In logic, the semantics of logic or formal semantics is the study of the meaning and interpretation of formal languages, formal systems, and (idealizations...

additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic...

In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic...

"necessarily P {\displaystyle P} ". In the standard relational semantics for modal logic, formulas are assigned truth values relative to a possible world...

classical logic. The standard explanation of intuitionistic logic is the BHK interpretation. Several systems of semantics for intuitionistic logic have been...

intuitionistic logic and other non-classical systems. The development of Kripke semantics was a breakthrough in the theory of non-classical logics, because...

Formal semantics relies on logic and mathematics to provide precise frameworks of the relation between language and meaning. Cognitive semantics examines...

either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the objects denoted by...

First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics,...

mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. For example, the modal logic S4 is characterized...

logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their metaphysical status has been a subject of controversy...

In semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression...

the meaning of a predicate is exactly a function from the domain of objects to the truth values "true" and "false". In the semantics of logic, predicates...

on Hoare logic seeded by Floyd's ideas, now sometimes collectively called axiomatic semantics. In the 1970s, the terms operational semantics and denotational...

including dialogical logic (developed by Paul Lorenzen and Kuno Lorenz in Germany starting in the 1950s) and game-theoretical semantics (developed by Jaakko...

Formal semantics is the scientific study of linguistic meaning through formal tools from logic and mathematics. It is an interdisciplinary field, sometimes...

article describes the syntax and semantics of the purely declarative subset of these languages. Confusingly, the name "logic programming" also refers to a...

logic has been spent studying specifically propositional and first-order logic, as opposed to the other forms of classical logic. Most semantics of classical...

fails to hold. Much of the research in the field of logic programming has been concerned with trying to develop a logical semantics for negation as failure...

formal semantics. Intensional logic is not alone in that: also Gottlob Frege accompanied his (extensional) calculus with detailed explanations of the semantical...

2007. Daniel Richardson, Formal systems, logic and semantics Formal System at PlanetMath. Encyclopedia of Mathematics, Formal system Peter Suber, Formal...

governing the composition of well-formed expressions in a programming language. As in mathematical logic, it is independent of semantics and interpretation....

Axiomatic semantics is an approach based on mathematical logic for proving the correctness of computer programs. It is closely related to Hoare logic. Axiomatic...

Proof-theoretic semantics is a branch of proof theory and an approach to the semantics of logic that attempts to locate the meaning of propositions and...

Reference Semantics Strict conditional Syntax (logic) Truth Truth value Validity Affine logic Alethic logic Aristotelian logic Boolean logic Buddhist logic Bunched...

beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing...

of interpretations of formal languages is called formal semantics. The most commonly studied formal logics are propositional logic, predicate logic and...

algebraic semantics. The algebraic semantics of intuitionistic logic is given in terms of Heyting algebras, compared to Boolean algebra semantics of classical...

of non-standard analysis Standard part function Set theory Forcing (mathematics) Boolean-valued model Kripke semantics General frame Predicate logic First-order...

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical...