by Schmidt, R. A. and Tishkovsky, D.
Abstract:
This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.
Reference:
Automated Synthesis of Tableau Calculi (Schmidt, R. A. and Tishkovsky, D.), In Logical Methods in Computer Science, volume 7, 2011.
Bibtex Entry:
@ARTICLE{SchmidtTishkovsky11a,
AUTHOR = {Schmidt, R. A. and Tishkovsky, D.},
YEAR = {2011},
TITLE = {Automated Synthesis of Tableau Calculi},
JOURNAL = {Logical Methods in Computer Science},
VOLUME = {7},
NUMBER = {2},
PAGES = {1--32},
DOI = {http://dx.doi.org/10.2168/LMCS-7(2:6)2011},
URL = {http://arxiv.org/pdf/1104.4131},
ABSTRACT = {This paper presents a method for synthesising sound and complete
tableau calculi. Given a specification of the formal semantics of a logic,
the method generates a set of tableau inference rules that can then be
used to reason within the logic. The method guarantees that the generated rules
form a calculus which is sound and constructively complete. If the logic
can be shown to admit finite filtration with respect to a well-defined
first-order semantics then adding a general blocking mechanism provides a
terminating tableau calculus. The process of generating tableau rules can
be completely automated and produces, together with the blocking mechanism,
an automated procedure for generating tableau decision procedures. For
illustration we show the workability of the approach for a description logic
with transitive roles and propositional intuitionistic logic.
},
}