Lattice Logic, Bilattice Logic and Paraconsistent Quantum Logic: a Unified Framework Based on Monosequent Systems

Journal of Philosophical Logic 50 (4):781-811 (2021)
  Copy   BIBTEX

Abstract

Lattice logic, bilattice logic, and paraconsistent quantum logic are investigated based on monosequent systems. Paraconsistent quantum logic is an extension of lattice logic, and bilattice logic is an extension of paraconsistent quantum logic. Monosequent system is a sequent calculus based on the restricted sequent that contains exactly one formula in both the antecedent and succedent. It is known that a completeness theorem with respect to a lattice-valued semantics holds for a monosequent system for lattice logic. A completeness theorem with respect to a lattice-valued semantics is proved for paraconsistent quantum logic, and a completeness theorem with respect to a bilattice-valued semantics is proved for bilattice logic. Some syntactical properties, including cut-elimination and duality, are also investigated for the monosequent systems for these logics.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,611

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Proof Theory of Paraconsistent Quantum Logic.Norihiro Kamide - 2018 - Journal of Philosophical Logic 47 (2):301-324.
Connecting bilattice theory with multivalued logic.Daniele Genito & Giangiacomo Gerla - 2014 - Logic and Logical Philosophy 23 (1):15-45.
Symmetric and dual paraconsistent logics.Norihiro Kamide & Heinrich Wansing - 2010 - Logic and Logical Philosophy 19 (1-2):7-30.
Systems of Quantum Logic.Satoko Titani, Heiji Kodera & Hiroshi Aoyama - 2013 - Studia Logica 101 (1):193-217.
Gentzen-Type Methods for Bilattice Negation.Norihiro Kamide - 2005 - Studia Logica 80 (2-3):265-289.
Operational foundation of quantum logic.P. Mittelstaedt & E. W. Stachow - 1974 - Foundations of Physics 4 (3):355-365.
New Directions in Paraconsistent Logic.Jean-Yves Beziau (ed.) - 2015 - New Delhi, India: Springer, India.

Analytics

Added to PP
2021-01-04

Downloads
33 (#488,740)

6 months
6 (#531,961)

Historical graph of downloads
How can I increase my downloads?