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Natural deduction

In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts wi

Calculus of structures

The calculus of structures is a proof calculus with deep inference for studying the structural proof theory of noncommutative logic. The calculus has since been applied to study linear logic, classica

Monadic predicate calculus

In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols in the signature are monadic (that is, they take onl

Domain relational calculus

In computer science, domain relational calculus (DRC) is a calculus that was introduced by Michel Lacroix and as a declarative database query language for the relational data model. In DRC, queries ha

Default logic

Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions. Default logic can express facts like “by default, something is true”; by contrast, st

Judgment (mathematical logic)

In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order logic would be that a string is a well-form

Cirquent calculus

Cirquent calculus is a proof calculus that manipulates graph-style constructs termed cirquents, as opposed to the traditional tree-style objects such as formulas or sequents. Cirquents come in a varie

Propositional calculus

Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions

Frege's propositional calculus

In mathematical logic, Frege's propositional calculus was the first axiomatization of propositional calculus. It was invented by Gottlob Frege, who also invented predicate calculus, in 1879 as part of

Hilbert system

In logic, especially mathematical logic, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of system of formal deduction attrib

Superposition calculus

The superposition calculus is a calculus for reasoning in equational first-order logic. It was developed in the early 1990s and combines concepts from first-order resolution with ordering-based equali

Event calculus

The event calculus is a logical language for representing and reasoning about events and their effects first presented by Robert Kowalski and in 1986. It was extended by Murray Shanahan and in the 199

Predicate calculus

No description available.

Nested sequent calculus

In structural proof theory, the nested sequent calculus is a reformulation of the sequent calculus to allow deep inference.

Model elimination

Model Elimination is the name attached to a pair of proof procedures invented by Donald W. Loveland, the first of which was published in 1968 in the Journal of the ACM. Their primary purpose is to car

Region connection calculus

The region connection calculus (RCC) is intended to serve for qualitative spatial representation and reasoning. RCC abstractly describes regions (in Euclidean space, or in a topological space) by thei

Sequent calculus

In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an uncondi

Existential graph

An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop t

Predicative programming

Predicative programming is the original name of a formal method for program specification and refinement, more recently called a Practical Theory of Programming, invented by Eric Hehner. The central i

Method of analytic tableaux

In proof theory, the semantic tableau (/tæˈbloʊ, ˈtæbloʊ/; plural: tableaux, also called truth tree) is a decision procedure for sentential and related logics, and a proof procedure for formulae of fi

Spatial–temporal reasoning

Spatial–temporal reasoning is an area of artificial intelligence which draws from the fields of computer science, cognitive science, and cognitive psychology. The theoretic goal—on the cognitive side—

Kappa calculus

In mathematical logic, category theory, andcomputer science, kappa calculus is aformal system for defining first-orderfunctions. Unlike lambda calculus, kappa calculus has nohigher-order functions; it

Laws of Form

Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems:
* The "p

Relational calculus

The relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that are part of the relational model for databases and provide a declarative way to

Cut rule

In mathematical logic, the cut rule is an inference rule of sequent calculus. It is a generalisation of the classical modus ponens inference rule. Its meaning is that, if a formula A appears as a conc

Fitch notation

Fitch notation, also known as Fitch diagrams (named after Frederic Fitch), is a notational system for constructing formal proofs used in sentential logics and predicate logics. Fitch-style proofs arra

Fluent calculus

The fluent calculus is a formalism for expressing dynamical domains in first-order logic. It is a variant of the situation calculus; the main difference is that situations are considered representatio

Proof calculus

In mathematical logic, a proof calculus or a proof system is built to prove statements.

Refinement calculus

The refinement calculus is a formalized approach to stepwise refinement for program construction. The required behaviour of the final executable program is specified as an abstract and perhaps non-exe

Tuple relational calculus

Tuple calculus is a calculus that was created and introduced by Edgar F. Codd as part of the relational model, in order to provide a declarative database-query language for data manipulation in this d

Situation calculus

The situation calculus is a logic formalism designed for representing and reasoning about dynamical domains. It was first introduced by John McCarthy in 1963. The main version of the situational calcu

Hidden algebra

Hidden algebra provides a formal semantics for use in the field of software engineering, especially for concurrent distributed object systems. It supports correctness proofs. Hidden algebra was studie

List of Hilbert systems

This article contains a list of sample Hilbert-style deductive systems for propositional logics.

Nondeterministic constraint logic

In theoretical computer science, nondeterministic constraint logic is a combinatorial system in which an orientation is given to the edges of a weighted undirected graph, subject to certain constraint

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