Logic and Implication: An Introduction to the General Algebraic Study of Non-Classical Logics

Springer Verlag (2021)
  Copy   BIBTEX

Abstract

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 101,505

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

Algebraic semantics for modal and superintuitionistic non-monotonic logics.David Pearce & Levan Uridia - 2013 - Journal of Applied Non-Classical Logics 23 (1-2):147-158.
An Algebraic View of the Mares-Goldblatt Semantics.Andrew Tedder - 2024 - Journal of Philosophical Logic 53 (2):331-349.

Analytics

Added to PP
2022-03-09

Downloads
35 (#648,941)

6 months
7 (#718,806)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

No cause for collapse.Dustin Gooßens & Andrew Tedder - 2023 - Asian Journal of Philosophy 2 (2):1-19.
An Algebraic View of the Mares-Goldblatt Semantics.Andrew Tedder - 2024 - Journal of Philosophical Logic 53 (2):331-349.
On Implicative and Positive Implicative GE Algebras.Andrzej Walendziak - 2023 - Bulletin of the Section of Logic 52 (4):497-515.

View all 6 citations / Add more citations

References found in this work

No references found.

Add more references