|
Formalizing
a
Seligman-Style
Tableau
System
for
Hybrid
Logic
Title: |
Formalizing a Seligman-Style Tableau System for Hybrid Logic |
Author:
|
Asta Halkjær From
|
Submission date: |
2019-12-20 |
Abstract: |
This work is a formalization of soundness and completeness proofs
for a Seligman-style tableau system for hybrid logic. The completeness
result is obtained via a synthetic approach using maximally
consistent sets of tableau blocks. The formalization differs from
previous work in a few ways. First, to avoid the need to backtrack in
the construction of a tableau, the formalized system has no unnamed
initial segment, and therefore no Name rule. Second, I show that the
full Bridge rule is admissible in the system. Third, I start from rules
restricted to only extend the branch with new formulas, including only
witnessing diamonds that are not already witnessed, and show that
the unrestricted rules are admissible. Similarly, I start from simpler
versions of the @-rules and show that these are sufficient.
The GoTo rule is restricted using a notion of potential such that each
application consumes potential and potential is earned through applications of
the remaining rules. I show that if a branch can be closed then it can
be closed starting from a single unit. Finally, Nom is restricted by
a fixed set of allowed nominals. The resulting system should be terminating. |
Change history: |
[2020-06-03]: The fully restricted system has been shown complete by updating the synthetic completeness proof. |
BibTeX: |
@article{Hybrid_Logic-AFP,
author = {Asta Halkjær From},
title = {Formalizing a Seligman-Style Tableau System for Hybrid Logic},
journal = {Archive of Formal Proofs},
month = dec,
year = 2019,
note = {\url{http://isa-afp.org/entries/Hybrid_Logic.html},
Formal proof development},
ISSN = {2150-914x},
}
|
License: |
BSD License |
Status: [ok] |
This is a development version of this entry. It might change over time
and is not stable. Please refer to release versions for citations.
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