inference rules. Frege systems (more often known as Hilbert systems in general proof theory) are named after Gottlob Frege. The name "Frege system" was first...

Friedrich Ludwig Gottlob Frege (/ˈfreɪɡə/; German: [ˈɡɔtloːp ˈfreːɡə]; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician...

Hilbert–Ackermann system, is a type of formal proof system attributed to Gottlob Frege and David Hilbert. These deductive systems are most often studied...

various propositional proof systems. For example, among the major challenges of proof complexity is showing that the Frege system, the usual propositional...

derived purely from a logical system, undermining the logicist program. Some notable logicists include: Gottlob Frege: Frege is often regarded as the founder...

Geometry, in propositional logic it dates back to Gottlob Frege's 1879 Begriffsschrift. Frege's system used only implication and negation as connectives, and...

commonly employed in axiomatic set theory, and a system based on equinumerosity that was proposed by Gottlob Frege and by Bertrand Russell. In Zermelo–Fraenkel...

In metalogic and metamathematics, Frege's theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived in second-order logic...

Natural deduction Sequent calculus Frege system Extended Frege system Polynomial calculus Nullstellensatz system Cutting-plane method Semantic tableau...

propositional proof systems such as Frege system and are, in particular, useful for constructing polynomial-size proofs in these systems. The characterization...

times, contributors include George Boole, Augustus De Morgan, and Gottlob Frege. Mathematical logic was developed in 19th century Europe. David Hilbert...

reference was an idea of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung")...

derived in the axiomatic system constructed by the German philosopher and mathematician Gottlob Frege, hence undermining Frege's attempt to reduce mathematics...

Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has...

"concept-writing") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book. Begriffsschrift is usually translated...

popular idea that would be followed closely by his successors such as Gottlob Frege and George Boole in forming modern symbolic logic. Leibniz was first introduced...

(modus ponens and substitution), and six axioms. Frege referred to the "completeness" of this system, but was unable to prove this. The most significant...

found in Gottlob Frege's criticisms in The Foundations of Arithmetic. According to Alan Weir, the formalism of Heine and Thomae that Frege attacks can be...

axiomatic systems were developed in the nineteenth century, including non-Euclidean geometry, the foundations of real analysis, Cantor's set theory, Frege's work...

rules used to combine them. The principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of...

A sign system is a key concept in semiotics and is used to refer to any system of signs and relations between signs. The term language is frequently used...

1900–1901). Frege gave up on the project after Russell recognized and communicated his paradox identifying an inconsistency in Frege's system set out in...

by such works as Boole's The Laws of Thought and Frege's Begriffsschrift. Building on Frege's system, Russell and Whitehead presented a formal treatment...

(1981), Frege: Philosophy of Language (second edition), Cambridge: Harvard University Press. Frege, Gottlob (ed. Michael Beaney, 1997), The Frege Reader...

Frege's rules of self-reference was self-contradictory. In an appendix to the second volume, Frege acknowledged that one of the axioms of his system did...

also imply the existence of non-polynomial bounds on certain types of Frege system in mathematical logic. The minimum size of an expression tree describing...

coined by George Boolos. HP plays a central role in Gottlob Frege's philosophy of mathematics. Frege shows that HP and suitable definitions of arithmetical...

roughly, "concept-script") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book. Begriffsschrift is usually translated...

to develop a logical system for relations and quantifiers, which he published in several papers from 1870 to 1885. Gottlob Frege presented an independent...

strong influence on scientists such as Dirac. A System of Logic also had an impression on Gottlob Frege, who rebuked many of Mill's ideas about the philosophy...