Phase semantics and Petri net interpretation for resource-sensitive strong negation

Wansing’s extended intuitionistic linear logic with strong negation, called WILL, is regarded as a resource-conscious refinment of Nelson’s constructive logics with strong negation. In this paper, (1) the completeness theorem with respect to phase semantics is proved for WILL using a method that simultaneously derives the cut-elimination theorem, (2) a simple correspondence between the class of Petri nets with inhibitor arcs and a fragment of WILL is obtained using a Kripke semantics, (3) a cut-free sequent calculus for WILL, called twist calculus, is presented, (4) a strongly normalizable typed λ-calculus is obtained for a fragment of WILL, and (5) new applications of WILL in medical diagnosis and electric circuit theory are proposed. Strong negation in WILL is found to be expressible as a resource-conscious refutability, and is shown to correspond to inhibitor arcs in Petri net theory.
Keywords electric circuit  linear logic with strong negation  medical diagnosis  Petri net with inhibitor arc  phase semantics
Categories (categorize this paper)
DOI 10.1007/s10849-005-9000-z
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 24,479
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

View all 19 references / Add more references

Citations of this work BETA
Heinrich Wansing (2008). Constructive Negation, Implication, and Co-Implication. Journal of Applied Non-Classical Logics 18 (2-3):341-364.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

18 ( #255,422 of 1,925,592 )

Recent downloads (6 months)

2 ( #308,517 of 1,925,592 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.