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39 relations: Atomic formula, Classical logic, Clause (logic), Contradiction, Cut-elimination theorem, De Morgan's laws, Decision problem, Evert Willem Beth, First-order logic, Formula, Handbook of Automated Reasoning, Iterative deepening depth-first search, List (abstract data type), Logical connective, Logical consequence, Logical equivalence, Logical truth, Material conditional, Modal logic, Multiset, Negation normal form, Proof procedure, Proof theory, Propositional calculus, Quantifier (logic), Raymond Smullyan, Resolution (logic), Richard Jeffrey, S5 (modal logic), Satisfiability, Semantics, Sequent calculus, Set (mathematics), Skolem normal form, Structural proof theory, Tautology (logic), Tree (data structure), Truth value, Walter Carnielli.
Atomic formula
In mathematical logic, an atomic formula (also known simply as an atom) 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.
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Classical logic
Classical logic (or standard logic) is an intensively studied and widely used class of formal logics.
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Clause (logic)
In logic, a clause is an expression formed from a finite collection of literals (atoms or their negations) that is true either whenever at least one of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive clause, a less common use of the term).
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Contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions.
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Cut-elimination theorem
The cut-elimination theorem (or Gentzen's Hauptsatz) is the central result establishing the significance of the sequent calculus.
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De Morgan's laws
In propositional logic and boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference.
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Decision problem
In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.
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Evert Willem Beth
Evert Willem Beth (7 July 1908 – 12 April 1964) was a Dutch philosopher and logician, whose work principally concerned the foundations of mathematics.
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First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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Formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula.
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Handbook of Automated Reasoning
The Handbook of Automated Reasoning (2128 pages) is a collection of survey articles on the field of automated reasoning.
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Iterative deepening depth-first search
In computer science, iterative deepening search or more specifically iterative deepening depth-first search (IDS or IDDFS) is a state space/graph search strategy in which a depth-limited version of depth-first search is run repeatedly with increasing depth limits until the goal is found.
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List (abstract data type)
In computer science, a list or sequence is an abstract data type that represents a countable number of ordered values, where the same value may occur more than once.
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Logical connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective.
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Logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
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Logical equivalence
In logic, statements p and q are logically equivalent if they have the same logical content.
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Logical truth
Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature.
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Material conditional
The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→".
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Modal logic
Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality.
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Multiset
In mathematics, a multiset (aka bag or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements.
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Negation normal form
In mathematical logic, a formula is in negation normal form if the negation operator (\lnot) is only applied to variables and the only other allowed Boolean operators are conjunction (\land) and disjunction (\lor). Negation normal form is not a canonical form: for example, a \land (b\lor \lnot c) and (a \land b) \lor (a \land \lnot c) are equivalent, and are both in negation normal form.
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Proof procedure
In logic, and in particular proof theory, a proof procedure for a given logic is a systematic method for producing proofs in some proof calculus of (provable) statements.
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Proof theory
Proof theory is a major branchAccording to Wang (1981), pp.
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Propositional calculus
Propositional calculus is a branch of logic.
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Quantifier (logic)
In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.
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Raymond Smullyan
Raymond Merrill Smullyan (May 25, 1919 – February 6, 2017) was an American mathematician, magician, concert pianist, logician, Taoist, and philosopher.
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Resolution (logic)
In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation theorem-proving technique for sentences in propositional logic and first-order logic.
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Richard Jeffrey
Richard Carl Jeffrey (August 5, 1926 – November 9, 2002) was an American philosopher, logician, and probability theorist.
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S5 (modal logic)
In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic Logic.
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Satisfiability
In mathematical logic, satisfiability and validity are elementary concepts of semantics.
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Semantics
Semantics (from σημαντικός sēmantikós, "significant") is the linguistic and philosophical study of meaning, in language, programming languages, formal logics, and semiotics.
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Sequent calculus
Sequent calculus is, in essence, a style of formal logical argumentation where every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Skolem normal form
In mathematical logic, a formula of first-order logic is in Skolem normal form if it is in prenex normal form with only universal first-order quantifiers.
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Structural proof theory
In mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof.
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Tautology (logic)
In logic, a tautology (from the Greek word ταυτολογία) is a formula or assertion that is true in every possible interpretation.
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Tree (data structure)
In computer science, a tree is a widely used abstract data type (ADT)—or data structure implementing this ADT—that simulates a hierarchical tree structure, with a root value and subtrees of children with a parent node, represented as a set of linked nodes.
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Truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.
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Walter Carnielli
Walter Alexandre Carnielli (born 11 January 1952 in Campinas, Brazil) is a Brazilian mathematician, logician, and philosopher, full professor of Logic at the.
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References
[1] https://en.wikipedia.org/wiki/Method_of_analytic_tableaux
