Transcription of List of logic symbols - jeiks.net
1 List of logic symbolsFrom Wikipedia, the free encyclopedia (Redirected from Table of logic symbols )See also: Logical connectiveIn logic , a set of symbols is commonly used to express logical representation. As logicians are familiar with thesesymbols, they are not explained each time they are used. So, for students of logic , the following table lists manycommon symbols together with their name, pronunciation, and the related field of mathematics. Additionally, the thirdcolumn contains an informal definition, and the fourth column gives a short aware that, outside of logic , different symbols have the same meaning, and the same symbol has, depending on thecontext, different logic symbolsSymbolNameExplanationExamplesUnic odeValueHTMLE ntityLaTeXsymbolShould beread asCategory materialimplicationA B is truejust in the casethat either A isfalse or B istrue, or both.
2 May meanthe same as (the symbolmay alsoindicate thedomain andcodomain of afunction seetable ofmathematicalsymbols). may meanthe same as (the symbolmay also meansuperset).x = 2 x2 = 4 is true,but x2 = 4 x = 2 is ingeneral false (since xcould be 2).U+21D2U+2192U+2283&rArr &rarr &sup \Rightarrow\to\supset\impliesimplies if ..thenpropositionallogic, Heytingalgebra materialequivalenceA B is truejust in caseeither both Aand B arefalse, or bothx + 5 = y + 2 x + 3 =yU+21D4U+2261&hArr &equiv \Leftrightarrow\equiv\leftrightarrowif and only if iff means thesame as propositionallogicfalse, or bothA and B +2194&harr \leftrightarrow\iff !negationThe statement A is true ifand only if A slash placedthroughanotheroperator is thesame as " "placed infront.
3 ( A) Ax y (x = y)U+00 ACU+02DC¬ &tilde ~\lnot or \neg\simnotpropositionallogic &logicalconjunctionThe statementA B is trueif A and B areboth true elseit is < 4 n >2 n = 3when n is a +2227U+0026&and & \wedge or\land\&[1]andpropositionallogic,Boolea nalgebra + logicaldisjunctionThe statementA B is trueif A or B (orboth) are true if both arefalse, thestatement 4 n 2 n 3when n is a +2228&or \lor or \veeorpropositionallogic,Booleanalgebra exclusivedisjunctionThe statementA B is truewhen either Aor B, but notboth, are B meansthe same.( A) A is always true,A A is always +2295U+22BB&oplus \oplus\veebarxorpropositionallogic,Boole analgebra TTautologyThe statement is always +22A4T\toptop, verumpropositionallogic,Boolean1 Booleanalgebra F0 ContradictionThe statement isunconditionallyfalse.
4 A is always +22A5&perp F\botbottom,falsumpropositionallogic,Boo leanalgebra ()universalquantification x: P(x) or(x) P(x)means P(x) istrue for all x. n : n2 +2200&forall \forallfor all forany for eachfirst orderlogic existentialquantification x: P(x)means there isat least one xsuch that P(x)is true. n : n is +2203&exist \existsthere existsfirst orderlogic !uniquenessquantification ! x: P(x)means there isexactly one xsuch that P(x)is true. ! n : n + 5 = +2203 U+0021&exist !\exists !there existsexactly onefirst orderlogic:= : definitionx := y or x ymeans x isdefined to beanother namefor y (but notethat can alsomean otherthings, such ascongruence).P : Q meansP is defined tobe logicallyequivalent x := (1/2)(exp x +exp ( x))A XOR B : (A B) (A B)U+2254(U+003A U+003D)U+2261U+003A U+229C:=:&equiv &hArr :=\equiv\Leftrightarrowis defined aseverywhereQ.
5 ( )precedencegroupingPerform theoperationsinside theparenthesesfirst.(8 4) 2 = 2 2 = 1,but 8 (4 2) = 8 2 = +0028 U+0029( ) ( )parentheses,bracketseverywhere Turnstilex y meansy is provablefrom x (insome specifiedformalsystem).A B B AU+22A2⊢ \vdashprovablepropositionallogic, first order logic doubleturnstilex y meansx semanticallyentails yA B B AU+22A8⊨ \modelsentailspropositionallogic, first order logicAdvanced and rarely used logical symbolsThese symbols are sorted by their Unicode value:U+00B7 MIDDLE DOT, an outdated way for denoting AND[citation needed], still in use in electronics forexample "A B" is the same as "A&B" : Center dot with a line above it. Outdated way for denoting NAND, for example "A B" is the same as "ANAND B" or "A|B" or " (A & B)".
