152 research outputs found
Paraconsistency in hybrid logic
As in standard knowledge bases, hybrid knowledge bases (i.e. sets of information specified by hybrid formulas) may contain inconsistencies arising from different sources, namely from the many mechanisms used to collect relevant information. Being a fact, rather than a queer anomaly, inconsistency also needs to be addressed in the context of hybrid logic applications. This article introduces a paraconsistent version of hybrid logic which is able to accommodate inconsistencies at local points without implying global failure. A main feature of the resulting logic, crucial to our approach, is the fact that every hybrid formula has an equivalent formula in negation normal form. The article also provides a measure to quantify the inconsistency of a hybrid knowledge base, useful as a possible basis for comparing knowledge bases. Finally, the concepts of extrinsic and intrinsic inconsistency of a theory are discussed
Reason Maintenance - State of the Art
This paper describes state of the art in reason maintenance with a focus on its future usage in the KiWi project. To give a bigger picture of the field, it also mentions closely related issues such as non-monotonic logic and paraconsistency. The paper is organized as follows: first, two motivating scenarios referring to semantic wikis are presented which are then used to introduce the different reason maintenance techniques
Paraconsistência em lógica híbrida
Mestrado em Matemática e AplicaçõesThe use of hybrid logics allows the description of relational structures, at the
same time that allows establishing accessibility relations between states and,
furthermore, nominating and making mention to what happens at speci c
states.
However, the information we collect is subject to inconsistencies, namely,
the search for di erent information sources can lead us to pick up contradictions.
Nowadays, by having so many means of dissemination available,
that happens frequently.
The aim of this work is to develop tools capable of dealing with contradictory
information that can be described as hybrid logics' formulas. To build
models, to compare inconsistency in di erent databases, and to see the applicability
of this method in day-to-day life are the basis for the development
of this dissertation.O uso de lógicas híbridas permite a descrição de estruturas relacionais, ao mesmo tempo que permite estabelecer relações de acessibilidade entre
estados, e, para além disso, nomear e fazer referência ao que acontece em
estados específicos.
No entanto, a informação que recolhemos está sujeita a inconsistências,
isto é, a procura de diferentes fontes de informação pode levar a recolha
de contradições. O que nos dias de hoje, com tantos meios de divulgação
disponíveis, acontece frequentemente.
O objetivo deste trabalho e desenvolver ferramentas capazes de lidar com informação contraditória que possa ser descrita através de fórmulas de lógicas
híbridas. Construir modelos e comparar a inconsistência de diferentes bases
de dados e ver a aplicabilidade deste método no dia-a-dia são a base para
o desenvolvimento desta dissertação
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
Andreas Kapsner, “Logics and Falsifications: A New Perspective on Constructivist Semantics”, Series Trends in Logic, vol. 40, Springer
Andreas Kapsner, Logics and Falsifications: A New Perspective on Constructivist Semantics, Series Trends in Logic, vol. 40, Springer, Cham, 215 pages, ISSN 1572-6126, ISBN 978-3-319-05205-2
Richard Dietz and Sebastiano Moruzzi (eds.), "Cuts and Clouds: Vagueness, its Nature, and its Logic"
Book Reviews:Richard Dietz and Sebastiano Moruzzi (eds.), Cuts and Clouds: Vagueness, its Nature, and its Logic, Oxford University Press, 2010, 586 pp., ISBN 9780199570386
Non-dual modal operators as a basis for 4-valued accessibility relations in Hybrid logic
The modal operators usually associated with the notions of possibility and necessity are classically duals. This paper aims to defy that duality in a paraconsistent environment, namely in a Belnapian Hybrid logic where both propositional variables and accessibility relations are four-valued. Hybrid logic, which is an extension of Modal logic, incorporates extra machinery such as nominals – for uniquely naming states – and a satisfaction operator – so that the formula under its scope is evaluated in the state whose name the satisfaction operator indicates.
In classical Hybrid logic the semantics of negation, when it appears before compound formulas, is carried towards subformulas, meaning that eventual inconsistencies can be found at the level of nominals or propositional variables but appear unrelated to the accessibility relations. In this paper we allow inconsistencies in propositional variables and, by breaking the duality between modal operators, inconsistencies at the level of accessibility relations arise. We introduce a sound and complete tableau system and a decision procedure to check if a formula is a consequence of a set of formulas. Tableaux will be used to extract syntactic models for databases, which will then be compared using different inconsistency measures. We conclude with a discussion about bisimulation
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