First-order logic—also known as predicate logic and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects and allows the use of sentences that contain variables, so that rather than propositions such as Socrates is a man one can have expressions in the form "there exists x such that x is Socrates and x is a man" and there exists is a quantifier while x is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.
In electronics, a logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more binary inputs and produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device.
In mathematical logic, a logical system has the soundness property if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system.
Semantics is the linguistic and philosophical study of meaning, in language, programming languages, formal logics, and semiotics. It is concerned with the relationship between signifiers—like words, phrases, signs, and symbols—and what they stand for in reality, their denotation.
George Boole was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, and is best known as the author of The Laws of Thought (1854) which contains Boolean algebra. Boolean logic is credited with laying the foundations for the information age. Boole maintained that:
No general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.
Discourse denotes written and spoken communications:
Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1 inclusive. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1.
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". Some sources use the term existentialization to refer to existential quantification. It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier. Existential quantification is distinct from universal quantification, which asserts that the property or relation holds for all members of the domain.
In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.
A mental model is an explanation of someone's thought process about how something works in the real world. It is a representation of the surrounding world, the relationships between its various parts and a person's intuitive perception about his or her own acts and their consequences. Mental models can help shape behaviour and set an approach to solving problems and doing tasks.
Argumentation theory, or argumentation, is the interdisciplinary study of how conclusions can be reached through logical reasoning; that is, claims based, soundly or not, on premises. It includes the arts and sciences of civil debate, dialogue, conversation, and persuasion. It studies rules of inference, logic, and procedural rules in both artificial and real world settings.
An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor of mathematics at what was then Queen's College, Cork, in Ireland.
Jerry R. Hobbs is an American researcher in the fields of computational linguistics, discourse analysis, and artificial intelligence.
In mathematical logic, an atomic formula is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas. Atoms are thus the simplest well-formed formulas of the logic. Compound formulas are formed by combining the atomic formulas using the logical connectives.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.
Situation semantics, pioneered by Jon Barwise and John Perry in the early 1980s, attempts to provide a solid theoretical foundation for reasoning about common-sense and real world situations, typically in the context of theoretical linguistics, philosophy, or applied natural language processing,
Informal logic, intuitively, refers to the principles of logic and logical thought outside of a formal setting. However, perhaps because of the "informal" in the title, the precise definition of "informal logic" is a matter of some dispute. Ralph H. Johnson and J. Anthony Blair define informal logic as "a branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation." This definition reflects what had been implicit in their practice and what others were doing in their informal logic texts.
Johan Anthony Willem "Hans" Kamp is a Dutch philosopher and linguist, responsible for introducing Discourse Representation Theory (DRT) in 1981.
A discourse relation is a description of how two segments of discourse are logically connected to one another.
This is an index of articles in philosophy of language
