263 research outputs found
Towards an efficient prover for the C1 paraconsistent logic
The KE inference system is a tableau method developed by Marco Mondadori
which was presented as an improvement, in the computational efficiency sense,
over Analytic Tableaux. In the literature, there is no description of a theorem
prover based on the KE method for the C1 paraconsistent logic. Paraconsistent
logics have several applications, such as in robot control and medicine. These
applications could benefit from the existence of such a prover. We present a
sound and complete KE system for C1, an informal specification of a strategy
for the C1 prover as well as problem families that can be used to evaluate
provers for C1. The C1 KE system and the strategy described in this paper will
be used to implement a KE based prover for C1, which will be useful for those
who study and apply paraconsistent logics.Comment: 16 page
A QBF-based Formalization of Abstract Argumentation Semantics
Supported by the National Research Fund, Luxembourg (LAAMI project) and by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant ref. EP/J012084/1 (SAsSY project).Peer reviewedPostprin
Transreal arithmetic as a consistent basis for paraconsistent logics
Paraconsistent logics are non-classical logics which allow non-trivial
and consistent reasoning about inconsistent axioms. They have been pro-
posed as a formal basis for handling inconsistent data, as commonly arise
in human enterprises, and as methods for fuzzy reasoning, with applica-
tions in Artificial Intelligence and the control of complex systems.
Formalisations of paraconsistent logics usually require heroic mathe-
matical efforts to provide a consistent axiomatisation of an inconsistent
system. Here we use transreal arithmetic, which is known to be consis-
tent, to arithmetise a paraconsistent logic. This is theoretically simple
and should lead to efficient computer implementations.
We introduce the metalogical principle of monotonicity which is a very
simple way of making logics paraconsistent.
Our logic has dialetheaic truth values which are both False and True.
It allows contradictory propositions, allows variable contradictions, but
blocks literal contradictions. Thus literal reasoning, in this logic, forms an
on-the-
y, syntactic partition of the propositions into internally consistent
sets. We show how the set of all paraconsistent, possible worlds can be
represented in a transreal space. During the development of our logic we
discuss how other paraconsistent logics could be arithmetised in transreal
arithmetic
Investigations in Belnap's Logic of Inconsistent and Unknown Information
Nuel Belnap schlug 1977 eine vierwertige Logik vor, die -- im Gegensatz zur klassischen Logik -- die Faehigkeit haben sollte, sowohl mit widerspruechlicher als auch mit fehlender Information umzugehen. Diese Logik hat jedoch den Nachteil, dass sie Saetze der Form 'wenn ..., dann ...' nicht ausdruecken kann. Ausgehend von dieser Beobachtung analysieren wir die beiden nichtklassischen Aspekte, Widerspruechlichkeit und fehlende Information, indem wir eine dreiwertige Logik entwickeln, die mit widerspruechlicher Information umgehen kann und eine Modallogik, die mit fehlender Information umgehen kann. Beide Logiken sind nicht monoton. Wir untersuchen Eigenschaften, wie z.B. Kompaktheit, Entscheidbarkeit, Deduktionstheoreme und Berechnungkomplexitaet dieser Logiken. Es stellt sich heraus, dass die dreiwertige Logik, nicht kompakt und ihre Folgerungsmenge im Allgemeinen nicht rekursiv aufzaehlbar ist. Beschraenkt man sich hingegen auf endliche Formelmengen, so ist die Folgerungsmenge rekursiv entscheidbar, liegt in der Klasse der polynomiellen Zeithierarchie und ist DIFFP-schwer. Wir geben ein auf semantischen Tableaux basierendes, korrektes und vollstaendiges Berechnungsverfahren fuer endliche Praemissenmengen an. Darueberhinaus untersuchen wir Abschwaechungen der Kompaktheitseigenschaft. Die nichtmonotone auf S5-Modellen basierende Modallogik stellt sich als nicht minder komplex heraus. Auch hier untersuchen wir eine sinnvolle Abschwaechung der Kompaktheitseigenschaft. Desweiteren studieren wir den Zusammenhang zu anderen nichtmonotonen Modallogiken wie Moores autoepistemischer Logik (AEL) und McDermotts NML-2. Wir zeigen, dass unsere Logik zwischen AEL und NML-2 liegt. Schliesslich koppeln wir die entworfene Modallogik mit der dreiwertigen Logik. Die dabei enstehende Logik MKT ist eine Erweiterung des nichtmonotonen Fragments von Belnaps Logik. Wir schliessen unsere Betrachtungen mit einem Vergleich von MKT und verschiedenen informationstheoretischen Logiken, wie z.B. Nelsons N und Heytings intuitionistischer Logik ab
Minimal Paradefinite Logics for Reasoning with Incompleteness and Inconsistency
Paradefinite (`beyond the definite\u27) logics are logics that can be
used for handling contradictory or partial information. As such,
paradefinite logics should be both paraconsistent and paracomplete. In
this paper we consider the simplest semantic framework for defining
paradefinite logics, consisting of four-valued matrices, and study the
better accepted logics that are induced by these matrices
Coherent Integration of Databases by Abductive Logic Programming
We introduce an abductive method for a coherent integration of independent
data-sources. The idea is to compute a list of data-facts that should be
inserted to the amalgamated database or retracted from it in order to restore
its consistency. This method is implemented by an abductive solver, called
Asystem, that applies SLDNFA-resolution on a meta-theory that relates
different, possibly contradicting, input databases. We also give a pure
model-theoretic analysis of the possible ways to `recover' consistent data from
an inconsistent database in terms of those models of the database that exhibit
as minimal inconsistent information as reasonably possible. This allows us to
characterize the `recovered databases' in terms of the `preferred' (i.e., most
consistent) models of the theory. The outcome is an abductive-based application
that is sound and complete with respect to a corresponding model-based,
preferential semantics, and -- to the best of our knowledge -- is more
expressive (thus more general) than any other implementation of coherent
integration of databases
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