4,599 research outputs found
Many-Valued Hybrid Logic
In this paper we define a family of many-valued semantics for hybrid logic, where each semantics is based on a finite Heyting algebra of truth-values. We provide sound and complete tableau systems for these semantics. Moreover, we show how the tableau systems can be made terminating and thereby give rise to decision procedures for the logics in question. Our many-valued hybrid logics turn out to be "intermediate" logics between intuitionistic hybrid logic and classical hybrid logic in a specific sense explained in the paper. Our results show that many-valued hybrid logic is indeed a natural enterprise
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
Grafting Hypersequents onto Nested Sequents
We introduce a new Gentzen-style framework of grafted hypersequents that
combines the formalism of nested sequents with that of hypersequents. To
illustrate the potential of the framework, we present novel calculi for the
modal logics and , as well as for extensions of the
modal logics and with the axiom for shift
reflexivity. The latter of these extensions is also known as
in the context of deontic logic. All our calculi enjoy syntactic cut
elimination and can be used in backwards proof search procedures of optimal
complexity. The tableaufication of the calculi for and
yields simplified prefixed tableau calculi for these logic
reminiscent of the simplified tableau system for , which might be
of independent interest
An Abstract Tableau Calculus for the Description Logic SHOI Using UnrestrictedBlocking and Rewriting
Abstract This paper presents an abstract tableau calculus for the description logic SHOI. SHOI is the extension of ALC with singleton concepts, role inverse, transitive roles and role inclusion axioms. The presented tableau calculus is inspired by a recently introduced tableau synthesis framework. Termination is achieved by a variation of the unrestricted blocking mechanism that immediately rewrites terms with respect to the conjectured equalities. This approach leads to reduced search space for decision procedures based on the calculus. We also discuss restrictions of the application of the blocking rule by means of additional side conditions and/or additional premises.
A Goal-Directed Implementation of Query Answering for Hybrid MKNF Knowledge Bases
Ontologies and rules are usually loosely coupled in knowledge representation
formalisms. In fact, ontologies use open-world reasoning while the leading
semantics for rules use non-monotonic, closed-world reasoning. One exception is
the tightly-coupled framework of Minimal Knowledge and Negation as Failure
(MKNF), which allows statements about individuals to be jointly derived via
entailment from an ontology and inferences from rules. Nonetheless, the
practical usefulness of MKNF has not always been clear, although recent work
has formalized a general resolution-based method for querying MKNF when rules
are taken to have the well-founded semantics, and the ontology is modeled by a
general oracle. That work leaves open what algorithms should be used to relate
the entailments of the ontology and the inferences of rules. In this paper we
provide such algorithms, and describe the implementation of a query-driven
system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic)
rules under the well-founded semantics and a (monotonic) ontology, represented
by a CDF Type-1 (ALQ) theory. To appear in Theory and Practice of Logic
Programming (TPLP
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