11864

10889

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

هشت، [54]ص.: مصور

ص.ع. به فارسي و انگليسي

مجتبي آقايي

مقداد قاري، مصطفي زارع

1395/09/02

كتابنامه

رياضي

ID10889

Admissibility and refutation some characterisations of intermediate logics Vali Allah Azadzad azadzad 72@gmail com 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mojtaba Aghaei aghaei@cc iut ac ir 2010 MSC 03B20 03B55 Keywords Intermediate logic Admissible rules Refutation Gabbay de Jongh logics Medvedev s logic AbstractThis thesis is based on the following paperGoudsmit Jeroen P Admissibility and refutation some characterisations of intermediate logics Archive for Mathematical Logic 53 7 8 2014 779 808 According to ukasiewicz we assert true propositions and reject false ones He remarked thatrejection had been neglected in the study of formal logic and introduced a formal system to inductivelyderive rejections of false propositions We call such systems refutation systems following Scott andSkura The general theory of such systems has been studied extensively by S upecki et al A refutation system can be thought of as a proof system for rejection Instead of deriving that one cancorrectly assert a statement through a series of truth preserving inferences from given axioms as onedoes in a proof system of assertion one derives the refutability of a propositional statement througha series of non truth preserving inferences from given anti axioms Proofs in a refutation system willbe called refutations and a formula will be called refutable whenever a refutation exists ending in thisformula Let us by way of example present a reformulation of the original refutation system for the classicalpropositional calculus CPC as given by ukasiewicz This particular presentation and all thefollowing will be in the style of Skura which goes back to Scott Here x denotes a propositionalvariable and both denote propositional formulae and denotes a substitution CP C AX Subs MT x

مجتبي آقايي

مقداد قاري، مصطفي زارع