Inference

Inference is the process by which conclusions are derived from initial premises or hypotheses. When a conclusion follows from its initial premises or hypotheses, through valid logical deductions, It is said that the premises imply the conclusion.

Inference is the traditional object of study of logic, just as life is the object of study of biology. Logic investigates the grounds on which some inferences are acceptable and others are not. When an inference is acceptable, it is because of its logical structure and not because of the specific content of the argument or the language used (rhetoric). For this reason, logical systems are built that capture the relevant factors of the deductions that appear in natural language.

Traditionally, three kinds of inferences are distinguished: deductions, inductions and abductions, although sometimes abduction is counted as a special case of induction. Inductions are studied from inductive logic and the problem of inference. induction. Deductions, on the other hand, are studied by most of contemporary logic.

In artificial intelligence research, inference is the logical operation used in the inference engines of expert systems.^{[citation needed]}

Logical inference

Aristotelian logic

In Aristotelian logic, the essential form of inference is a form of deductive reasoning. However, some direct or immediate inferences were recognized.^{[citation required]}

Aristotelian logic considered the possibility of immediate inferences: those that can be obtained directly from the relationship established by a judgment with respect to the terms, subject and predicate, that constitute it, depending on the quality (affirmative-negative) and the quantity (universal-particular) of it.

Aristotle studied in detail certain operations that allowed such immediate or direct inferences. To do this, he developed the so-called opposition table of judgments, in which given the relationships that each Aristotelian judgment, A, E, I, O, implies, certain direct inferences can be established. Likewise, in traditional logic, certain logical operations of transformation of a judgment were admitted while maintaining its truth conditions. Such operations were:

• Logical conversion
• Logical contract
• Logical investment
• Logical

Traditional Aristotelian logic does not resolve the problems that arise from negative judgments very well, which is why this type of logical operations lend themselves to arguments that produce aberrant results.

Current logic formalizes linguistic statements either as class relations or as propositional functions or relations. Today the formal rigor of the application of a rule of inference is required. The idea of immediate inference is nothing more than the application of an implicit mode rule. Logical formality, however, requires that the rule that allows the transformation of an EBF be explicit.^{[citation required]}

Modern logic

Logical inference is called the application of a transformation rule that allows transforming a well-formed formula or expression (EBF) of a formal system into another EBF as a theorem of the same system. Both expressions are related through a relationship of equivalence, that is, they both have the same truth values or, in other words, the truth of one co-implies the truth of the other.^{[citation required]}

Thus arises what is known as a postulate or transformation of an original expression in accordance with previously established rules, which can be framed in one or several diverse referential contexts, obtaining in each of them a meaning as an equivalent truth value.

(p∧ ∧ q)→ → (r∧ ∧ s) (t v){displaystyle (pland q)rightarrow (rland s)lor (tlor v)}could be transformed into:

A→ → B C{displaystyle Arightarrow Blor C}

where A=(p∧ ∧ q){displaystyle A=(pland q)}; B=(r∧ ∧ s){displaystyle B=(rland s)} and C=(t v){displaystyle C=(tlor v)}.

Preparing the table of truth values of said equivalence contained in the function of the biconditional, the result must be a tautology.^{[citation required]}

Inference scheme

It refers to the logical-formal structure that allows obtaining a free, well-formed expression (EBF), as theorem of a formal system previously defined by the strict separation rule of formation and transformation of formulas.^{[ citation required]}

This structure is the foundation of a logical-formal argument through the application of the formula substitution rule.^{[citation required]}

(A∧ ∧ B∧ ∧ C...∧ ∧ N)→ → D{displaystyle (Aland Bland C...land N)rightarrow D} where (A∧ ∧ B∧ ∧ C...∧ ∧ N){displaystyle (Aland Bland C...land N)} represents each variable the premise of an argument. Knowing the truth of each one, as premises of an argument, his true product demands the truth of each and every one of these expressions; which allows to establish D as a free expression and conclusion of the argument.

Inference by evidence

• Inductive evidence: It emerges from the finding of the same occurrence in a number of cases. Noting that many wolves have long tails, I do not trust that “wolves have long tails”, as a generalization.
• Listing evidence or complete induction: When all cases are listed, inference becomes a proven truth, as a complete induction. This is the case that after each and every one can be inferred: “The students of this class are 22”.

Aristotle and, with him, traditional scholasticism admitted a perfect induction, as long as the relationship between individuals and the class, as a concept, is learned as a necessary essential connection of a process of abstraction; or between classes as concepts included in another class, as a concept. In this way, such induction became a form of syllogism, in the relationship of concepts to each other. Thus, to the extent that eagles, storks, sparrows, etc., fly, and all kinds of such animals are birds, it can be concluded that the connection between "birds" and "flying" is essential: "All birds fly.».^{[citation required]}

Arguments like this caused incidents as unusual in the history of science as the appearance of the platypus.

On the other hand, the knowledge of experience that is always singular, each case unique and unrepeatable, makes problematic the possibility of reaching knowledge of universal, essential concepts and raises the problem of the epistemological status of science as knowledge of concepts and laws. universals.^{[citation required]}

When questioning the world of essential forms and the conceptual entity itself understood as a logical class, and the possibility of the non-existence of individuals within a well-defined class, the inductive inference about a universe not known in all its occurrences produces the so-called problem of induction which, due to its nature, exceeds the case of this article referring to inference (see inductivism).^{[citation required]}

Types of inference

• Infer by classical logic: Inference that only supports two values: true or false.
• Tri-valued interference: An inference of this style results three values.
• Multi-valued interference: An inference of this style gives as possible multiple values.
• Diffuse interference: An inference of this style describes all multi-valued cases with accuracy and accuracy.
• Probabilistic interference: it is the sense of induction that allows to establish a truth with a higher probability rate than others.

Although when the possible universe has infinite occurrences, the probability will always be 0. Therefore, some establish falsificationism for the statute of science, as a scientific method and contrast of theories and human logic.^{[ citation required]} among others

Statistical inference (administration and management)

When the description is applied to conditions of certainty, as in stock market tables that show a census of traded values, it becomes a methodological entity. However, in most current statistical problems a sample is used more than a census, and the description has become simply a preparation for the next branch of statistics: inference.^{[citation required]}

When inference is used, we reach a conclusion or formulate a statement under certain conditions of uncertainty. Uncertainty can be the result of random conditions, implicit in working with samples, or of ignorance of the precise random laws that are applicable to a specific situation. However, in conclusion theory, uncertainty about the accuracy of the statement that has been made or the conclusion that has been drawn is stated simply in terms of the probability of its occurrence.^{[citation needed]}

Inference deals with two main types of problems: estimation and hypothesis testing.^{[citation required]}

Inference applied to the knowledge of human behavior

Everything that is intelligible can be inferred. Within the field of human intelligence, we find very interesting fields, such as emotional intelligence. Given that the human brain is subject to physical laws, there is the possibility that human behavior is potentially predictable, with a degree of uncertainty, to the same degree that the rest of the sciences could be, since they are all based on human intelligence.. The ability to infer human feeling is called empathy; Each feeling motivates us to act in a certain way. The ability to predict how a certain person is going to act borders on the esoteric, but nothing could be further from reality. Models of human behavior can be generated and the degree of accuracy of the prediction will depend on how empathetic the person is (given that the only machine capable of reproducing a mind, to date, is a human brain). ^{[citation required]}