A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2014; you can also visit the original URL.
The file type is application/pdf.
Filters
Examining Fragments of the Quantified Propositional Calculus
2008
Journal of Symbolic Logic (JSL)
Preserved Fulltext
When restricted to proving formulas, the quantified propositional proof system is closely related to the theorems of Buss's theory . ...
Namely, has polynomial-size proofs of the translations of theorems of , and proves that is sound. However, little is known about when proving more complex formulas. ...
In [9] , Krajicek and Pudlak introduced the quantified propositional proof system G and its fragments. These fragments have close connections with bounded arithmetic and computational complexity. ...
doi:10.2178/jsl/1230396765
fatcat:file2pnqujgvliksajephdbn34
Page 228 of Computational Linguistics Vol. 25, Issue 2
[page]
1999
Computational Linguistics
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
,An)> [An}~,...4er
A.2 The Calculus A (a Fragment of N-ILL) (proofs)
In this section, we give the proofs for the various propositions presented in the paper. ...
In Figure 19, we give the one-sided sequent calculus for the multiplicative fragment of noncommu- tative linear logic (N-LL), and in Figure 3 in Section 3, the two-sided sequent calculus for the multiplicative ...
First-Order Game Logic and Modal Mu-Calculus
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Other Versions
The differential mu-calculus is complete with respect to first-order fixpoint logic and differential game logic is complete with respect to its ODE-free fragment. ...
This paper investigates first-order game logic and first-order modal mu-calculus, which extend their propositional modal logic counterparts with first-order modalities of interpreted effects such as variable ...
structures, -calculus embeds into game logic, which embeds into the two-propositional-variable fragment of the modal -calculus. ...
arXiv:2201.10012v2
fatcat:u3en3eie7fewdm66ueavq7b4sy
On the universal and existential fragments of the μ-calculus
2006
Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We therefore study the problems of satisfiability, validity, model checking, and implication for the universal and existential fragments of the -calculus, in which only one branching mode is allowed. ...
We also show the corresponding results for the alternation-free fragment of the -calculus, where no alternations between least and greatest fixed points are allowed. ...
Acknowledgements We thank the anonymous reviewers for their detailed comments on the organization and on the proofs. ...
doi:10.1016/j.tcs.2005.11.015
fatcat:zulrihp2krb6bgjxfworh4upwm
Sequent Calculi for the classical fragment of Bochvar and Halldén's Nonsense Logics
2013
Electronic Proceedings in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
These calculi are obtained by restricting in an appropriate way the application of the rules of a sequent calculus for classical propositional logic CPL. ...
In this paper sequent calculi for the classical fragment (that is, the conjunction-disjunction-implication-negation fragment) of the nonsense logics B3, introduced by Bochvar, and H3, introduced by Halld ...
Acknowledgements: We would like to thank the anonymous referees for their extremely useful comments on an earlier draft, which have helped to improve the paper. ...
doi:10.4204/eptcs.113.12
fatcat:pwvpvsv7frbgbahxqnkazkib2q
A ZX-Calculus with Triangles for Toffoli-Hadamard, Clifford+T, and Beyond
2019
Electronic Proceedings in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We consider a ZX-calculus augmented with triangle nodes which is well-suited to reason on the so-called Toffoli-Hadamard fragment of quantum mechanics. ...
We precisely show the form of the matrices it represents, and we provide an axiomatisation which makes the language complete for the Toffoli-Hadamard quantum mechanics. ...
All diagrams were written with the help of TikZit. The author would like to thank Emmanuel Jeandel and Simon Perdrix for fruitful discussions and suggestions. ...
doi:10.4204/eptcs.287.18
fatcat:nj5va3jysfcvnfuvicusni2qrq
Polynomial Approximations for Model Checking
[chapter]
2004
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2012; you can also visit the original URL.
The file type is application/pdf.
The µ-Calculus of D. Kozen (1983) is a very powerful propositional program logic with fixpoints. It is widely used for specification and verification. ...
A.Emerson, C.Jutla, and P.Sistla studied (1993) the first fragment of the µ-Calculus that permits arbitrary nesting and alternations of fixpoints, and polynomial model checking in finite state systems. ...
But all proofs and the full-body version of the paper are available upon request. ...
doi:10.1007/978-3-540-39866-0_39
fatcat:rgvcbox3mvhzto5djc7pacgkiy
Page 2442 of Mathematical Reviews Vol. , Issue 89E
[page]
1989
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
A propositional fragment F is to be understood as a set of formulas containing all propositional variables and closed under substitution of formulas from F. ...
