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
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