42 lines
1.3 KiB
Plaintext
42 lines
1.3 KiB
Plaintext
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grammar aussagenlogik;
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// Standardtokens:
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NUMBER: [0-9]+;
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WHITESPACE: [ \r\n\t]+ -> skip;
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LBRACE: '(';
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RBRACE: ')';
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LCURLYBRACE: '{';
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RCURLYBRACE: '}';
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// Symbole (erlaube mehrere Varianten)
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SYMB_NOT: ('!'|'~'|'not');
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SYMB_AND: ('&'+|'^'|'and');
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SYMB_OR: ('|'+|'v'|'or');
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SYMB_IMPL: ('->'|'=>');
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// Rules
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start: open <EOF> | closed <EOF>;
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closed: atomic | not | LBRACE open RBRACE;
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open: and2 | and | or2 | or | implies;
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// Schemata für atomische Ausdrücke
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atomic: taut | contradiction | atom; //| generic;
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taut: ('1'|'true');
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contradiction: ('0'|'false');
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atom: 'A0' | 'A1' | 'A' NUMBER; // muss A0, A1 wegen falsum/verum extra auflisten
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// // als 'generische' Formeln schreibe bspw. {F}, {G}, {F1}, usw.
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// // generic: LCURLYBRACE (.*?) RCURLYBRACE;
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// FIXME: dieses Schema führt zu Konflikten
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// Schema für Negation: ¬ F
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not: symb=SYMB_NOT closed;
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// Schemata für Konjunktion: F1 ⋀ F2 bzw. F1 ⋀ F2 ⋀ ... ⋀ Fn
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and2: closed symb=SYMB_AND closed;
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and: ( closed ( symb=SYMB_AND closed )+ );
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// Schemata für Disjunktion: F1 ⋁ F2 bzw. F1 ⋁ F2 ⋁ ... ⋁ Fn
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or2: closed symb=SYMB_OR closed;
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or: ( closed ( symb=SYMB_OR closed )+ );
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// Schema für Implikation: F1 ⟶ F2
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implies: closed symb=SYMB_IMPL closed;
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