6 See also Unicode U+22C5 DOT +0305 COMBINING OVERLINE, used as abbreviation for standard numerals. For example, using HTML style"4 " is a shorthand for the standard numeral "SSSS0".Overline, is also a rarely used format for denoting G del numbers, for example "AVB" says the G del numberof "(AVB)"Overline is also an outdated way for denoting negation, still in use in electronics for example "AVB" is the sameas " (AVB)"U+2191 UPWARDS ARROW or U+007C | VERTICAL LINE: Sheffer stroke, the sign for the NAND +2201 COMPLEMENTU+2204 THERE DOES NOT EXIST: strike out existential quantifier same as " "U+2234 THEREFOREU+2235 BECAUSEU+22A7 MODELS: is a model ofU+22A8 TRUE: is true ofU+22AC DOES NOT PROVE: negated , the sign for "does not prove", for example T P says "P is not atheorem of T"U+22AD NOT TRUE: is not true ofU+22BC NAND: another NAND operator, can also be rendered as U+22BD NOR.
7 Another NOR operator, can also be rendered as VU+22C4 DIAMOND OPERATOR: modal operator for "it is possible that", "it is not necessarily not" or rarely "it isnot provable not" (in most modal logics it is defined as " ")U+22C6 STAR OPERATOR: usually used for ad hoc operatorsU+22A5 UP TACK or U+2193 DOWNWARDS ARROW: Webb operator or Peirce arrow, the sign for , " " is also the sign for contradiction or +2310 REVERSED NOT SIGNU+231C TOP LEFT CORNER and U+231D TOP RIGHT CORNER: corner quotes, also called "Quine quotes" forquasi quotation, quoting specific context of unspecified ("variable") expressions [2] also the standardsymbol[citation needed] used for denoting G del number for example " G " denotes the G del number of G.(Typographical note: although the quotes appears as a "pair" in unicode (231C and 231D), they are notsymmetrical in some fonts.)
8 And in some fonts (for example Arial) they are only symmetrical in certain the quotes can be rendered as and (U+2308 and U+2309) or by using a negation symbol anda reversed negation symbol in superscript mode. )U+25FB WHITE MEDIUM SQUARE or U+25A1 WHITE SQUARE: modal operator for "it is necessary that" (inmodal logic ), or "it is provable that" (in provability logic ), or "it is obligatory that" (in deontic logic ), or "it isbelieved that" (in doxastic logic ).Note that the following operators are rarely supported by natively installed fonts. If you wish to use these in a webpage, you should always embed the necessary fonts so the page viewer can see the web page without having thenecessary fonts installed in their +27E1 WHITE CONCAVE SIDED DIAMONDU+27E2 WHITE CONCAVE SIDED DIAMOND WITH LEFTWARDS TICK: modal operator for was neverU+27E3 WHITE CONCAVE SIDED DIAMOND WITH RIGHTWARDS TICK: modal operator for will never beU+27E4 WHITE SQUARE WITH LEFTWARDS TICK: modal operator for was alwaysU+27E5 WHITE SQUARE WITH RIGHTWARDS TICK: modal operator for will always beU+297D RIGHT FISH TAIL.
9 Sometimes used for "relation", also used for denoting various ad hoc relations (forexample, for denoting "witnessing" in the context of Rosser's trick) The fish hook is also used as strictimplication by , the corresponding LaTeX macro is \strictif. See here( ) for an image of glyph. Added to Unicode alsoLogic Alphabet, a suggested set of logical symbolsMathematical operators and symbols in UnicodePolish notationList of mathematical symbolsNotes1. ^ Although this character is available in LaTeX, the MediaWiki TeX system doesn't support this ^ Quine, (1981): Mathematical logic , 6 External linksNamed character entities ( html40 970708/ ) in HTML from " "Categories: Mathematical notationLogic symbolsThis page was last modified on 7 January 2014 at 10 is available under the Creative Commons Attribution ShareAlike License additional terms may apply.
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