Kalkulus proposisional

Kalkulus proposisional adalah sistem formal untuk menyatakan rumus proposisi dan membuktikannya dengan cara menggabungkan rumus atomik dan operator logika.

Beberapa contoh operator logika adalah:

• $\lnot$ (negasi)
• $\land$ (konjungsi)
• $\lor$ (disjungsi)
• $\rightarrow$ (implikasi)
• $\leftrightarrow$ (ekuivalensi)

Bentuk-bentuk argumen
Nama	Sequent
Modus Ponens	$((p\to q)\land p)\vdash q$
Modus Tollens	$((p\to q)\land \neg q)\vdash \neg p$
Silogisme Hipotesis	$((p\to q)\land (q\to r))\vdash (p\to r)$
Silogisme Disjungtif	$((p\lor q)\land \neg p)\vdash q$
Dilema Konstruktif	$((p\to q)\land (r\to s)\land (p\lor r))\vdash (q\lor s)$
Dilema Destruktif	$((p\to q)\land (r\to s)\land (\neg q\lor \neg s))\vdash (\neg p\lor \neg r)$
Dilema Bidireksi	$((p\to q)\land (r\to s)\land (p\lor \neg s))\vdash (q\lor \neg r)$
Simplifikasi	$(p\land q)\vdash p$
Konjungsi	$p,q\vdash (p\land q)$
Penambahan	$p\vdash (p\lor q)$
Komposisi	$((p\to q)\land (p\to r))\vdash (p\to (q\land r))$
Teorema De Morgan	$\neg (p\land q)\vdash (\neg p\lor \neg q)$
Komutasi	$(p\lor q)\vdash (q\lor p)$
Asosiasi	$(p\lor (q\lor r))\vdash ((p\lor q)\lor r)$
Distribusi	$(p\land (q\lor r))\vdash ((p\land q)\lor (p\land r))$
Dobel Negasi	$p\vdash \neg \neg p$
Transposisi	$(p\to q)\vdash (\neg q\to \neg p)$
Implikasi	$(p\to q)\vdash (\neg p\lor q)$
Ekuivalensi	$(p\leftrightarrow q)\vdash ((p\to q)\land (q\to p))$
Tautologi	$p\vdash (p\lor p)$
Tertium non datur	$\vdash (p\lor \neg p)$
Non-Kontradiksi	$\vdash \neg (p\land \neg p)$

Pustaka

• Brown, 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

• www.ltn.lv/~podnieks/mlog/ml2.htm
• www.fecundity.com/logic/