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Kalkulus proposisional adalah sistem formal untuk menyatakan rumus proposisi dan membuktikannya dengan cara menggabungkan rumus atomik dan operator logika Beberapa contoh operator logika adalah displaystyle lnot negasi displaystyle land konjungsi displaystyle lor disjungsi displaystyle rightarrow implikasi displaystyle leftrightarrow ekuivalensi Bentuk bentuk argumenNama SequentModus Ponens p q p q displaystyle p to q land p vdash q Modus Tollens p q q p displaystyle p to q land neg q vdash neg p Silogisme Hipotesis p q q r p r displaystyle p to q land q to r vdash p to r Silogisme Disjungtif p q p q displaystyle p lor q land neg p vdash q Dilema Konstruktif p q r s p r q s displaystyle p to q land r to s land p lor r vdash q lor s Dilema Destruktif p q r s q s p r displaystyle p to q land r to s land neg q lor neg s vdash neg p lor neg r Dilema Bidireksi p q r s p s q r displaystyle p to q land r to s land p lor neg s vdash q lor neg r Simplifikasi p q p displaystyle p land q vdash p Konjungsi p q p q displaystyle p q vdash p land q Penambahan p p q displaystyle p vdash p lor q Komposisi p q p r p q r displaystyle p to q land p to r vdash p to q land r Teorema De Morgan p q p q displaystyle neg p land q vdash neg p lor neg q Komutasi p q q p displaystyle p lor q vdash q lor p Asosiasi p q r p q r displaystyle p lor q lor r vdash p lor q lor r Distribusi p q r p q p r displaystyle p land q lor r vdash p land q lor p land r Dobel Negasi p p displaystyle p vdash neg neg p Transposisi p q q p displaystyle p to q vdash neg q to neg p Implikasi p q p q displaystyle p to q vdash neg p lor q Ekuivalensi p q p q q p displaystyle p leftrightarrow q vdash p to q land q to p Tautologi p p p displaystyle p vdash p lor p Tertium non datur p p displaystyle vdash p lor neg p Non Kontradiksi p p displaystyle vdash neg p land neg p Pustaka SuntingBrown Frank Markham 2003 Boolean Reasoning The Logic of Boolean Equations 1st edition Kluwer Academic Publishers Norwell MA 2nd edition Dover Publications Mineola NY Chang C C dan Keisler H J 1973 Model Theory North Holland Amsterdam Netherlands Kohavi Zvi 1978 Switching and Finite Automata Theory 1st edition McGraw Hill 1970 2nd edition McGraw Hill 1978 Korfhage Robert R 1974 Discrete Computational Structures Academic Press New York NY Lambek J dan Scott P J 1986 Introduction to Higher Order Categorical Logic Cambridge University Press Cambridge UK Mendelson Elliot 1964 Introduction to Mathematical Logic D Van Nostrand Company Pranala luar Suntingwww ltn lv podnieks mlog ml2 htm www fecundity com logic Diperoleh dari https id wikipedia org w index php title Kalkulus proposisional amp oldid 6711403