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== その他の論理記号 ==
{|class="wikitable"
以下では、発展的または稀に用いられる論理記号について述べる。
!A!!B!!C
 
|-
; {{Unichar|00B7|MIDDLE DOT}}
|style="margin: 0; padding: 0;"|
; {{Unichar|22C5|dot operator}}
{|style="border-collapse:collapse; margin: 0; padding: 0;"
: [[中黒|中点]]は[[論理積]] AND を表す<ref>{{citation|title=Logic: theoretical and applied|first=Baruch A.|last=Brody|publisher=Prentice-Hall|year=1973|isbn=9780135401460|page=93|quote=We turn now to the second of our connective symbols, the centered dot, which is called the conjunction sign.}}</ref>。{{math|''A'' &middot; ''B''}} は {{math|''A'' &amp; ''B''}} と等価。
|-style="border-bottom:1px solid #a2a9b1; border-collapse:collapse; border-spacing:1px; "
; {{math|{{overline|&middot;}}}}
|あいう||えお
: [[オーバーライン]]の引かれた中点は[[否定論理積]] NAND を表す。{{math|''A'' {{overline|&middot;}} ''B''}} は {{math|&not; (''A'' &amp; ''B'')}} と等価。
|-
; {{unichar|0305|COMBINING OVERLINE|nlink=overline|cwith=&nbsp;}}
|かき||くけこ
: used as abbreviation for standard numerals ([[Typographical Number Theory]]). For example, using HTML style "4&#x0305;" is a shorthand for the standard numeral "SSSS0".
|}
; オーバーライン
|-
: 数式の上に引かれたオーバーラインは、[[ゲーデル数]]を表すことがある。例えば {{math|{{overline|''A'' &or; ''B''}}}} は、論理式 {{math|''A'' &or; ''B''}} のゲーデル数を意味する。
|Hello||World||...
: またオーバーラインで否定を表すこともある。例えば {{math|{{overline|''A'' &or; ''B''}}}} は、{{math|&not;(''A'' &or; ''B'')}} と等価。
|}
; {{Unichar|007C|VERTICAL LINE}}
; {{Unichar|2191|UPWARDS ARROW}}
: シェファーの棒記号 ({{En|Sheffer stroke}}) とも呼ばれ、否定論理積 NAND 演算子である。
; {{Unichar|2193|DOWNWARDS ARROW}}
: パースの矢印 ({{En|Peirce arrow}}) とも呼ばれ、[[否定論理和]] NOR 演算子である。
; {{Unichar|2201|Complement}}
: 集合論において[[差集合#補集合|補集合]]を表す。例えば、全体集合が了解されている集合 {{mvar|A}} について、その補集合は <math>\complement A</math> と表される。
; {{Unichar|2204|THERE DOES NOT EXIST}}
: [[スラッシュ (記号)|斜線]]の引かれた存在量化子は、{{math|&not;&exist;}} と等価である。すなわち存在の否定を意味する。
; {{Unichar|2234|Therefore|nlink=∴}}
: 「故に、従って ({{En|therefore}})」を意味する。
; {{Unichar|2235|Because|nlink=∵}}
: 「なぜならば ({{En|because}})」を意味する。
; {{unichar|22A7|Models}}
: is a [[Model theory|model]] of
; {{unichar|22A8|True}}
: is true of
; {{unichar|22AC|DOES NOT PROVE}}
: negated ⊢, the sign for "does not prove", for example ''T'' ⊬ ''P'' says "''P'' is not a theorem of ''T''"
; {{unichar|22AD|Not true}}
: is not true of
; {{unichar|22BC|NAND}}
: NAND operator. In HTML, it can also be produced by <code>&lt;span style="text-decoration: overline"&gt;&amp;and;&lt;/span&gt;</code>: <span style="text-decoration: overline">&and;</span>
; {{unichar|22BD|Nor}}
: NOR operator. In HTML, it can also be produced by <code>&lt;span style="text-decoration: overline"&gt;&amp;or;&lt;/span&gt;</code>: <span style="text-decoration: overline">&or;</span>
; {{unichar|25C7|WHITE DIAMOND}}
: modal operator for "it is possible that", "it is not necessarily not" or rarely "it is not provable not" (in most modal logics it is defined as "¬◻¬")
; {{unichar|22C6|STAR OPERATOR}}
: usually used for ad-hoc operators
; {{unichar|22A5|UP TACK}}
; {{unichar|2193|DOWNWARDS ARROW}}
: Webb-operator or Peirce arrow, the sign for [[Logical NOR|NOR]]. Confusingly, "⊥" is also the sign for contradiction or absurdity.
; {{unichar|2310|REVERSED NOT SIGN}}
; {{unichar|231C|TOP LEFT CORNER}}
; {{unichar|231D|TOP RIGHT CORNER}}
: corner quotes, also called "Quine quotes"; for quasi-quotation, i.e. quoting specific context of unspecified ("variable") expressions;<ref>[[Willard Van Orman Quine|Quine, W.V.]] (1981): ''Mathematical Logic'', §6</ref> also used for denoting [[Gödel number]];<ref>{{citation|title=The Principles of Mathematics Revisited|first=Jaakko|last=Hintikka|publisher=Cambridge University Press|year=1998|isbn=9780521624985|page=113|url=https://books.google.com/books?id=JHBnE0EQ6VgC&pg=PA113}}.</ref> for example "⌜G⌝" denotes the Gödel number of G. (Typographical note: although the quotes appears as a "pair" in unicode (231C and 231D), they are not symmetrical in some fonts. And in some fonts (for example Arial) they are only symmetrical in certain sizes. Alternatively the quotes can be rendered as ⌈ and ⌉ (U+2308 and U+2309) or by using a negation symbol and a reversed negation symbol ⌐ ¬ in superscript mode. )
; {{unichar|25FB|WHITE MEDIUM SQUARE}}
; {{unichar|25A1|WHITE SQUARE}}
: modal operator for "it is necessary that" (in [[modal logic]]), or "it is provable that" (in [[provability logic]]), or "it is obligatory that" (in [[deontic logic]]), or "it is believed that" (in [[doxastic logic]]); also as [[Clause (logic)#Empty clauses|empty clause]] (alternatives: <math>\empty</math> and ⊥).
 
