Propositional logic for Beginners

Propositional Logic for Programmers ,[object Object]

Propositions ,[object Object],[object Object],[object Object],[object Object]

[object Object],￢ (NOT) ∧ (AND) ∨ (OR) P Q P ∧ Q TRUE TRUE TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE P Q P ∨ Q TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE FALSE FALSE P ￢ P TRUE FALSE FALSE TRUE

[object Object],For a given proposition - express results for all combinations of inputs. P Q ￢ P ∨ ( P ∧ Q ) TRUE TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE FALSE FALSE TRUE

[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],Two propositions are equivalent if their truth tables are the same. P Q P ∧ ( ￢ Q ∨ P) TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE

[object Object],￢ (P ∧ Q) === ￢ P ∨ ￢ Q ￢ (P ∨ Q) === ￢ P ∧ ￢ Q

[object Object],Some operations *unavoidably* cost more than others to execute. Aim: Juggle evaluation order so lower cost operations are evaluated first and if possible reduce the number of calls to more expensive operations.

[object Object],Eager - Will evaluate both sides of expression. Lazy (Short Circuit) - Will only evaluate RHS of expression if will effect return. (Most developers use lazy without realising the full implication) Operator C-Standard Lazy C-Standard Eager ￢ (NOT) ! ! ∧ (AND) && & ∨ (OR) || |

[object Object],class A { int _a; public awesome() { _a++; return true; } public freakin() { return true; } } a.awesome() && a.freakin() > true (A._a == 1) a.freakin() && a.awesome() > true (A._a == 0) Make sure you understand the side effects of methods before refactoring expressions.

[object Object],[object Object],[object Object]

[object Object],Succeeds where the first proposition is true. Therefore - if we can express a statement with a cheap successful first proposition, then we limit the number of calls to second proposition.

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object]

Propositional logic for Beginners

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Propositional logic for Beginners