in essenza
5<7 vera; 5>7 falsa;
Attenzione! qui di seguito il segno "=" non significa "risultato", bensi "affermazione" che i membri sono uguali. ref: I significati spontanei del segno uguale.
5= 4+2 falsa; 5≠ 4+2 vera
5= 3+2 vera 5≠ 3+2 falsa
3+2 = 4+1 vera
3+3 = 4+1 falsa 3+3 > 4+1 vera
sono fatte da 2 proposizioni elementari ed un Connettivo logico.
`and', `or', `if', `not' propositional or sentential connectives
wp/Propositional_calculus | Logica_proposizionale | Proposizione_(logica)
In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value.
If the values of all variables in a propositional formula are given, it determines a unique truth value.
A propositional formula is constructed from simple propositions, such as "five is greater than three" or propositional variables such as P and Q, using connectives or logical operators such as NOT, AND, OR, or IMPLIES; for example:
(P AND NOT Q) IMPLIES (P OR Q).
In mathematics, a propositional formula is often more briefly referred to as a "proposition", but, more precisely, a propositional formula is not a proposition but a formal expression that denotes a proposition, a formal object under discussion, just like an expression such as "x + y" is not a value, but denotes a value. In some contexts, maintaining the distinction may be of importance.
∧∨¬ and or not
≡ logica matematica delle proposizioni
≡ logica proposizionale
≡ propositional logic
≡ propositional calculus
≡ 2-valued propositional calculus
≡ statement logic
≡ sentential calculus
≡ sentential logic
≡ zeroth-order logic
≡ proposizione composta
≡ propositional formula
≡ propositional expression
≡ sentence
≡ sentential formula
and or not if
≡ propositional connectives
≡ sentential connectives
wp/History
Logic sentences that can be expressed in classical propositional calculus have an equivalent expression in Boolean algebra. Thus, Boolean logic is sometimes used to denote propositional calculus performed in this way.
Boolean algebra is not sufficient to capture logic formulas using quantifiers, like those from first order logic.
Although the development of mathematical logic did not follow Boole's program, the connection between his algebra and logic was later put on firm ground in the setting of algebraic logic, which also studies the algebraic systems of many other logics.
wp/Boolean_algebra#Propositional_logic Propositional logic and boolean logic.
Propositional logic is a logical system that is intimately connected to Boolean algebra.
1) | 3<5 e 5<7 | vera | 3>5 e 5<7 | falsa | in gergo ivece di "e" ... | |
2) | 3<5 AND 5<7 | vera | 3>5 AND 5<7 | falsa | in gergo "e" si scrive AND | |
3) | 3<5 ∧ 5<7 | vera | 3>5 ∧ 5<7 | falsa | in gergo "e" si scrive ∧ |