Studia Logica:1-27 (forthcoming)

Authors
Pilar Herraiz Oliva
University of Murcia
Elisha Robinson
San Jose State University
Abstract
This paper proposes a generalization of the Kripke semantics of intuitionistic logic IL appropriate for intuitionistic Łukasiewicz logic IŁL — a logic in the intersection between IL and (classical) Łukasiewicz logic. This generalised Kripke semantics is based on the poset sum construction, used in Bova and Montagna (Theoret Comput Sci 410(12):1143–1158, 2009) to show the decidability (and PSPACE completeness) of the quasiequational theory of commutative, integral and bounded GBL algebras. The main idea is that w \Vdash \sigma—which for IL is a relation between worlds w and formulas \sigma, and can be seen as a function taking values in the booleans w \Vdash \sigma \in {B}—becomes a function taking values in the unit interval w \Vdash \sigma \in [0,1]. An appropriate monotonicity restriction (which we call sloping functions) needs to be put on such functions in order to ensure soundness and completeness of the semantics.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/s11225-020-09908-z
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: 51,508
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

Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Truth-Maker Semantics for Intuitionistic Logic.Kit Fine - 2014 - Journal of Philosophical Logic 43 (2-3):549-577.
On Adopting Kripke Semantics in Set Theory.Luca Incurvati - 2008 - Review of Symbolic Logic 1 (1):81-96.
Reference and Perspective in Intuitionistic Logics.John Nolt - 2006 - Journal of Logic, Language and Information 16 (1):91-115.
Dualising Intuitionictic Negation.Graham Priest - 2009 - Principia: An International Journal of Epistemology 13 (2):165-184.
Incompleteness Results in Kripke Bundle Semantics.Kazuaki Nagaoka & Eiko Isoda - 1997 - Mathematical Logic Quarterly 43 (4):485-498.
Kripke Bundle Semantics and C-Set Semantics.Eiko Isoda - 1997 - Studia Logica 58 (3):395-401.
Constants in Kripke Models for Intuitionistic Logic.Daniel Dzierzgowski - 1995 - Mathematical Logic Quarterly 41 (4):431-441.
Completeness and Incompleteness for Intuitionistic Logic.Charles McCarty - 2008 - Journal of Symbolic Logic 73 (4):1315-1327.

Analytics

Added to PP index
2020-04-21

Total views
9 ( #852,975 of 2,330,888 )

Recent downloads (6 months)
9 ( #69,634 of 2,330,888 )

How can I increase my downloads?

Downloads

My notes