Review of Symbolic Logic 10 (1):116-144 (2017)

Authors
Johan Van Benthem
University of Amsterdam
Nick Bezhanishvili
University of Amsterdam
Abstract
This paper explores a new language of neighbourhood structures where existential information can be given about what kind of worlds occur in a neighbourhood of a current world. The resulting system of ‘instantial neighbourhood logic’ INL has a nontrivial mix of features from relational semantics and from neighbourhood semantics. We explore some basic model-theoretic behavior, including a matching notion of bisimulation, and give a complete axiom system for which we prove completeness by a new normal form technique. In addition, we relate INL to other modal logics by means of translations, and determine its precise SAT complexity. Finally, we discuss proof-theoretic fine-structure of INL in terms of semantic tableaux and some expressive fine-structure in terms of fragments, while discussing concrete illustrations of the instantial neighborhood language in topological spaces, in games with powers for players construed in a new way, as well as in dynamic logics of acquiring or deleting evidence. We conclude with some coalgebraic perspectives on what is achieved in this paper. Many of these final themes suggest follow-up work of independent interest.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1017/s1755020316000447
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,464
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

Universal Grammar.Richard Montague - 1970 - Theoria 36 (3):373--398.
Dynamic Logics of Evidence-Based Beliefs.J. Benthem & E. Pacuit - 2011 - Studia Logica 99 (1-3):61-92.
Normal Forms in Modal Logic.Kit Fine - 1975 - Notre Dame Journal of Formal Logic 16 (2):229-237.
Normal Monomodal Logics Can Simulate All Others.Marcus Kracht & Frank Wolter - 1999 - Journal of Symbolic Logic 64 (1):99-138.

View all 8 references / Add more references

Citations of this work BETA

Neighborhood Semantics for Modal Logic.Eric Pacuit - 2017 - Cham, Switzerland: Springer.

View all 9 citations / Add more citations

Similar books and articles

Atom Exchangeability and Instantial Relevance.J. B. Paris & P. Waterhouse - 2009 - Journal of Philosophical Logic 38 (3):313-332.
Some Connections Between Topological and Modal Logic.Kurt Engesser - 1995 - Mathematical Logic Quarterly 41 (1):49-64.
Simplicity as a Criterion of Induction.R. Harré - 1959 - Philosophy 34 (130):229 - 234.
A Neighbourhood Semantics for the Logic TK.Cezar A. Mortari & Hércules de Araújo Feitosa - 2011 - Principia: An International Journal of Epistemology 15 (2):287.
Instantial Logic.Wilfried Meyer-Viol - 1995 - Universtiteit Utrecht.
Laws and Instantial Statements.Alex Blum - 1970 - British Journal for the Philosophy of Science 21 (4):371-378.
Universal, Basic and Instantial Statements in the Logic of Scientific Discovery.S. Godlovitch - 1969 - British Journal for the Philosophy of Science 20 (4):355-356.
From BDI and Stit to Bdi-Stit Logic.Caroline Semmling & Heinrich Wansing - 2008 - Logic and Logical Philosophy 17 (1-2):185-207.
A Note on Neighbourhoods.Peter Steinacker - 1985 - Bulletin of the Section of Logic 14 (3):94-97.

Analytics

Added to PP index
2018-02-09

Total views
22 ( #515,925 of 2,520,783 )

Recent downloads (6 months)
2 ( #270,509 of 2,520,783 )

How can I increase my downloads?

Downloads

My notes