Note that the following operators are rarely supported by natively installed fonts. If you wish to use these in a web page, you should always embed the necessary fonts so the page viewer can see the web page without having the necessary fonts installed in their computer.
 
; {{unichar|27E1|WHITE CONCAVE-SIDED DIAMOND}}
; {{unichar|27E2|WHITE CONCAVE-SIDED DIAMOND WITH LEFTWARDS TICK}}
: modal operator for was never
; {{unichar|27E3|WHITE CONCAVE-SIDED DIAMOND WITH RIGHTWARDS TICK}}
: modal operator for will never be
; {{unichar|27E4|WHITE SQUARE WITH LEFTWARDS TICK}}
: modal operator for was always
; {{unichar|27E5|WHITE SQUARE WITH RIGHTWARDS TICK}}
: modal operator for will always be
; {{unichar|297D|RIGHT FISH TAIL}}
: sometimes used for "relation", also used for denoting various ad hoc relations (for example, for denoting "witnessing" in the context of [[Rosser's trick]]) The fish hook is also used as strict implication by C.I.Lewis <math> p </math> &#x297D; <math> q \equiv \Box(p\rightarrow q)</math>, the corresponding LaTeX macro is \strictif. [http://www.fileformat.info/info/unicode/char/297d/index.htm See here] for an image of glyph. Added to Unicode 3.2.0.
; {{unichar|2A07|TWO LOGICAL AND OPERATOR}}
 
==注釈==
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