Proof Mining: a Systematic Way of Analysing Proofs in Mathematics
نویسندگان
چکیده
We call proof mining the process of logically analyzing proofs in mathematics with the aim of obtaining new information. In this survey paper we discuss, by means of examples from mathematics, some of the main techniques used in proof mining. We show that those techniques not only apply to proofs based on classical logic, but also to proofs which involve non-effective principles such as the attainment of the infimum of f ∈ C[0, 1] and the convergence for bounded monotone sequences of reals. We also report on recent case studies in approximation theory and fixed point theory where new results
منابع مشابه
Quranic way of presenting proofs for God`s existence
Regardless of the view of those philosophers like Plantinga who see no need in any proof for the existence of God, scholars have presented four views on Quranic way of proving the existence of God including demonstration, awakening, implication and clear demonstration. Describing and criticizing the views in detail, the author has viewed differently. God has regarded the level of the addressee`...
متن کاملProof-theoretic aspects of obtaining a constructive version of the mean ergodic theorem
Proof-theoretic aspects of obtaining a constructive version of the mean ergodic theorem – p. 1/27 Introduction 'Proof mining' is the subfield of mathematical logic that is concerned with the extraction of additional information from proofs in mathematics and computer science. G. Kreisel: What more do we know if we have proved a theorem by restricted means other than if we merely know the theore...
متن کاملThe logical structures of theological proofs, with an emphasis on the proof of love to God
This article has no abstract.
متن کاملRecent Progress in Proof Mining in Nonlinear Analysis
During the last two decades the program of ‘proof mining’ emerged which uses tools from mathematical logic (so-called proof interpretations) to systematically extract explicit quantitative information (e.g. rates of convergence) from prima facie nonconstructive proofs (e.g. convergence proofs). This has been applied particularly successful in the context of nonlinear analysis: fixed point theor...
متن کاملThe computational content of Nonstandard Analysis
Kohlenbach’s proof mining program deals with the extraction of effective information from typically ineffective proofs. Proof mining has its roots in Kreisel’s pioneering work on the so-called unwinding of proofs. The proof mining of classical mathematics is rather restricted in scope due to the existence of sentences without computational content which are provable from the law of excluded mid...
متن کامل