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 the cited 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 derivable 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 derivable. Similarly, I start from simpler versions of the @-rules and derive the general ones. These restrictions are imposed to rule out some means of nontermination.
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

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