345 research outputs found
Contradiction-tolerant process algebra with propositional signals
In a previous paper, an ACP-style process algebra was proposed in which
propositions are used as the visible part of the state of processes and as
state conditions under which processes may proceed. This process algebra,
called ACPps, is built on classical propositional logic. In this paper, we
present a version of ACPps built on a paraconsistent propositional logic which
is essentially the same as CLuNs. There are many systems that would have to
deal with self-contradictory states if no special measures were taken. For a
number of these systems, it is conceivable that accepting self-contradictory
states and dealing with them in a way based on a paraconsistent logic is an
alternative to taking special measures. The presented version of ACPps can be
suited for the description and analysis of systems that deal with
self-contradictory states in a way based on the above-mentioned paraconsistent
logic.Comment: 25 pages; 26 pages, occurrences of wrong symbol for bisimulation
equivalence replaced; 26 pages, Proposition 1 added; 27 pages, explanation of
the phrase 'in contradiction' added to section 2 and presentation of the
completeness result in section 2 improved; 27 pages, uniqueness result in
section 2 revised; 27 pages, last paragraph of section 8 revise
Handling Inconsistency in Knowledge Bases
Real-world automated reasoning systems, based on classical logic, face logically inconsistent information, and they must cope with it. It is onerous to develop such systems because classical logic is explosive. Recently, progress has been made towards semantics that deal with logical inconsistency. However, such semantics was never analyzed in the aspect of inconsistency tolerant relational model.
In our research work, we use an inconsistency and incompleteness tolerant relational model called Paraconsistent Relational Model. The paraconsistent relational model is an extension of the ordinary relational model that can store, not only positive information but also negative information. Therefore, a piece of information in the paraconsistent relational model has four truth values: true, false, both, and unknown.
However, the paraconsistent relational model cannot represent disjunctive information (disjunctive tuples). We then introduce an extended paraconsistent relational model called disjunctive paraconsistent relational model. By using both the models, we handle inconsistency - similar to the notion of quasi-classic logic or four-valued logic -- in deductive databases (logic programs with no functional symbols).
In addition to handling inconsistencies in extended databases, we also apply inconsistent tolerant reasoning technique in semantic web knowledge bases. Specifically, we handle inconsistency assosciated with closed predicates in semantic web. We use again the paraconsistent approach to handle inconsistency.
We further extend the same idea to description logic programs (combination of semantic web and logic programs) and introduce dl-relation to represent inconsistency associated with description logic programs
Paraconsistent Reasoning for OWL 2
A four-valued description logic has been proposed to reason with description logic based inconsistent knowledge bases. This approach has a distinct advantage that it can be implemented by invoking classical reasoners to keep the same complexity as under the classical semantics. However, this approach has so far only been studied for the basid description logic ALC. In this paper, we further study how to extend the four-valued semantics to the more expressive description logic SROIQ which underlies the forthcoming revision of the Web Ontology Language, OWL 2, and also investigate how it fares when adapated to tractable description logics including EL++, DL-Lite, and Horn-DLs. We define the four-valued semantics along the same lines as for ALC and show that we can retain most of the desired properties
Real Islamic Logic
Four options for assigning a meaning to Islamic Logic are surveyed including
a new proposal for an option named "Real Islamic Logic" (RIL). That approach to
Islamic Logic should serve modern Islamic objectives in a way comparable to the
functionality of Islamic Finance. The prospective role of RIL is analyzed from
several perspectives: (i) parallel distributed systems design, (ii) reception
by a community structured audience, (iii) informal logic and applied
non-classical logics, and (iv) (in)tractability and artificial intelligence
On the Satisfiability of Quasi-Classical Description Logics
Though quasi-classical description logic (QCDL) can tolerate the inconsistency of description logic in reasoning, a knowledge base in QCDL possibly has no model. In this paper, we investigate the satisfiability of QCDL, namely, QC-coherency and QC-consistency and develop a tableau calculus, as a formal proof, to determine whether a knowledge base in QCDL is QC-consistent. To do so, we repair the standard tableau for DL by introducing several new expansion rules and defining a new closeness condition. Finally, we prove that this calculus is sound and complete. Based on this calculus, we implement an OWL paraconsistent reasoner called QC-OWL. Preliminary experiments show that QC-OWL is highly efficient in checking QC-consistency
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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