Cut-elimination for the mu-calculus with one variable
نویسندگان
چکیده
We establish syntactic cut-elimination for the one-variable fragment of the modal mu-calculus. Our method is based on a recent cut-elimination technique by Mints that makes use of Buchholz' Ω-rule.
منابع مشابه
Syntactic cut-elimination for a fragment of the modal mu-calculus
For some modal fixed point logics, there are deductive systems that enjoy syntactic cut-elimination. An early example is the system in Pliuskevicius [15] for LTL. More recent examples are the systems by the authors of this paper for the logic of common knowledge [5] and by Hill and Poggiolesi for PDL [8], which are based on a form of deep inference. These logics can be seen as fragments of the ...
متن کاملTerms for Natural Deduction, Sequent Calculus and Cut Elimination in Classical Logic
This paper revisits the results of Barendregt and Ghilezan [3] and generalizes them for classical logic. Instead of λ-calculus, we use here λμ-calculus as the basic term calculus. We consider two extensionally equivalent type assignment systems for λμ-calculus, one corresponding to classical natural deduction, and the other to classical sequent calculus. Their relations and normalisation proper...
متن کاملCurry-Howard Term Calculi for Gentzen-Style Classical Logics
This thesis is concerned with the extension of the Curry-Howard Correspondence to classical logic. Although much progress has been made in this area since the seminal paper by Griffin, we believe that the question of finding canonical calculi corresponding to classical logics has not yet been resolved. We examine computational interpretations of classical logics which we keep as close as possib...
متن کاملCall-By-Value λμ-calculus and Its Simulation by the Cut-Elimination Procedure for LKQ
We show Call-By-Value(CBV) normalization forCND (Parigot 92) can be simulated by by cut-elimination for LKQ (Danos-JoinetSchellinx 93), namely q-protocol. For this, a new term calculus was made for each classical logic. A term calculus for CND is a CBV version of Parigot’s λμ-calculus. A completely new term calculus for LKQ is presented in a style of classical extension of λ-calculus with a let...
متن کاملSuperdeduction in Lambda-Bar-Mu-Mu-Tilde
Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. A proof-term language and a cut-elimination reduction already exist for superdeduction, both based on Christian Urban’s work on classical sequent calculus. However the compu...
متن کامل