Logic
It is a science that studies scientific language, its approach, its organization, in hierarchical entities and the methods as its formulas to analyze all written form. To communicate, human beings use discursive languages, these languages are full of logical particles.
The logical particles: fundamentally the quantifiers are the connectives with them the discourses are formed.
Propositional Logic
It is a branch of classical logic that studies propositional variables or logical sentences, their possible implications, evaluations of truth and in some cases their absolute level of truth. Some authors also identify it with mathematical logic or symbolic logic, since it uses a series of special symbols that bring it closer to mathematical language.
Propositions
Tautology: tautology or validity is defined as that formula that is always true.
Contradiction: it is a proposition that is always false for all truth values. For any truth value of the propositions, whatever the result of the logical formula studied is always going to be false.
Conjunction: is the formula that is true or false. The expressions on which the validity of the arguments depends are defined logical constants.
Connectors
Negation: no ->>, ~
In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or in general, semantic values. Intuitively, the negation of a proposition is true when said proposition is false, and vice versa. In classical logic negation is usually identified with the truth function that changes its value from true to false and vice versa.
Conjunction: Y ∧, Only if the components of the conjunction are true, the conjunction is true.
Disjunction: O ∨, The disjunction is only false if its two components are.
Conditional: ⇒ then
Typically the truth values of two statements, returning the true value false only when the first statement is true and the second is false.
Biconditional: ⇔ if only yes.
The Biconditional or double implication is an operator that works on two truth values, typically the truth values of two propositions, returning the truth value true when both propositions have the same truth value, and false when their truth values differ.
Propositions
Variables: In the symbolic language of propositional logic, simple, atomic or elementary statements are those that cannot be decomposed into simpler ones. They are called variables, and are written with the lower case letters at the end of the alphabet: «p», «q», «r», «s»… for particular cases, or with the upper case letters at the beginning of the alphabet when they are general cases: «A», «B», «C», «D»…
In addition to variables, propositional logic has other elements in its alphabet: logical constants and auxiliary symbols that make up compound sentences.
Some of the natural language lexical marks are translated with one of the following five logical constants:
¬ DENIAL: No
٧ INCLUSIVE DISJUNCTION: either, or, whether… or whether, ٨ CONJUNCTION: y, e, or ni (= and not)
→ CONDITIONAL: yes…. so
↔ BICONDITIONAL: yes and only if
Table of Truth
Negation: When the variable is true, denying it becomes false, and if it is false, denying it becomes true.
| TO | ~ A |
| V | F |
| F | V |
The disjunction: It is only false when all the variables are false.
| TO | B | AVB |
| V | V | V |
| V | F | V |
| F | V | V |
| F | F | F |
The conjunction: It is only true when all the variables are also true.
| TO | B | A ∧ B |
| V | V | V |
| V | F | F |
| F | V | F |
| F | F | F |
The conditional: Only when the first variable or antecedent is true and the second or consequent false, the result is false.
| TO | B | A ⇒ B |
| V | V | V |
| V | F | F |
| F | V | V |
| F | F | V |
The Biconditional: It is true when the two variables have the same value.
| TO | B | A ⇔ B |
| V | V | V |
| V | F | F |
| F | V | F |
| F | F | V |
Through the following video course you can learn more about propositional logic, an excellent resource to strengthen your knowledge in this branch of classical logic. (TareasPlus.com, 29 videos)
