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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{https://isa-afp.org/entries/Hybrid_Logic.html},
Formal proof development},
ISSN = {2150-914x},
}
|
| License: | BSD License |
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