2,681 research outputs found
Fuzzy inequational logic
We present a logic for reasoning about graded inequalities which generalizes
the ordinary inequational logic used in universal algebra. The logic deals with
atomic predicate formulas of the form of inequalities between terms and
formalizes their semantic entailment and provability in graded setting which
allows to draw partially true conclusions from partially true assumptions. We
follow the Pavelka approach and define general degrees of semantic entailment
and provability using complete residuated lattices as structures of truth
degrees. We prove the logic is Pavelka-style complete. Furthermore, we present
a logic for reasoning about graded if-then rules which is obtained as
particular case of the general result
Stone-type representations and dualities for varieties of bisemilattices
In this article we will focus our attention on the variety of distributive
bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and
involutive bisemilattices. After extending Balbes' representation theorem to
bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas-Dunn
duality and introduce the categories of 2spaces and 2spaces. The
categories of 2spaces and 2spaces will play with respect to the
categories of distributive bisemilattices and De Morgan bisemilattices,
respectively, a role analogous to the category of Stone spaces with respect to
the category of Boolean algebras. Actually, the aim of this work is to show
that these categories are, in fact, dually equivalent
A General Framework for Representing, Reasoning and Querying with Annotated Semantic Web Data
We describe a generic framework for representing and reasoning with annotated
Semantic Web data, a task becoming more important with the recent increased
amount of inconsistent and non-reliable meta-data on the web. We formalise the
annotated language, the corresponding deductive system and address the query
answering problem. Previous contributions on specific RDF annotation domains
are encompassed by our unified reasoning formalism as we show by instantiating
it on (i) temporal, (ii) fuzzy, and (iii) provenance annotations. Moreover, we
provide a generic method for combining multiple annotation domains allowing to
represent, e.g. temporally-annotated fuzzy RDF. Furthermore, we address the
development of a query language -- AnQL -- that is inspired by SPARQL,
including several features of SPARQL 1.1 (subqueries, aggregates, assignment,
solution modifiers) along with the formal definitions of their semantics
- …