether an expression is true or whether an argument is valid. The logical expressions are necessarily true, contingently true, or necessarily false. Because the enumeration of possible truth-values for A and B yields the same truth-value under both (A ∧ B) and ~(~A ∨ ~B), the two are logically equivalent, and may be substituted for each other. www.teachersparadise.com /ency/en/wikipedia/t/tr/truth_table.html   (465 words)

Read about Logical biconditional at WorldVillage Encyclopedia. Research Logical biconditional and learn about Logical ...   (Site not responding. Last check: 2007-08-08) Research Logical biconditional and learn about Logical biconditional here! logical operator connecting two statements to assert, p if and only if q where p is a hypothesis (or antecedent) and q is a when we shall have to demonstrate a biconditional we shall usually analyze it into two converse encyclopedia.worldvillage.com /s/b/Biconditional   (538 words)

List of topics in logic - Wikipedia, the free encyclopedia Abacus logic -- Abduction (logic) -- Abductive validation -- Affine logic -- Affirming the antecedent --Affirming the consequent -- Antecedent -- Antinomy -- Argument form -- Aristotelian logic -- Axiom -- Axiomatic system -- Axiomatization Paraconsistent logics -- Paradox -- Pierce's law -- Plural quantification --Polish notation -- Polysyllogism --Predicate -- Principia Mathematica -- Principle of bivalence -- Proof theory -- Proposition -- Propositional calculus -- Provability logic Satisfiability -- Scholastic logic -- Second-order predicate -- Self-reference -- Sequent -- Sequent calculus -- Sequential logic -- Sheffer stroke -- Singular term -- Soundness -- Square of opposition -- Strict conditional -- Strict implication -- Strict logic -- Structural rule -- Sufficient condition -- Syllogism -- Syllogistic fallacy www.wikipedia.org /wiki/List_of_topics_in_logic   (480 words)

truth tables, logical equivalence, biconditional The biconditional p <-> q means (p -> q) and (q -> p), as indicated below. The statements A and B in the figure below are not logically equivalent, since if you are not nice but still get to eat it follows that statement A is true while statement B is false. We can thus see that 'if p then q' has the same meaning as 'p only if q', but is not logically equivalent to 'q only if p'. www.vhcc.edu /lib1spring98/lectures/990201/class_notes.htm   (333 words)

Logical biconditional - Encyclopedia, History, Geography and Biography Logical biconditional - Encyclopedia, History, Geography and Biography This article incorporates material from Biconditional (http://planetmath.org/?op=getobjandfrom=objectsandid=484) on PlanetMath, which is licensed under the GFDL. This encyclopedia, history, geography and biography article about Logical biconditional contains research on www.arikah.com /encyclopedia/Biconditional   (581 words)

[No title] The oyster the oyster bit bit.} \glossaryentry{classical logic}{classical logic}{}{The most taught kind of logic which has just two truth values (true and false), and \glossaryterm{truth functional semantics}.} \glossaryentry{competence theory}{competence theory}{}{An idealized theory specifying what it is to know a language as opposed to a performance theory explaining how the language is actually processed by users. The term is also use more broadly outside linguistics to contrast abstract theories of a task (such as drawing inferences) as opposed to a reasoning mechanism.} \glossaryentry{concatenated}{concatenated}{}{Strung together in a one dimensional sequence.} \glossaryentry{cooperative communication}{cooperative communication}{}{In cooperative communication, speaker and hearer engage in the task of constructing the same intended model of the discourse. Legal laws are obvious examples of deontic statements.} \glossaryentry{interpretation, direct}{interpretation, direct}{}{Interpretation of a diagram where no abstract syntax is interposed between the representation and the interpretation.} \glossaryentry{domain}{domain}{}{} \glossaryentry{elimination rule}{elimination rule}{}{A logical rule of inference which eliminates from the conclusion a connective which appears in the premises. www.cogsci.ed.ac.uk /~keith/HC1H/CourseText/missingglosses   (605 words)

No Title If two formulas are logically equivalent, their syntax may be different, but their semantics is the same. The logical form of the proposition ``I passed the exam and I did not pass the exam'' is represented by Note that implication is logically equivalent to the contrapositive, and that the inverse is logically equivalent to the converse! www.cs.sunysb.edu /~skiena/113/lectures/lecture3/lecture3.html   (662 words)

[No title] The logical consequence relation is defined in terms of the semantics of the predicate calculus, which are too complicated for us to explore here. However, the definition of the logical consequence relation and the inference rules are arranged so that for any wff's $p_{1},p_{2},\ldots,p_{k}$, and $q$, \[ p_{1},p_{2},\ldots,p_{k}\vdash q \mbox{ if and only if } p_{1},p_{2},\ldots,p_{k}\models q \] so that we may use the notions of deducibility and entailment interchangeably. Since we could recognize instances of logical consequence in the propositional logic but can only generate them in the predicate calculus, we are computationally in a weaker position in the predicate calculus than in the propositional logic. www.cs.usm.maine.edu /class/cos480/discrete.tex   (12501 words)

Philosophical Dictionary: Beauty-Blanshard Although arguments of this sort are formally valid because it is impossible for their conclusions to be false if their premises are true, they fail to provide logical support for their conclusions, which have already been accepted without proof at the outset. Logical or linguistic behaviorism, like that of Gilbert Ryle, holds that assertions about mental events can always be analyzed in behavioral terms. The conjunction of two conditionals, the antecedent of each of which is the consequent of the other; that is, any statement of the form: "P if and only if Q." Although they may have other uses, all biconditionals involve at least the logical structure of material equivalence. www.philosophypages.com /dy/b2.htm   (1118 words)

Statement Forms In exactly the same sense that individual arguments may be substitution-instances of general argument forms, individual compound statements can be substitution-instances of general statement forms. Statements that are substitution-instances of these two component statement-forms are then said to be logically equivalent: no matter what their content may happen to be, the conditions for their truth or falsity are exactly the same. Again, the logical equivalence of these three expressions provides us with a convenient way to comprehend and employ what is asserted in any statement of material equivalence. www.philosophypages.com /lg/e10c.htm   (708 words)

List of topics in logic   (Site not responding. Last check: 2007-08-08) Abacus logic -- Abduction (logic) -- Abductivevalidation -- Affine logic -- Affirming the antecedent -- Affirming the consequent -- Antecedent -- Antinomy -- Argument form -- Aristotelian logic -- Axiom -- Axiomaticsystem -- Axiomatization Law of excluded middle -- Law of non-contradiction -- Laws of logic -- Linear logic -- Logic -- Logic gate -- Logical assertion -- Logical biconditional -- Logicalconditional -- Logical conjunction -- Logical disjunction -- Logical equivalence -- Logical fallacy -- Logical language -- Logical nor -- Logical operator -- Logicism -- Logicprogramming Paraconsistent logics -- Paradox -- Pierce's law -- [Plural quantification]]-- Polish notation -- Polylogic -- Polysyllogism -- Predicate -- Principia Mathematica -- Principle of bivalence -- Proof theory -- Proposition -- Propositional calculus -- Provability logic www.therfcc.org /list-of-topics-in-logic-16494.html   (498 words)

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