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2002, CSLI lecture notes, ISBN 9781575864051, Volume no. 141., x, 276
Book
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2015, Volume 9195, pp. 272 - 281
Journal Article
ZDM, ISSN 1863-9690, 10/2019, Volume 51, Issue 5, pp. 825 - 834
The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view... 
Argumentation schemes | Argument | Education | Derivation | Proof | Mathematics Education | Mathematics, general | Evidence | MATHEMATICS | EDUCATION & EDUCATIONAL RESEARCH | LOGIC | Persuasive Discourse | Logical Thinking | Mathematics Instruction | Mathematical Concepts | Computer Software | Mathematical Logic | Teaching Methods | Mathematics - History and Overview
Journal Article
Erkenntnis (1975-), ISSN 0165-0106, 1/2014, Volume 79, Issue S2, pp. 279 - 291
Beall and Restall's Logical Pluralism (2006) characterises pluralism about logical consequence in terms of the different ways cases can be selected in the... 
Intuitionistic logic | Sequents | Constructive mathematics | Model theory | Logical proofs | Counterexamples | Pluralist school | Logic | Mathematical intuitionism | Truth | Ethics | Epistemology | Ontology | Philosophy | LOGICAL PLURALISM | PHILOSOPHY
Journal Article
Synthese, ISSN 0039-7857, 04/2019
Journal Article
Educational Studies in Mathematics, ISSN 0013-1954, 11/2014, Volume 87, Issue 3, pp. 297 - 321
Journal Article
The Journal of Symbolic Logic, ISSN 0022-4812, 3/2002, Volume 67, Issue 1, pp. 260 - 278
In this article we provide wellordering proofs for metapredicative systems of explicit mathematics and admissible set theory featuring suitable axioms about... 
Mathematical set theory | Admissible sets | Axioms | Mathematical induction | Natural numbers | Logical givens | Mathematical logic | Connectivity | Explicit mathematics | Induction assumption | MATHEMATICS | POINT | Axiomatic set theory | Symbolic and mathematical logic | Analysis | 03F35 | 03F15
Journal Article
Synthese, ISSN 0039-7857, 7/2010, Volume 175, Issue 2, pp. 255 - 287
Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical... 
Circles | Geometry | Mathematical theorems | Axioms | Logical proofs | Reasoning | Diagrams | Triangles | Inference | Mathematics | Proof | Logic | HISTORY & PHILOSOPHY OF SCIENCE | Philosophers | 20th century | Cognition & reasoning | Books | 19th century | Essays | Philosophy
Journal Article
Journal for Research in Mathematics Education, ISSN 0021-8251, 7/2012, Volume 43, Issue 4, pp. 358 - 390
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 08/2019, Volume 781, pp. 63 - 91
In this paper we provide a proof theoretical investigation of logical argumentation, where arguments are represented by sequents, conflicts between arguments... 
Dynamic derivations | Logical argumentation | Sequent calculi | FRAMEWORK | COMPUTER SCIENCE, THEORY & METHODS | INFERENCE | Computer science
Journal Article
Studia Logica, ISSN 0039-3215, 06/2017, Volume 105, Issue 3, pp. 611 - 624
Starting in 2005, general logical metatheorems have been developed that guarantee the extractability of uniform effective bounds from large classes of proofs... 
CAT(κ) -spaces | Effective bounds | Proof mining | MATHEMATICS | GEODESIC SPACES | PHILOSOPHY | FUNCTIONAL-ANALYSIS | CAT(kappa)-spaces | LOGICAL METATHEOREMS | LOGIC | Mineral industry | Numerical analysis | Mining industry | Analysis
Journal Article
JOURNAL OF SYMBOLIC LOGIC, ISSN 0022-4812, 12/2019, Volume 84, Issue 4, pp. 1612 - 1629
We obtain an equivalent implicit characterization of L-p Banach spaces that is amenable to a logical treatment. Using that, we obtain an axiomatization for... 
MATHEMATICS | proof mining | metatheorems | Lp spaces | uniform convexity | LOGICAL METATHEOREMS | LOGIC
Journal Article
The Bulletin of Symbolic Logic, ISSN 1079-8986, 6/2016, Volume 22, Issue 2, pp. 215 - 237
In his early Contributions to a Better-Grounded Presentation of Mathematics (1810) Bernard Bolzano tries to characterize rigorous proofs (strenge Beweise).... 
Rules of inference | Logical theorems | Logical proofs | Metatheorems | Geometric shapes | Inference | Mathematics | Predicates | Cognitive space | Judgment | intermediate concepts | ground-consequence | rigorous proofs | Bolzano | MATHEMATICS | LOGIC | Bernard Bolzano
Journal Article
Synthese, ISSN 0039-7857, 2/2006, Volume 148, Issue 3, pp. 507 - 524
According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea... 
Mathematical validity | Rules of inference | Linguistic meaning | Logical proofs | Natural deduction calculus | Canonical forms | Inference | Skeleton | Verificationism | Truth | Metaphysics | Philosophy of Language | Epistemology | Logic | Philosophy | HISTORY & PHILOSOPHY OF SCIENCE | language | semantics | proof | Philosophy of science | Proof theory | Language | Semantics | Meaning
Journal Article
Annals of Mathematics, ISSN 0003-486X, 11/2006, Volume 164, Issue 3, pp. 1065 - 1076
Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional calculus... 
Homomorphisms | Axioms | Logical proofs | Syntactics | Syntactic theory | Mathematical logic | Mathematics | Syntax | Vertices | Grammatical clauses | MATHEMATICS | GRAPHS
Journal Article
The Bulletin of Symbolic Logic, ISSN 1079-8986, 12/2007, Volume 13, Issue 4, pp. 417 - 481
Journal Article
Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, 12/2016, Volume 104, Issue 6, pp. 1205 - 1224
Journal Article
Mathematical Structures in Computer Science, ISSN 0960-1295, 2018, Volume 29, Issue 8, pp. 1309 - 1343
Bisimulation proofs play a central role in programming languages in establishing rich properties such as contextual equivalence. They are also challenging to... 
SYSTEM | FRAMEWORK | SYNTACTIC LOGICAL RELATIONS | COMPUTER SCIENCE, THEORY & METHODS | TERMINATION
Journal Article
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