Logic

thumb|alt=Depiction of inference using modus ponens|Logic studies valid forms of inference like .

subfield of mathematics

method of reasoning in which a body of observations is synthesized to hypothesize a general principle

method of reasoning by which premises understood to be true produce logically certain conclusions

Inferences are steps in logical reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that dates at least to Aristotle (300s BC). Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, c

Vaisheshika (IAST: Vaiśeṣika; ; ) is one of the six schools of Hindu philosophy from ancient India. In its early stages, Vaiśeṣika was an independent philosophy with its own metaphysics, epistemology, logic, ethics, and soteriology. Over time, the Vaiśeṣika system became similar in its philosophical procedures, ethical conclusions and soteriology to the Nyāya school of Hinduism, but retained its difference in epistemology and metaphysics.

thought experiment concerning the continuity of identity of an item which has all its parts replaced

logical operator specifying how many entities in the domain of discourse that satisfy an open formula

200px|thumb|In this image, the universal set U (the entire rectangle) is dichotomized into the two sets A (in pink) and its complement Ac (in grey). A dichotomy () is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be jointly exhaustive: everything must belong to one part or the other, and mutually exclusive: nothing can belong simultaneously to both parts.

formal logic able to express concepts such as necessity, possibility, provability, obligation, knowledge etc.

programming paradigm based on formal logic

A counterexample is a specific example that contradicts a claim, hypothesis, or generalization. In logic a counterexample disproves a universally stated claim, and does so rigorously in the fields of mathematics and philosophy. For example, the statement that "student John Smith is not lazy" is a counterexample to the generalization "students are lazy", and both a counterexample to, and disproof of, the universal quantification "all students are lazy."

class of formal logics

thumb|The ancient symbol Ouroboros, a dragon that continually consumes itself, denotes self-reference.

branch of logic related to reasoning and argumentation

tendency not to side in a conflict

logic statement saying that each thing is the same as itself

thumb|The title page of the Principia Mathematica (shortened version), an important work of metamathematics

study of the scope and nature of logic

aspect of history

situation in which an individual cannot or is incapable of avoiding a problem because of contradictory constraints or rules

set of properties by which one entity is distinguished from another

Apophasis (; , ) is a rhetorical device wherein the speaker or writer brings up a subject by either denying it, or denying that it should be brought up. Accordingly, it can be seen as a rhetorical relative of irony. A classic example of apophasis is "I'm not going to say that I told you so".

Relevance is the connection between topics that makes one useful for dealing with the other. Relevance is studied in many different fields, including cognitive science, logic, and library and information science. Epistemology studies it in general, and different theories of knowledge have different implications for what is considered relevant.

sentence coined by Noam Chomsky to describe proper syntax with improper semantics

two propositions or events that cannot both be true

rules that are not written down

classical logic of two values, either true and false

type of logic whose elements are concepts

International day proclaimed by UNESCO

concept in Boolean algebra

short story by Lewis Carroll

thumb|A module with two input streams at the top, an AND gate|AND output bucket in the middle, and an XOR output stream at the bottom.

Testability is a primary aspect of science and the scientific method. There are two components to testability: Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logically possible. The practical feasibility of observing a reproducible series of such counterexamples if they do exist.

word that expresses a property it also possesses

system of resource-aware logic

rule or body of rules or principles generally established as valid and fundamental in a field of art or philosophy

typed lambda calculus

"natural" grouping, not an artificial one; family of entities possessing properties bound by natural law

conveying the meaning of a term by pointing out examples

diagrammatic notation for logical expressions proposed by Peirce

diagram that shows events over time

visual diagram of structured arguments

false dilemma in which contradictory observations lead to the same conclusion

definition of a taxon

The tetralemma is a figure that features prominently in the logic of India.

linguistic and philosophical concept

Erotetics or erotetic logic is a part of logic, devoted to logical analysis of questions. It is sometimes called the logic of questions and answers.

process of changing beliefs to take into account a new piece of information

maxim of logic formulated by Charles Sanders Peirce

sequence of ideas expressed during a connected discourse or thought

n-ary relation on the domain of a structure whose elements satisfy some formula in the

idea that refutes itself

Input where a function output doesn't matter.

semantics of concepts

in constructive mathematics and computability theory, the axiom that given a decidable predicate on natural numbers, if it cannot be false for all numbers, then it is true for some number

formal proof

identity on affine spaces

a pragmatic approach to the semantics of logic

example of lexical used as an adjective is the phrase lexical similarity which means words that appear to be similar to other words