Summary: “A reversible syntactic and semantic translation between m-valued propositional calculus on a superintuitionistic base and intuitionistic propositional calculus is constructed. ...
ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T quantum mechanics
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
axiom that cannot be derived from the existing rules of the ZX-Calculus, implying in particular the incompleteness of the language for the so-called Clifford+T quantum mechanics. ...
We end up with a new axiomatisation of an extended ZX-Calculus, including an axiom schema for the cyclotomic supplementarity. ...
Since the diagrams of equation (E) are in the π 4 -fragment, it implies that the π 4 -fragment of the ZX-calculus is not complete. Remark 1. ...
arXiv:1702.01945v2
fatcat:yj7ep6hjpvb2bb2g6ix3iz3eny
A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We prove the completeness of the Clifford+T fragment of the ZX-Calculus using the recently studied ZW-Calculus, a calculus dealing with integer matrices. ...
We also prove that the Clifford+T fragment of the ZX-Calculus represents exactly all the matrices over some finite dimensional extension of the ring of dyadic rationals. ...
All diagrams were written with the help of TikZit. ...
arXiv:1705.11151v2
fatcat:qj3fahvg5ncwrndq4awlohw6ie
Specialization of antecedent negation loop-rule for a fragment of propositional intuitionistic logic sequent calculus
2009
Lietuvos matematikos rinkinys
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
The paper deals with specialization of the antecedent negation loop-rule for the negative implication free fragment of the propositional intuitionistic logic. ...
Introduction We investigate a fragment of the propositional intuitionistic logic without negative implication. ...
Calculus LJ * 0 The calculus LJ * 0 is a variant of the multisuccedent intuitionistic propositional Gentzen-like sequent calculus. It is defined as follows: 1. Axioms: , E → E, . 2. ...
doi:10.15388/lmr.2009.42
fatcat:wlz4hrpr6zay5gymlikfkxhhpy
THE LOGIC OF LEIBNIZ'S GENERALES INQUISITIONES DE ANALYSI NOTIONUM ET VERITATUM
2016
The Review of Symbolic Logic
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Moreover, we show that Leibniz's calculus can reproduce all the laws of classical propositional logic, thus allowing Leibniz to achieve his goal of reducing propositional reasoning to algebraic reasoning ...
The present paper provides a systematic reconstruction of the calculus developed by Leibniz in theGenerales Inquisitiones. ...
The year 1686 marked an exceptionally fruitful period in the intellectual life of Gottfried ...
doi:10.1017/s1755020316000137
fatcat:wulqblhirnacxpgi3iw4dfizde
A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics
2018
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '18
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
All diagrams were written with the help of TikZit. ...
Acknowledgements The authors acknowledge support from the projects ANR-17-CE25-0009 SoftQPro, ANR-17-CE24-0035 VanQuTe, PIA-GDN/Quantex, and STIC-AmSud 16-STIC-05 FoQCoSS. ...
Completeness of the π 4 -fragment of the ZX-Calculus To finish the proof it remains to compose the two interpretations: Proposition 8. ...
doi:10.1145/3209108.3209131
dblp:conf/lics/JeandelPV18
fatcat:eoixhygq7nfsraj25qctolozeu
An integration of model checking with automated proof checking
[chapter]
1995
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We describe an approach for such an integration where a BDD-based model checker for the propositional mu-calculus has been used as a decision procedure within the framework of the PVS proof checker. ...
If the expressiveness is constrained, there are useful logic fragments for which efficient decision procedures can be found. ...
is provided from the mu-cMculus fragment of the PVS language to propositional mu-calculus. ...
doi:10.1007/3-540-60045-0_42
fatcat:inwlv6nsyzdgzjbzrk3qhrrjri
ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T Quantum Mechanics
2017
International Symposium on Mathematical Foundations of Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
We exhibit another new simple axiom that cannot be derived from the existing rules of the ZX-Calculus, implying in particular the incompleteness of the language for the so-called Clifford+T quantum mechanics ...
We end up with a new axiomatisation of an extended ZX-Calculus, including an axiom schema for the cyclotomic supplementarity. ...
Since the diagrams of equation (E) are in the π 4 -fragment, it implies that the π 4 -fragment of the ZX-calculus is not complete. Remark. ...
doi:10.4230/lipics.mfcs.2017.11
dblp:conf/mfcs/JeandelPVW17
fatcat:cx3hip6azvcvxe4xsh2nrtd7oi
« Previous
Showing results 1 — 15 out of 18,877 results