LOGICAL SYSTEMS

LOGICAL SYSTEMS

1. There is a debate about whether it is correct to speak of a logic, or of several logics, but in the twentieth century not one has developed, but several different logical systems, which capture and formalize different parts of natural language. It could define a logical system as a set of things, which we help in making decisions that are most convenient.

2. Composed of: a set of primitive symbols (the alphabet or vocabulary). a set of training rules (grammar) that tells us how to build well-formed formulas from of the primitive symbols. a set of axioms or axiom schemes. each axiom must Be a well made formula. A set of inference rules. For example, a rule of classical inference is the Modus Ponens according to which, given a formula A, and another formula A → B, the rule allows us to affirm that B. a formal interpretation: in natural language a word It can mean different things depending on the meaning that is given. an example that they give us it is the word "Bank" that in the Spanish language means a building or a seat, while for other languages it can mean something completely different.

3. PROPOSITIONAL LOGIC: it is a branch of classical logic that studies propositions or sentences logical, its possible evaluations of truth and in the ideal case, its absolute level of truth. In it there symbols for propositional variables (which can be interpreted informally as statements which may be true or false) classical logic usually makes use of the following symbols: ¬ it reads "no" ^ reads "and" v reads "o" reads "... implies ..." or "yes, ... then ...," reads "... equivalent to ..." or "... yes, only yes ..."

4. The modal logics are designed to deal with expressions that qualify the truth of the judgments. Example, the expression "always" qualifies a true judgment. It is not the same to say "it is raining" than to say "always it's raining. "Modal logic: Deal with the notions of need, possibility, impossibility and contingency. Deontic logic: It deals with the moral notions of obligation and permissibility. Temporary logic: Abarca Temporary operators such as "always", "never", "before", "after", etc. Epistemic logic: It is the logic that formalize the reasoning related to knowledge. Doxastic logic: It is the logic that deals with reasoning about beliefs.

5. Non-classical logical systems are those that reject one or more of the principles of logic classic Some of these systems are: Intuitionist logic: Emphasize the evidence, instead of the truth, throughout the transformations of the propositions. Second order predicate logic: It is an extension of the first order logic in this variables and quantifiers that operate are added about sets of individuals