Results 191 to 200 of about 47,415 (256)
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Learning algorithms versus automatability of Frege systems

International Colloquium on Automata, Languages and Programming, 2021
We connect learning algorithms and algorithms automating proof search in propositional proof systems: for every sufficiently strong, well-behaved propositional proof system $P$, we prove that the following statements are equivalent, 1. Provable learning:
J. Pich, R. Santhanam
semanticscholar   +1 more source

Did Frege Believe Frege's Principle?

Journal of Logic, Language and Information, 2001
The author surveys different positions concerning the so-called `Frege Principle' held within the `Frege Industry'. In fact, two principles are called `Frege Principle', (1) the Principle of Semantic Compositionality, according to which ``the meaning of a syntactically complex expression is a function (only) of the meanings of its syntactic parts and ...
openaire   +2 more sources

Frege’s Begriffsschrift Theory of Identity Vindicated

Oxford Studies in Philosophy of Language Volume 1, 2019
In the Begriffsschrift, Frege held that identity is a relation between names, to wit, the relation of co-reference. The verdict of Frege scholarship on this conception of identity has not been favorable, to say the least; indeed, commentators including ...
Ulrich Pardey, K. Wehmeier
semanticscholar   +1 more source

On Small-Depth Frege Proofs for Tseitin for Grids

IEEE Annual Symposium on Foundations of Computer Science, 2017
We prove a lower bound on the size of a small depth Frege refutation of the Tseitin contradiction on the grid. We conclude that polynomial size such refutations must use formulas of almost logarithmic depth.
J. Håstad
semanticscholar   +1 more source

Hilbertian Structuralism and the Frege-Hilbert Controversy†

Philosophia Mathematica, 2019
This paper reveals David Hilbert’s position in the philosophy of mathematics, circa 1900, to be a form of non-eliminative structuralism, predating his formalism.
Fiona T Doherty
semanticscholar   +1 more source

Infinitesimals, Magnitudes, and Definition in Frege

Essays on Frege's Basic Laws of Arithmetic, 2019
Frege offers a contextual definition of infinitesimal in Grundlagen and in his review of Hermann Cohen’s book on infinitesimal methods. A scholarly puzzle is that Frege explicitly rejects exactly that definition in Grundgesetze, without any explanation ...
Jamie Tappenden
semanticscholar   +1 more source

Essays on Frege's Basic Laws of Arithmetic

, 2017
This volume is the first collection of essays that focuses on Frege’s Basic Laws of Arithmetic, vol. I and II, and aims to highlight the technical as well as philosophical richness of Gottlob Frege’s (1848–1925) major work.
M. Beaney
semanticscholar   +1 more source

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