111 research outputs found
Hypertableau Reasoning for Description Logics
We present a novel reasoning calculus for the description logic SHOIQ^+---a
knowledge representation formalism with applications in areas such as the
Semantic Web. Unnecessary nondeterminism and the construction of large models
are two primary sources of inefficiency in the tableau-based reasoning calculi
used in state-of-the-art reasoners. In order to reduce nondeterminism, we base
our calculus on hypertableau and hyperresolution calculi, which we extend with
a blocking condition to ensure termination. In order to reduce the size of the
constructed models, we introduce anywhere pairwise blocking. We also present an
improved nominal introduction rule that ensures termination in the presence of
nominals, inverse roles, and number restrictions---a combination of DL
constructs that has proven notoriously difficult to handle. Our implementation
shows significant performance improvements over state-of-the-art reasoners on
several well-known ontologies
And-or tableaux for fixpoint logics with converse: LTL, CTL, PDL and CPDL
Over the last forty years, computer scientists have invented or borrowed numerous logics for reasoning about digital systems. Here, I would like to concentrate on three of them: Linear Time Temporal Logic (LTL), branching time Computation Tree temporal Logic (CTL), and Propositional Dynamic Logic (PDL), with and without converse. More specifically, I would like to present results and techniques on how to solve the satisfiability problem in these logics, with global assumptions, using the tableau method. The issues that arise are the typical tensions between computational complexity, practicality and scalability. This is joint work with Linh Anh Nguyen, Pietro Abate, Linda Postniece, Florian Widmann and Jimmy Thomson
Automated Synthesis of Tableau Calculi
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.Comment: 32 page
Reasoning with Very Expressive Fuzzy Description Logics
It is widely recognized today that the management of imprecision and
vagueness will yield more intelligent and realistic knowledge-based
applications. Description Logics (DLs) are a family of knowledge representation
languages that have gained considerable attention the last decade, mainly due
to their decidability and the existence of empirically high performance of
reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to
the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms
(S), inverse roles (I), role hierarchies (H) and number restrictions (N). We
illustrate why transitive role axioms are difficult to handle in the presence
of fuzzy interpretations and how to handle them properly. Then we extend these
results by adding role hierarchies and finally number restrictions. The main
contributions of the paper are the decidability proof of the fuzzy DL languages
fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base
satisfiability problem of the fuzzy-SI and fuzzy-SHIN
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