Journal of Philosophical Logic 50 (1):117-148 (2021)

Authors
Abstract
Free logics is a family of first-order logics which came about as a result of examining the existence assumptions of classical logic. What those assumptions are varies, but the central ones are that the domain of interpretation is not empty, every name denotes exactly one object in the domain and the quantifiers have existential import. Free logics usually reject the claim that names need to denote in, and of the systems considered in this paper, the positive free logic concedes that some atomic formulas containing non-denoting names are true, while negative free logic rejects even the latter claim. Inclusive logics, which reject, are likewise considered. These logics have complex and varied axiomatizations and semantics, and the goal of this paper is to present an orderly examination of the various systems and their mutual relations. This is done by first offering a formalization, using sequent calculi which possess all the desired structural properties of a good proof system, including admissibility of contraction and cut, while streamlining free logics in a way no other approach has. We then present a simple and unified system of abstract semantics, which allows for a straightforward demonstration of the meta-theoretical properties, and offers insights into the relationship between different logics. The final part of this paper is dedicated to extending the system with modalities by using a labeled sequent calculus, and here we are again able to map out the different approaches and their mutual relations using the same framework.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s10992-020-09564-7
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 59,968
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
HYPE: A System of Hyperintensional Logic.Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (2):305-405.
Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
Cut Elimination in the Presence of Axioms.Sara Negri & Jan Von Plato - 1998 - Bulletin of Symbolic Logic 4 (4):418-435.

View all 24 references / Add more references

Citations of this work BETA

Free Logics Are Cut-Free.Andrzej Indrzejczak - forthcoming - Studia Logica:1-28.

Add more citations

Similar books and articles

Cut-Free Calculi and Relational Semantics for Temporal STIT Logics.Tim Lyon & Kees van Berkel - 2019 - In Francesco Calimeri, Nicola Leone & Marco Manna (eds.), Logics in Artificial Intelligence. Springer International Publishing. pp. 803 - 819.
Labeled Sequent Calculus for Justification Logics.Meghdad Ghari - 2017 - Annals of Pure and Applied Logic 168 (1):72-111.
Labeled Sequent Calculi for Modal Logics and Implicit Contractions.Pierluigi Minari - 2013 - Archive for Mathematical Logic 52 (7-8):881-907.
Current Trends in Substructural Logics.Katalin Bimbó - 2015 - Journal of Philosophical Logic 44 (6):609-624.
Logics Without Existence Assumptions. [REVIEW]H. K. R. - 1970 - Review of Metaphysics 23 (3):565-565.
Four-Valued Semantics for Relevant Logics (and Some of Their Rivals).Greg Restall - 1995 - Journal of Philosophical Logic 24 (2):139 - 160.
Semantics for Structurally Free Logics LC+.K. Bimbó - 2001 - Logic Journal of the IGPL 9 (4):525-539.
LP, K3, and FDE as Substructural Logics.Lionel Shapiro - 2017 - In Pavel Arazim & Tomáš Lavička (eds.), The Logica Yearbook 2016. London: College Publications.
A Universal Logic Approach to Adaptive Logics.Diderik Batens - 2007 - Logica Universalis 1 (1):221-242.
Implicational F-Structures and Implicational Relevance Logics.A. Avron - 2000 - Journal of Symbolic Logic 65 (2):788-802.

Analytics

Added to PP index
2020-08-17

Total views
20 ( #525,373 of 59,975 )

Recent downloads (6 months)
6 ( #116,077 of 59,975 )

How can I increase my downloads?

Downloads

My notes