18 research outputs found
Automated deduction with built-in theories: completeness results and constraint solving techniques
Postprint (published version
Deciding regular grammar logics with converse through first-order logic
We provide a simple translation of the satisfiability problem for regular
grammar logics with converse into GF2, which is the intersection of the guarded
fragment and the 2-variable fragment of first-order logic. This translation is
theoretically interesting because it translates modal logics with certain frame
conditions into first-order logic, without explicitly expressing the frame
conditions.
A consequence of the translation is that the general satisfiability problem
for regular grammar logics with converse is in EXPTIME. This extends a previous
result of the first author for grammar logics without converse. Using the same
method, we show how some other modal logics can be naturally translated into
GF2, including nominal tense logics and intuitionistic logic.
In our view, the results in this paper show that the natural first-order
fragment corresponding to regular grammar logics is simply GF2 without extra
machinery such as fixed point-operators.Comment: 34 page
A Polynomial Translation from the Two-Variable Guarded Fragment with Number Restrictions to the Guarded Fragment
We consider a two-variable guarded fragment with number restrictions for binary relations and give a satisfiability preserving transformation of formulas in this fragment to the three-variable guarded fragment. The translation can be computed in polynomial time and produces a formula that is linear in the size of the initial formula even for the binary coding of number restrictions. This allows one to reduce reasoning problems for many description logics to the satisfiability problem for the guarded fragment
Hyperresolution for guarded formulae
AbstractThis paper investigates the use of hyperresolution as a decision procedure and model builder for guarded formulae. In general, hyperresolution is not a decision procedure for the entire guarded fragment. However we show that there are natural fragments of the guarded fragment which can be decided by hyperresolution. In particular, we prove decidability of hyperresolution with or without splitting for the fragment GF1− and point out several ways of extending this fragment without losing decidability. As hyperresolution is closely related to various tableaux methods the present work is also relevant for tableaux methods. We compare our approach to hypertableaux, and mention the relationship to other clausal classes which are decidable by hyperresolution
Consequence-based Reasoning for Description Logics with Disjunction, Inverse Roles, Number Restrictions, and Nominals
We present a consequence-based calculus for concept subsumption and
classification in the description logic ALCHOIQ, which extends ALC with role
hierarchies, inverse roles, number restrictions, and nominals. By using
standard transformations, our calculus extends to SROIQ, which covers all of
OWL 2 DL except for datatypes. A key feature of our calculus is its
pay-as-you-go behaviour: unlike existing algorithms, our calculus is worst-case
optimal for all the well-known proper fragments of ALCHOIQ, albeit not for the
full logic